DMAIC Book of Knowledge Green Belt

DMAIC GB A TX PG

© GE Capital, Inc., 2000

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Total Topic StepMin

60 Introductions and Expectations N/A

20 Meeting Skills N/A

20 Define A,B and C Review and CAP A,B,C

10 Break

10 Measure Overview 1,2,3

90 Measure 1 Review CTQ Tools 1

60 Measure 1–CTQ Tools continued 1

10 Break

45 Measure 2–Performance Standards 2

5 Break

120 Minitab Tutorial and Graphical Analysis various

Classroom Session Agenda–Day 1 1

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Classroom Session Agenda–Day 2* 2

Total Topic StepMin

30 Day 1–General Review and Homework A,B,C,1,2

30 Minitab–continued various

15 Measure 3–Overview 3

15 Break

45 Measure 3–Data Collection Plan 3

75 Measure 3–Sampling 3

60 Measurement System Analysis (MSA) 3

15 Break

15 Analyze Overview 4,5,6

150 Analyze 4–Establish Process Capability 4

* Elevator Speeches will be shared throughout the day

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Classroom Session Agenda–Day 3* 3

Total Topic StepMin

30 Day 2–General Review various

15 Analyze 5–Define Performance Objective 5

15 Break

150 Analyze 6–Identify Variation Sources 6

30 Analyze 6–continued 6

15 Improve Preview 7,8,9

30 Improve 7 and 8–Design Of Experiment 7,8

15 Break

30 Improve 9–Statistical Tolerancing 9

15 Control Preview 10,11,12

60 Control 12–Control Charts 12

* Elevator Speeches will be shared throughout the day

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Introductions1Assessment Strategy

The Learning Objectives are divided in 3 categories:1. Classroom2. Project, and3. Test

It is expected that a Green Belt be proficient in all learning objectives, however, only those designated Test represent the content of the certification exam.Each phase of the DMAIC cycle is listed below and the learning objectives have classified into the 3 categories within each phase.

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2Overview–Classroom Learning Objectives

1 Explain the benefits of Six Sigma to GE’s business.Compare and contrast Six Sigma’s process improvement approach to quality with traditional defect prevention strategies (i.e., inspection and testing).Identify the “vital few” CTQs that apply to all GE customers: responsiveness; marketplace competitiveness; on time, accurate and complete deliverables; and product/service technical performance.Explain the relationship between increasing levels of process complexity and quality improvement results.

2 Describe the Six Sigma Methodology for quality improvement.Define the term “sigma” (standard deviation) as it relates to the sigma capability (z value) of a business or manufacturing process.Recognize a Six Sigma level of quality (i.e., 99.99966% probability that defects will not be passed on to the customer).Define key Six Sigma terms and acronyms, including CTQ, opportunity, defect, DPMO, and Six Sigma capability (Z value).Explain the Master Back Belt (MBB), Black Belt (BB) and Green Belt (GB) roles in Six Sigma.Describe Six Sigma’s focus on repeatable processes.Describe Six Sigma’s focus on inputs (X’s) over outputs (Y’s) using the formula Y=f (X).Describe the statistical objective of Six Sigma (i.e., reduce process variation).Describe the relationship between DPMO and process capability (i.e., as DPMO goes down, process capability goes up.Describe the financial benefits of Six Sigma to GE.

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3Overview–Project Learning Objectives

1. Determine if DMAIC is the right strategy by identifying the conditions under which the DFSS methodology would be more appropriate.Compare and contrast the DFSS design methodologies to DMAIC.

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4Overview–Test Learning Objectives

1 Describe the 5 phases of DMAIC, including the purpose, tools, and outputs for each phase.

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5Define–Project Learning Objectives

1 Identify project CTQs.Define “CTQ” (Critical to Quality Characteristic).Identify customer(s) in a quantifiable way.– Recognize the components of a process (i.e., supplier, input(s), sub-

process, output(s), customer(s).– Distinguish between internal and external customers.

Compile and evaluate customer CTQ data.– Distinguish between customer driven CTQs and process driven CTQs.– Recognize sources of existing customer data.– Assess customer requirements and expectations.– Recall the vital few customer CTQs.– Analyze the voice of the customer and it’s impact on CTQ data.– Translate customer needs into requirements (CTQs).

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6Define–Project Learning Objectives (continued)

2 Use a process/product drill-down tree to: define the limits of a project (project bounding); clarify what the project is and is not; identify other areas for improvement.Create a process/product drill-down tree.Integrate measurements to clarify areas needing improvement.Given an example of a process/product drill down tree, identify viable Six Sigma projects.

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3 Develop a team charter.Describe the purpose of a charter.Identify the five major elements of a charter.Define the business case for a project in terms of its potential benefits, the consequences of not doing it, its relationship to other activities, and its fit with business initiatives/target.Develop a problem statement.Describe the customer’s pain.Identify key considerations and potential pitfalls to consider when developing a problem statement.Develop a SMART goal statement (specific, measurable, attainable, relevant, time bound).Assess the scope of the project.Identify the 8 steps for bounding a project.Define project milestones.Select a project team and define team roles.Identify team roles and responsibilities.Evaluate a proposed Six Sigma project.Recognize characteristics of a “good” project.Recognize characteristics of a “bad” project.

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4 Map a business process.Describe the goal of process mapping.Identify the components of a process map (COPIS).Describe the steps involved in creating a process map. Define and name a process.Given a business process, use brainstorming and storyboarding techniques to: identify its outputs, customers, suppliers, and inputs; identify customer requirements for primary outputs; and identify process steps

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5 Obtain approval for a Six Sigma project.Identify the steps in the project approval process.Enter a project into QPT.

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10Define–Test Learning Objectives

1 Recognize the components of the 12 Step Process and how they may be applied to a Six Sigma project.

2 Describe the purpose of the define phase and it’s key deliverables: CTQs, team charter, and process map.Identify the five key objectives of the Define Phase.

3 Describe the CAP tools and their connection to Six Sigma.

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11Measure1–Classroom Learning Objectives

1 Describe and define the deliverables of Step 1.

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12Measure 1–Project Learning Objectives

1 Identify the project Y. Identify the tools that may be used to select the relevant CTQ or Y on which to focus.Explain the purpose Quality Function Deployment, Process Map, and FMEA tools have.Define performance standards for Y including specification limits as well as defect and opportunity definitions.

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13Measure 1–Project Learning Objectives (continued)

2 Select CTQ characteristics. Select the Critical to Quality (CTQ) characteristic to be improved in a project.Narrow the focus of a project to an actionable level.

Establish the project team and gained consensus on the project definition.

3 Select and apply appropriate tools to narrow the focus of a Six Sigma project by identifying key areas for improvement. Identify tools that may be used to narrow the focus of a project, including Process Map, and FMEA.Recognize the purpose and benefits of each tool.

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4 Use Process Mapping to identify potential breakdowns, rework loops, and sources of variation in a process.

Use the C.O.P.I.S. model to illustrate a customer focused process. Identify the elements of a process (input, mechanism, control, output, process boundary).Identify and distinguish between internal and external process controls.Recognize the purpose and benefits of process mapping. Recognize the three types of process maps.Describe the process mapping process, including the following steps:Determine the scope.Determine the steps in the process.Arrange the steps in order.Recognize ISO 9000 standard symbols for process mapping.Validate a process map. Evaluate a process map.

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5 Use a Failure Modes and Effects Analysis to identify the potential failure modes of a process or product. Recognize the purpose and benefits of FMEA.Describe how FEMA works.Describe FMEA, including preparation, process, and improvement steps. Define the terms “failure mode,” “cause,” and “effect,” as they relate to FMEA, and recognize examples of each. Assign degree of severity, likelihood of occurrence, and abilityto detect ratings, and calculate a risk priority number (RPN).Complete an FMEA form.– Recognize when and by whom an FMEA is prepared, updated, and

completed.

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6 Conduct a test-retest study and analyze the results. Describe the purpose and procedure for conducting a test-retest study. Plot and test-retest study data.Use descriptive statistics to evaluate test-retest study data.

7 Establish a Data Collection Plan for a Six Sigma project. Describe the purpose and benefits of a Data Collection Plan.Write a data collection strategy. Define a clear strategy for collecting reliable data efficiently.

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17Measure–Test Learning Objectives

1 Recall the DMAIC 12 Step process, and distinguish between characterization phases (DMA) and optimization phases (IC).

Define product characterization. Define process optimization.

2 Recognize how statistics can be applied to the problem solving process. Define the terms “precision” and “accuracy” as they relate to a Six Sigma process.Relate precision/variation and accuracy/mean to quality and customer satisfaction.State the goal of Six Sigma in statistical terms.Define the term “Upper Specification Limit (USL).”Define the term “Lower Specification Limit (LSL).”Define the term “target (T).”Define “σ.”

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3 Explain how statistics can be used to solve problems. Identify project variables using the formula Y = f (X1,…..,Xn ).Describe the relationship between any dependent variable (Y) and independent variables (X).Explain how the shape, mean, and standard deviation characterize a process. Express the capability of a process in terms of a standard measure (z-value).Define hidden factories and how capability impacts cycle time.

4 Identify the key deliverables of the Measure phase of DMAIC.

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5 Relate and apply the Quality Function Deployment (QFD) process to Six Sigma.

Explain the purpose of QFD.Describe the phases of QFD.Explain QFD flowdown for product and service applications.Generate/build a House of Quality (Product Planning Chart).Identify what the customer wants (the “what’s”).Identify the functions or processes that impact customer wants (the how’s). Evaluate the impact of each function/process on customer wants.Calculate the overall magnitude of the impact each function/process has on customer wants (prioritize actions).Analyze and diagnose a completed House of Quality.Describe other QFD applications.Determine when QFD is appropriate to use.Recognize QFD pitfalls.Describe an example of QFD from GE Medical Systems.


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7 Define Performance Standards for a Six Sigma project. Describe the purpose and characteristics of a performance standard.Describe the purpose and characteristics of an operational definition.Define the term “defect.”Given an example of a problem or process, write an operational definition.Describe and distinguish between continuous and discrete data.Recognize the components of a performance standard, including product/process characteristic, measure, target value, specification limits, and defect.Given a CTQ type, identify performance standard sources and discrete/continuous data measurement methods.Given an example, define the measurable characteristic, determine whether it is continuous or discrete, determine the specification limit if applicable, identify a defect.


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9 Establish the accuracy of the measurement system and the data (Analyze the measurement system). Describe measurement as a process that includes Measurement, Analysis, Improvement, and Control phases. Describe measurement as a system that includes operators, gages, and environment.Define the terms “(gage) resolution,” “precision,” “accuracy,” and “bias” as used in Measurements System Analysis (MSA). Using the MSA checklist, document the existing measurement system.Recognize the sources of variation in a measurement system.

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10 Conduct a Gage R&R study and analyze the results. Develop and implement a Data Collection Plan to collect Gage R&R study data.Describe equipment and appraiser sources of variation.Describe the total R&R variation in terms of Reproducibility (AV) and Repeatability (EV).Set up, collect, and enter data into a Minitab data sheet. Calculate both the appraiser variation (reproducibility) and equipment variation (repeatability). Describe the concepts of stability and linearity in gage studies.Compare R&R variation to the tolerance (specification window). Create graphs and charts (ANOVA method) to analyze study results.Recall and apply rules of thumb (guidelines) for analyzing R&R study results.

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11 Describe and define the use of gage R& R for discrete data. Describe the use of the attribute R & R spreadsheet for discretedata.

12 Recall and list the deliverables of the Measure phase of DMAIC.

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24Analyze–Classroom Learning Objectives

1 Perform hypothesis testing for a continuous Y and discrete X. Determine process stability with run charts and other toolsDetermine the data shape with histograms, normal probability plots, and Anderson-Darling tests.Select and use the appropriate tool to determine the p-value.Determine whether or not to accept the null hypothesis or the alternative hypothesis.

2 Perform hypothesis testing for a discrete Y and discrete X. Use chi-square testing to determine the goodness-of-fit and as a test of independence.Based on the chi-square test, determine whether or not to accept the null hypothesis or the alternative hypothesis.

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25Analyze–Classroom Learning Objective (continued)

3 Perform hypothesis testing for a continuous Y and continuous X. Use a scatterplot to determine correlations between variables.Use a linear regression analysis to quantify correlations and predict values.Determine process stability with run charts and other tools.Determine whether or not to accept the null hypothesis or the alternative hypothesis.Describe the use of multiple regression for this type of data.Describe the implications of multiple regression in statistical analysis.

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26Analyze–Project Learning Objectives

1 Use benchmarking to assist in developing project goals. Describe the purpose of benchmarking.Describe the uses of five different types of benchmarking, including competitive benchmarking, product benchmarking, process benchmarking, best practices benchmarking, strategic benchmarking, and parameter benchmarking.Apply benchmarking methodology to a variety of situations.List potential sources of benchmarking data and how to access such sources.Describe the advantages and disadvantages of Internal, Competitive, and Functional benchmarking and their relationship to Best Practices.

2 Set realistic and achievable defect reduction goals based on current baseline, GE guidelines, benchmarking results, and the process entitlement.

Describe the methods used to set project goals.Use GE Standards for defect reduction in combination with benchmark results to determine project goals.Use the process entitlement to validate the achievability of the project goals.

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27Analyze–Test Learning Objectives

3 Develop consensus within a project team on the acceptability of the project goals.Use a Cause & Effect (Fishbone) diagram to identify Xs that may impact the Y that is important in a project and provide a visual display of all possible causes of a specific problem. Recognize the purpose and benefits of a Cause & Effect diagram.Write a problem statement.Brainstorm categories appropriate to a problem.Recognize the 4 Ps: policies, procedures, people and plant.Brainstorm and analyze causes for each category to identify the most likely cause(s) of a problem.Determine which causes need to be verified with data.

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4 Use a Pareto Chart to separate the vital few from the trivial many in a process to determine where to focus improvement efforts. Recognize the purpose and benefits of a Pareto Chart.Describe the Pareto Principle.Describe the steps involved in building a Pareto Chart:Collect data. Total results and arrange data in descending order.Draw and label a Pareto Chart.Analyze results.Compare before and after Pareto Chart to evaluate improvement effectiveness.

5 Describe process map analysis. Describe value added/ non-value added analysis.

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6 Identify variation sources. Brainstorm a list of potential vital X’s.Use a histogram to aid in determining variation, center, and shape of a process.Use a dot plot to aid in determining variation, center, and shape of a process.Use a box plot to aid in determining variation, center, and shape of a process.Use a run chart to determine process stability.Define the terms population and sample and relate the two to each other.Use statistical tests to validate sampling techniques.Define the theoretical framework for hypothesis testing.Define and follow the hypothesis testing protocol.Define the terms null hypothesis and alternative hypothesis.Develop the null hypothesis for your project.Develop the alternative hypothesis for your project.Define type I and type II errors in relation to hypothesis testing.Define the relationship between the confidence interval and the p-value.

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2 Apply statistical principles of the Standard Normal Probability Distribution to predict the probability of a defect and process capability.

Use continuous data to describe a process by its average, standard deviation, and normal curve. Define the term “random variable.”Interpret uniform, triangular, normal, and exponential distributions. Relate probability to distribution curves.Define the terms “mean” and “standard deviation” as they relates to a normal distribution curve. Recognize and distinguish between population and sample computational equations.Use Minitab to calculate a mean and standard deviation.Recognize the Descriptive Statistics tool as a method for validating calculations.Calculate statistical measures of variation, including range, deviation, sum-of-square, standard deviation, and coefficient of variation.Calculate capability (Z value). Perform basic statistic calculations using Minitab. Describe the purpose and characteristics of Descriptive Statistics tools, including Histogram, Dot Plot, Box and Whisker Plot, Run Chart. Be able to distinguish a normal distribution from other common non-normal distributions.

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31Analyze–Test Learning Objectives (continued)

3 Characterize a process using discrete data. Define the terms unit (U), opportunity (OP), and defect (D). Recognize formulas for DPU, TOP, DPO, and DPMO. Use Z tables to convert DPMO to “Z”.Run and interpret a Minitab Product Report.Compare and contrast Classical Yield (Yc), Throughput Yield (YTP), and Rolled Yield (YRT).Calculation the distribution of defects for a given DPU.Calculate submitted, observed, and escaping defect levels.Recall DPU application rules.Determine how DPU controls Throughput Yield (YTP).Explain how complexity impacts quality.

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4 Use Process Centering strategies to perform a capabilities analysis. Explain the concept of Process Centering. Distinguish between special (assignable) and common (random) cause variation. Choose rational subgroups for proper sampling and analysis. Differentiate between entitlement, short term process capability, and long term process capability. Interpret Minitab “hand calculations,” histogram, and box plots.Calculate the long and short term standard deviation and Z-values. Explain the general long term 1.5 Z shift.Use Minitab Six Sigma Process Report to obtain short and long term process capability measures - ZST, ZLT, ZbenchLT, Zshift, DPMOST, DPMOLT. Using capability measures and a 2x2 matrix, determine if there is a control problem or a technology problem.

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5 Determine process capability. Define the term “process entitlement” as it relates to process capability.Define and provide examples of common cause and special cause variation.Define and use rational subgrouping of data.Define shift and drift of a process.Describe the components of variation.Calculate variation for a given process.Calculate the standard deviation for a process.Calculate process capability.Define the difference between long term and short term capability and their uses in a six sigma project.Define the use of the sum of squares and the standard deviation.Use the universal equation for Z to calculate Z scores.Define, derive, and use the Z-Bench for a process.Relate and convert between the Z score and Defects per Million Opportunities.Use data collected in the Measure phase to generate a process capability chart for a process.Interpret the results generated by the process capability report to determine the short term and long term process capability of a process.Use process capabilities to compare your process with a benchmark process.Determine whether the deficiencies in a process are due to control problems or technology problems.

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8 Describe the statistical analysis tools and process for normal/non-normal data. Describe the use of the normality test.Describe the use of Mood’s median for non-normal data.

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35Improve–Project Learning Objectives

1 Characterize X’s as either operating parameters or critical elements.

2 Develop a strategy for those X’s identified as operating parameters.Develop a mathematical model of a proposed solution.Determine the best configuration or combination of X’s

3 Develop a strategy for those X’s identified as critical elements. Optimize process flow issues.Standardize the process.Develop a practical solution.Explain the needs and process to do screening experiments. The implications for this in DOE is described.

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4 Perform optimizing experiments in order to develop a proposed solution. Identify factors for optimization experiments.Identify factor levels for optimizing experiments.Design optimizing experiment to include randomization and replication.Perform experiments and collect data.Analyze data with various tools including regression analysis.

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5 Develop a proposed solution. Interpret the outputs of various tools to determine the optimum solution.Determine if the optimum solution will meet project goals.Present the proposed solution to management.Use statistical tolerancing to define the control mechanisms for implementation.

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6 Establish operating tolerances. Describe the concept of tolerances and describe an example of this concept.Describe the use of simulation and the use of Crystal Ball.Describe and show an example of Crystal Ball.

7 Pilot the proposed solution.

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39Improve–Test Learning Objectives

1 Describe and define the deliverables of Steps 7 and 8 in Six Sigma.

2 Describe and define the deliverables of Step 9 in Six Sigma.

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40Control–Project Learning Objectives

1 Develop/modify and implement Quality Plans. Describe the purpose and characteristics of a Quality Plan. Recognize the components of a Quality Plan.Plan ongoing process controls, including monitoring and auditing strategies.Explain the benefits of monitoring as compared to First Article Inspection (FAI) and Information Management methods.Determine what to monitor for a given process. Determine the appropriate amount of monitoring data to collect, and how frequently the monitoring should occur.Recognize methods for detecting changes in a process.Recognize the steps that should be taken if a process change is detected. Explain the purpose of auditing.Describe guidelines for effective auditing.Compare and contrast manufacturing control methods.Explain the purpose and process of variable data charting (SPC).Explain the purpose and process of process management charting.

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2 Develop and implement risk management strategies. Explain the value of a risk management process.Define the terms “risk” and “risk management” as they relate to DMAIC/Six Sigma.Determine when to use risk management.Recognize different types of risks.Recognize the steps involved in risk management, including identifying risks, rating risks, abating risks, and executing risk management plans. Recognize methods for identifying risks.Describe methods and tools for rating risks. Using the Probability of Occurrence Rating guide and Consequence of Occurrence/Risk Impact chart, prioritize risks according to risk factor score.Determine when and how to implement a Risk Abatement plan.Integrate lessons learned from prior risk management efforts. Describe the formal risk review process.Explain the criticality of tracking and executing risk abatement plans.

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3 Develop and implement mistake proofing strategies.Recognize examples of mistake proofing.Describe principles underlying the process of mistake proofing.Recognize the difference between errors and defects.Explain how defects originate.Identify ten types of human error. Recognize human error-provoking conditions. Identify the three key mistake proofing techniques: shutdown, control, and warning.Distinguish between prediction/prevention and detection methods of mistake proofing.Recognize typical mistake proofing tools.Describe the 5 steps involved in mistake proofing, including identifying problems, prioritizing problems, finding the root cause, creating solutions, and measuring results.Recognize the advantages of mistake proofing as a proactive tool.Explain how mistake proofing fits into the Six Sigma process.

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4 Select and apply the appropriate Control Chart.Recall and explain SPC Concepts, including controlled variation, uncontrolled variation, common causes, and special causes.Recognize the five main uses of control charts. Distinguish between variable, attribute, and process focused control charts.Determine control limits.Distinguish between control limits and specification limits. Recognize the four states of a process.

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44Control–Test Learning Objectives

1 Describe and define the deliverables of Steps 10 and 11 in Six Sigma.

2 Describe and define the deliverables of Step 12 in Six Sigma.

3 Develop and implement Variable Control Charts.Describe the purpose of Statistical Process Control Charts.Given a control chart, recognize when a special cause is acting on a process.Recognize other types of variable control charts, including X Bar Chart, R Chart, Individuals Chart, and Moving Range Chart.State the five main uses of control charts.Describe data collection and sampling techniques.Establish and maintain control limits. Select the appropriate Variable Control Chart. Distinguish between control limits and specification limits. Determine whether a process is “in control” or “out of control.”Recognize Western Electric rules for identifying an out of control process.Recognize and apply Minitab rules.Build an Individuals and Moving Range chart.Use knowledge of the process to eliminate or reduce assignable/special causes.

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45Control–Test Learning Objectives

4 Develop and implement Attribute Control Charts.Describe the purpose of Attribute Control Charts.Define and relate the terms “a defect” and “a defective.”Recognize types of Attribute Control Charts, including C-Charts, U-Charts, P-Charts, NP Charts.Select the appropriate Attribute Control Chart.Use Minitab to generate each type of Attribute Control Chart.Determine the appropriate Attribute Chart subgroup size.

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46Glossary And Minitab Primer

1 Define the typical terms used in Six Sigma methodologies.

2 Describe the use of the Minitab software program.

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IntroductionsDesired Outcome: Introduction of Classmates and CD Rom Learnings

Introduction Exercise (60 Minutes) 1

1 min.When asked by the instructor, each team member will introduce themselves:

– Name– How long you’ve been

with GE– Your Title and what you do– Previous Quality

Experience– What Phase your project

is inAfter last team member has introduced himself/herself, the spokesperson will discuss the deliverables of the above-mentioned exercise.

ReportOut

1 min.Choose a spokesperson to report out

CloseExercise

7 mins.AllDiscuss the importance of the DMAIC Step that your team has been assigned.

Create a list of items that describe the deliverables for the step and why this step is important in the DMAIC cycle. Use your knowledge from your CD Rom Learnings.

Exercise

2 mins.AllGo around your tables and introduce yourself to your table-team members (name and business only, at this time.)

Team Preparation

TimingWhoHowWhat

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2Classroom Session–Objectives

Share and get feedback on project deliverables for Define and Measure phasesReview Define phaseReview Measure phaseLearn how to apply CTQ tools in the Measure phase of a projectLearn how to use Minitab for statistical and graphical analysis during a projectLearn knowledge and skills in Analyze phase and apply to Capital Logistics casePreview Improve phaseLearn how to apply Design of Experiment (DOE) in the Improve phase of a projectPreview Control phaseLearn how to apply control charts in the Control phase of a project

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3Iterative Process

Steps A,B,C

Steps 1,2,3

Steps 4,5,6Steps 7,8,9

Steps 10,11,12

The Phases of the 12-Step Process

Phase 1 (Define). This phase defines the project. It identifies customer CTQ’s and ties them to business needs. Further, it defines a project charter and the business process bounded by the project.

Phase 2 (Measure). This phase is concerned with selecting one or more product characteristics; i.e., dependent variables, mapping the respective process, making sure the measurement system is valid, making the necessary measurements, and recording the results.

Phase 3 (Analyze). This phase entails estimating the short and long-term process capabilities and benchmarking the key product performance metrics. Following this, a gap analysis is often undertaken to identify the common factors of successful performance; i.e., what factors explain best-in-class performance.

Phase 4 (Improvement). This phase is usually initiated by selecting those product performance characteristics which must be improved to achieve the goal. Once this is done, the characteristics are diagnosed to reveal the major sources of variation. Next, the key process variables are identified by way of statistically designed experiments. For each process variable which proves to be significant, performance specifications are established.

Phase 5 (Control). This phase is related to ensuring that the new process conditions are documented and monitored via statistical process control methods. After a “settling in” period, the process capability would be reassessed. Depending upon the outcomes of such a follow-up analysis, it may be necessary to revisit one or more of the preceding phases.

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4Statistical Thinking

Root cause analysis

– Critical X’sMeasure the influence of the critical X’s on the mean and variability

– Test– Model– Estimate

Practical Problem

Statistical Problem

Statistical Solution

Practical Solution

D M A I C

Characterize the process

– Stability– Shape– Center– Variation

Verify critical X’s and ƒ(x)Change processControl the gains

– Risk analysis

– Control plans

Problem statement– Project Y– Magnitude– Impact

Data Integrity– MSA– Brainstorm

potential X’s– Sampling plan

Collect data

Capability– ZBench ST & LT

The Practical-To-Statistical-To-Practical Transformation Process


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The 12-Step Process 5

Process Capability Y, X Capability IndicesY, XDetermine Process Capability

11

Proposed Solution Factorial DesignsXDiscover Variable Relationships

8List of Vital Few X’s DOE-ScreeningXScreen Potential Causes7

Control

Piloted Solution SimulationY, XEstablish Operating Tolerances

9

MSAContinuous Gage R&R, Test/Retest, Attribute R&R

Y, XDefine & Validate Measurement System on X’s in Actual Application

10

Sustained Solution, Documentation

Control Charts, Mistake Proofing, FMEA

XImplement Process Control12

Improve

Prioritized List of all X’s Process Analysis, Graphical Analysis, Hypothesis Tests

XIdentify Variation Sources6

Improvement Goal for Project Y

Team, BenchmarkingYDefine Performance Objectives

5

Process Capability for Project Y

Capability IndicesYEstablish Process Capabilities

4Analyze

Data Collection Plan & MSA Data for Project Y

Continuous Gage R&R, test/Retest, Attribute R&R

YMeasurement System Analysis

3

Performance Standard for Project Y

Customer, BlueprintsYDefine Performance Standards

2Project Y Customer, QFD, FMEAYSelect CTQ Characteristics1

MeasureHigh Level Process MapDefine Process MapCApproved Charter Develop Team CharterBProject CTQ’s Identify Project CTQ’sA

DefineDeliverablesToolsFocusDescriptionStep

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6The “Basics” For Effective Meetings

DMAIC is a powerful methodology which will allow teams to significantly improve the processes on which they are working. However, in order for teams to efficiently use the tools and techniques associated with DMAIC, they must be able to work together effectively. Although not the focus of this class, we will briefly focus on the minimum requirements for effective meetings.Further training in effective meeting skills is provided in “Facilitating Teams through Change Projects” Training

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7Meeting Skills

The “Basics” For Effective Meetings

Roles:Leader or FacilitatorTimekeeperScribe Note Taker

Tools:AgendaDesired OutcomesGround RulesDecision-Making ProcessBrainstorming

Define These Roles For A Meeting Or Any Team

During this training, you will practice these roles so that you can use them in your project team meetings to improve meeting effectiveness.

The effectiveness of any meeting can be improved simply by having an agenda. That effectiveness can be improved even further by including the desired outcomes. Desired outcomes, or the goals you hope to achieve during the meeting, provide additional focus and give clear purpose for your meeting.

Ground rules, or the “code of conduct,” further increase the effectiveness of your meeting by specifying the behavior that is expected from all participants. For ongoing teams, such as DMAIC teams, ground rules should be established and agreed upon by all team members early in the project.

Rules Of Brainstorming:

No judgment of ideasRecord all ideasNo discussion of ideas during brainstorming

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Desired Outcome: Name your team

* N/3 is a prioritization technique used to narrow a large list down to the top priorities. The number of ideas (N) is divided by 3 (N/3) and team members get that number of votes to identify their top choices. All votes should not be put on one choice.

Practice Meeting (5 minutes) 7

4 mins.FacilitatorBrainstorm a list of possible team names

Using N/3*, prioritize your brainstormed list

Identify your top name

DetermineTeam Name

30 secs.AllChoose a spokesperson to report out

CloseExercise

30 secs.AllChoose a facilitator, timekeeper and scribe

Team Preparation

TimingWhoHowWhat

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Define Review Objectives

Review Steps in Define phase

Review and get feedback on Greenbelt project deliverables for Define phase

1Define Review Module Objectives

Review CAP ToolsReview steps in Define phaseReview and get feedback on Green Belt project deliverables for Define phase

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Desired Outcome: Learning the components for successful change

First Things First (10 minutes) 2

5 mins.FacilitatorOn a flip chart, list your group’s ideas for why change initiatives fail. What are the common themes?Be prepared to report findings.

Prepare List

5 mins.Each Team

Member

Think of a change initiative that youhave experienced in the past inwhich the change was unsuccessful.Why did the change initiative fail?

Team Preparation

TimingWhoHowWhat

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3Change Acceleration Process (CAP)

Change Initiative(Target)

Cultural/Organizational Strategy

Technical Strategy

CAP Complements Technical Strategy With Cultural Tools To Achieve The Change Initiative

CAP Complements Technical Strategy With Cultural Tools To Achieve The Change Initiative

Change can be depicted via the equation:

Q x A = E

Q = Quality of solution to be implemented

A = Acceptance of solution to be implemented

E = Effectiveness of the implemented solution

It is as important to have a strategy for developing acceptance as it is to have a plan for implementing the solution.

A Technical Strategy and a Cultural/Organizational Strategy are both necessary in order to effectively achieve your change target. CAP gives us tools to develop the Cultural/Organizational or Influence Strategy.

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4Cap Model

TransitionState

CurrentState

ImprovedState

Leading Change

Changing Systems And Structures

Creating A Shared NeedCreating A Shared NeedShaping A Vision

Mobilizing CommitmentMobilizing Commitment

Making Change LastMaking Change Last

Monitoring Progress

Leading ChangeAll implementation projects require a Champion who sponsors the change if they are to be successful.

Creating A Shared NeedThe reason to change, whether driven by threat or opportunity, is instilled within the organization and widely shared through data, demonstration, demand, or diagnosis. The need for change must exceed the resistance to change.

Shaping A VisionThe desired outcome of change is clear, legitimate, widely understood, and shared.

Mobilizing CommitmentThere is a strong commitment from key constituents to invest in the change, make it work, and demand and receive management attention.

Making Change LastOnce change is started, it endures and flourishes, andlearnings are transferred throughout the organization.

Monitoring ProgressProgress is real; benchmarks are set and realized; indicators are established to guarantee accountability.

Changing Systems And StructuresManagement practices are used to complement and reinforce change.

Did the themes that you’ve developed in your last exercise alignwith our CAP Model? This CAP Model helps us to focus on the organizational changes aspect of projects.

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5Cap Tools And Six Sigma

Control

Making Change Last ChecklistControl PansMeasures And Rewards


Improve

Analyze

Measure

Threat vs. Opportunity MatrixGRPIARMI

In Frame / Out Of Frame

SIPOCThreat vs. Opportunity MatrixProject Scope Contract

Define

Monitoring Progress

Making Change Last

Mobilizing Commitment

Shaping A Vision

Creating A Shared Need

Control



Improve

Analyze

Measure

Threat vs. Opportunity MatrixGRPIARMI

In Frame / Out Of Frame

SIPOCThreat vs. Opportunity MatrixProject Scope Contract

Define

Monitoring Progress

Making Change Last

Mobilizing Commitment

Shaping A Vision

Creating A Shared Need

The above-mentioned tools are covered in the Tools Section of the Self-Paced Workbook. For further training, you can attend the week-long course sponsored by Learning Services.

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Homework 6

Desired Outcome: Identify Cap Tools which you will use in your project

AsHomework

Each Student

Identify at least one CAP Tool that you have used in your projectthus far

If you have not used any CAP Tools, then identify a CAP Tool thatyou could, in retrospect, have used

For tomorrow, be prepared to share with the class which tool you used, how you used it, and how it helped you with your project

Prepare a plan for CAP Tools

TimingWhoHowWhat

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7Define Phase Flowchart

D M A I C

DEFINE PHASE

OVERVIEW

Define A:Identify Project CTQ’s

Define B:Develop Team Charter

Define C:Define Process Map

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8Define Phase Overview

What is the Define phase?The Define phase is when your team identifies:

Who your customers are and what their requirements are for your products and services The reason for doing the project and project boundaries The project team members and how they will work together What process you are trying to improve and what the process map looks like

Why is the Define phase important?This phase is important because it clearly and precisely describes the goals of the project, aligns the project with organizational priorities and lays the groundwork that will allow the team to remain focused.

Steps involved in the Define phase:Define A: Identify Project CTQ’sDefine B: Develop Team CharterDefine C: Define Process Map

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What does it mean to Identify Project CTQ’s?Critical to Quality Characteristics, CTQ’s, are the key measurable characteristics of a project or process whose performance standards must be met in order to satisfy the customer. Green Belt improvement projects typically focus on one or two CTQ’s of a process or product.

Why is it important to Identify Project CTQ’s?Project CTQ’s are important because they ensure that the improvement team is solving problems that are both critical to your customer and aligned with your business strategy. If project CTQ’s are not identified and validated in this manner, valuable resources may be wasted on counterproductive projects that neither increase customer satisfaction nor add value to the business.

What are the project tasks for completing Define A?A.1: Identify CustomerA.2: Collect Voice of the Customer data to identify customer CTQA.3: Build a process/product drill-down tree to identify project CTQ’s

DEFINE STEP OVERVIEW

Define A:Identify ProjectCTQ’s

Define B:Develop TeamCharter

Define C:Define ProcessMap

A.1 Identify CustomerA.2 Collect Voice of the Customer data to Identify Project CTQ’sA.3 Build a process/product drill-down tree to Identify Project CTQ’s

Define A–Identify Project CTQ’s 9

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What does it mean to Develop a Team Charter?A charter is a document that establishes a purpose and plan for the project. It contains a statement of the problem, the scope of the project (including the process to be improved), and an improvement goal, a plan and schedule for the project, estimated financial benefits, and a list of team members and their roles. The charter becomes the blueprint for the project when key stakeholders approve it.

Why is it important to Develop a Team Charter?The charter documents the expectations, boundaries, and business case for your project and can help you identify necessary resources. It is also a key communication tool that can help your team stay focused and help you share information about your project with each other and with the business. An approved charter ensures that your team, sponsor, and stakeholders agree up front on what is being done and that your project will have a beneficial impact on the business.

What are the project tasks for completing Define B?B.1 Define the business caseB.2 Develop problem statementB.3 Develop goal statementB.4 Assess project scopeB.5 Select project team and define rolesB.6 Develop charterB.7 Get sign-off for team charter





B.1 Define the business case B.5 Select project team and define rolesB.2 Develop problem statement B.6 Develop charterB.3 Develop goal statement B.7 Get sign-off for team charterB.4 Assess project scope

Define B–Define Team Charter 10

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C.1 Develop high-level Process Map

What does it mean to Define a Process Map?A high-level process map is a chronological display of the most significant four to five steps, events, and operations in a process. It provides a structure for defining a process in a simplified, visual manner. The high-level map gives you an overall view of an entire process and lays the foundation for thinking about the process in more detail.

Why is it important to Define a Process Map?A high-level (COPIS) map will help you understand the process and validate your project scope. It is a bridge between the problem and scope statements in your charter and the more detailed maps you will develop to help you improve the process. A high-level map provides focus for the team and helps you identify areas that are within (as well as beyond) your control. In addition, process mapping serves as a communication tool that helps you to clarify the process to others, both internally and externally to the business.

What are the project tasks for completing Define C?C.1 Develop high-level Process Map

Define C–Define Process Map 11

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Elevator Speech–Homework Activity* 12

Elevator speeches will be shared with the entire class throughout the 3-day workshop.

* For additional information on elevator speeches, see the Self-Paced Workbook, pp 197-198

Desired Outcome: Share elevator speech for the project with members of your team

Each Team

Member

Each team member shares the elevator speech for their project. (See the description of an elevator speech on the following page.)

ElevatorSpeech

AllMake a note of any feedback you receive from your class members. Did your elevator speech provide a clear understanding of your project?

Feedback

AllDevelop an elevator speech for your project.Preparation

WhoHowWhat

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13Elevator Speech

Here is what our project is about (describe the problem or issue)Here is why it’s important to you (describe the benefit of doingthe project)Here is what success will look like (describe the goal of the project and where we currently are)

What is it?

This is a tool that helps the team members put together a short “sell” pitch for the project. Being able to clearly and simply state the need for change and describe the future state is essential for rallying the support and commitment of key constituents.

The metaphor of the elevator is useful in challenging the team to be clear, precise and simple.

Imagine a chance meeting of a team member and a key stakeholder in an empty elevator with a 90-second ride.

Describe the need for change and the vision of the new state, as one might respond to the question, “Why are we doing this project?”

Why use it?

It helps the team link the need for change with the vision of the future. All the team members will be using a common “sell” pitch. For teams that have thoroughly debated and documented both the need and vision, this is the synthesis event whereby they distill the essence of the project. For teams struggling to get started in terms of need and vision, it can be the place to begin to bring some focus to the team’s more rambling discussion of need and/or vision.

The elevator speech should be able to deal with the questions that will arise once the project is announced to the broader constituent base.

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14DMAIC Checklist–Define A

A.1 Identify customerHave you considered both internal and external customers?Have you focused on the most important customer segment(s)?

A.2 Collect voice of the customer data to identify customer CTQ’sHave you collected data to understand customer requirements?Have you coordinated your data collection with others who are collecting similar data, so as not to overwhelm the customer?Have you validated the customer CTQ’s (Big Y) with the customer?Have you verified a VOC Research method that you’ve selected that reflects the true VOC?

A.3 Build a process/product drill-down tree to identify project CTQ’sIs your project CTQ focused on what’s most important to the customer?If you have multiple CTQ’s, have you used the appropriate tool to prioritize them?

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15DMAIC Checklist–Define B

B.1 Define the business caseIs the business case compelling to the team?Does this business case illustrate why this project needs to be done now ?Have I considered intellectual infringements?

B.2 Develop problem statementDoes your problem statement identify a problem and not prejudge a root cause or attempt to solve a problem?Is the problem statement linked to the project CTQ?Is the problem statement based on facts not assumptions?Has another Improvement Team tried to solve this or a similar problem? What can you learn from their effort?

B.3 Develop goal statementIs your goal statement SMART (Specific, Measurable, Attainable, Relevant, Time-bound)?Does your goal statement focus on what needs to be improved, and without predetermining a solution?How will you know the team is successful?

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16DMAIC Checklist–Define B (continued)

B.4 Project scopeDoes your team agree on the project scope?Is your project scope within the team’s control?

B.5 RolesAre all functions represented?Does each team member fully represent their manager’s input on the project?

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17DMAIC Checklist–Define C

C.1 Develop high-level process mapDoes the COPIS scope (start and stop) match the scope definition in your team charter?Have you mapped the process from your customer's perspective?Is this the “As-Is” process? Was the map validated with the people who actually do the process

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18Forms Of Intellectual Property

PatentBest Protection against independent development by othersGives right to exclude others from making, using selling, the invention of 20 years from filingCan wait 2-3 years for patent to issueRight granted by the government for new, useful, non-obvious inventions

Trade SecretRights exist only so long as actually kept secretProtects against theft or misappropriation, not independent developmentDoes not require inventiveness in the patent sense

CopyrightProtects original works of authorship fixed in a tangible mediumDoes not protect against independent development

TrademarkDefines sources of goods or servicesArbitrary, fanciful marks get stronger protection

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19Intellectual Property Assessment in Chartering Phase

Throughout the project consider implications to Intellectual Property Policies and Procedures through the following:

Commercial benefit for licensing–consider this in the cost/benefitInfringement Avoidance–GE has a policy covering avoiding infringing on other’s IP-Assure no infringementIdentify and Capture IP–Throughout this project consider whether IP is developed and take actions to capture and protect

Note: When writing your Business Case be certain to consider and include IP issues.

Consult the business’ IP Business Champion and IP Designer with questions, and for guidance

Consult the business’ IP Business Champion and IP Designer with questions, and for guidance

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1Measure Module Objectives

Review steps in Measure phase

Start work on Green Belt project deliverables for Measure phase

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2Measure Phase Flowchart

MD A I C

MEASURE PHASE

OVERVIEW

Measure 1:Select CTQ Characteristic

Measure 2: Define Performance Standards

Measure 3:Establish Data Collection Plan, Validate Measurement System, & Collect Data

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The12-Step Process 3


11



Control


9



10




Improve





5



4Analyze




3






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4Measure Phase Overview

What is the Measure phase? This phase is concerned with selecting one or more product characteristics to measure, defining how the characteristics will be measured, planning data collection, and collecting data.

Why is the Measure phase important?This phase is important because it ensures that accurate and reliable data is collected to measure current process performance related to the customer CTQ.

Steps involved in the Measure phase:Measure 1: Select CTQ CharacteristicMeasure 2: Define Performance StandardsMeasure 3: Establish Data Collection Plan, Validate Measurement

System & Collect Data

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Mapping Tools To Generation Of CTQ Components 5

Output UnitOutput Unit

CTQCTQCTQ

High Level Need (VOC)

Output Characteristic


Project Y OperationalDefinition


SpecificationLimits

SpecificationLimits

TargetTarget

Defect Defect

# of Defect Opportunities

Per Unit


Per UnitFMEAProcess Map

FMEAProcess Map

Measure 2

FMEAC&E

FMEAC&E

Measure 2

QFDParetoVOC

QFDParetoVOC

Measure 2

VOCQFD

VOCQFD

Measure 2

QFDProcess MapC&EPareto


Measure 1

QFDC&EC-O-P-I-S

QFDC&EC-O-P-I-S

Measure 1

C-O-P-I-SC-O-P-I-S

Define A

C-O-P-I-SC-O-P-I-S

Define A

Project Y Measure

Project Y Measure

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Practical Problem

Statistical Problem


Practical Solution

D M A I C




– Risk analysis

– Control plans




Collect data




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MEASURE STEP OVERVIEW

1.1 Identify measurable CTQ characteristics that will be improved (Project Y).


Measure 2:Define Performance Standards

Measure 3:Establish Data Collection, Validate MSA

What does it mean to Select a CTQ Characteristic?The goal for this step is to drill-down from what you learned in Define to identify the specific sub-process or system characteristic that will be the subject of your Green Belt project. In the Measure phase, you need to further narrow the scope by focusing on one particular factor that impacts the CTQ. Remember that every project is different, and the level that you need to drill-down to depends on how broad in scope you want your project to be. By the end of this step, you should have identified exactly what aspect of the product/service you will measure for your project.

Why is it important to Select a CTQ Characteristic? It is important to manage the scope of your project. By drilling-down to a sub-process or sub-system, if necessary, you keep the connection to the high-level customer CTQ while, at the same time, keeping the project scope manageable.

What are the project tasks for completing Measure 1?1.1 Identify the measurable CTQ characteristic that will be improved (Project Y).

Measure 1–Select CTQ Characteristics 1

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CTQCTQCTQ






SpecificationLimits

SpecificationLimits

TargetTarget

Defect Defect


Per Unit


Per UnitFMEAProcess Map

FMEAProcess Map

Measure 2

FMEAC&E

FMEAC&E

Measure 2

QFDParetoVOC

QFDParetoVOC

Measure 2

VOCQFD

VOCQFD

Measure 2



Measure 1

QFDC&EC-O-P-I-S

QFDC&EC-O-P-I-S

Measure 1

C-O-P-I-SC-O-P-I-S

Define A

C-O-P-I-SC-O-P-I-S

Define A

Project Y Measure

Project Y Measure

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1CTQ Tools Module Objectives

Learn how to apply a variety of CTQ tools to help prioritize & define CTQ elements to be improvedIf you don’t already know your Project Y, then one or more of these tools can help you:– Process Mapping– Cause & Effect (Fishbone)– Failure Modes and Effects Analysis (FMEA)– Pareto Charts– Quality Function Deployment (QFD)

This group of CTQ tools can be used to do some preliminary analysis of your process in order to identify the sub-processes that contribute most to satisfying the customer CTQ requirement. Most likely, you will use 1 or 2 of these tools to gather your Project Y (Measure, Step 1 deliverable).

Note: FMEA’s and Pareto Charts can also be used in other DMAIC phases and will be covered in detail in later sections of the program.

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2

Process Mapping

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3Process Mapping–CTQ Tool #1

A Graphical Representation of Steps, Events, Operations, and Relationships

of Resources Within a Process

ApplicationsTechniques for examining a process to determine where and why major breakdowns occurGraphically displays steps, events, operations and relationships of resourcesUsed to design an improved processBenefitsProvides a structure for breaking down a complex processUncovers problem spotsDetermines what data to collect.Targets selected improvements.

Enables group to see the entire process as a teamMagnifies normally overlooked areas and displays their relevancy

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4Levels Of A Process

Core

COPIS/SIPOC

Detailed Subprocess

Map

Acquire New Acquire New BusinessBusiness

Obtain Request toObtain Request toBuy ServiceBuy Service

ConductConductUnderwritingUnderwriting

PreparePrepareContractContract

InitializeInitializeCustomer ServiceCustomer Service

Establish Terms

PrepareDocs

NegotiateContract

CloseDeal

Underwriters

SS CC

Tasks Procedures

Customer/Customer Service

Earlier in Define, you developed a high-level or COPIS process map. By looking at a process from a “big picture” perspective, you evaluated customer needs and supplier inputs, and determined initial measurement objectives.

Now, you will look in more detail at the subprocessesdefined in the COPIS map. Subprocess maps provide specifics on the process flow that you can then analyze using several useful techniques. Choose what to subprocess map by determining which of the major steps in the COPIS have the biggest impact on the output (Y’s). The block (or blocks) selected is the one on which you create a subprocess map–using it to understand how and why it impacts the output.

If the Project Y is a time measure, which of the blocks consumes the largest portion of total time, or which one has the most variation or delays?

If the Project Y is a cost measure, which of the blocks adds the most cost?

If the Project Y is a function measure, which block has the most errors or problems?

Like working with a puzzle, you begin to assemble the pieces of an area on which it makes sense to focus our efforts.

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5Versions Of A Process

What You Think It Is... What It Really Is.. What It Should Be... What It Could Be...

Subprocess mapping is simply drawing a picture of the process–documenting the flow of the process. But, there are at least four major versions of a process map that you can draw.

First, you can document what individuals who touch the process think it is. Certainly with the daily contact, you would expect people to know how the process works. But many people can easily explain how things work when things go right. You need to know how the process works in all conditions, so you need to go further.

Reconciling what the process map is, into what it really is, is a second version of the process. These first two versions of the process constitute what is referred to as the “as is” process map. A thorough “as is” process map is one of the short-term goals of good process mapping and a deliverable for the Analyze phase.

Reconciling the map requires your team to observe the process–making sure you have recorded all the existing steps.

As the team moves forward and does process analysis and problem-solving, eventually you will move toward the third version of the process map–the “should be” map created as part of their Improvement plan. At this point, a check must be made as to whether customer CTQ’s have been met or exceeded.

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6Outside-In Focus

Does your process overlap with the customer’s?Should the customer’s process be mapped?Should you partner with the customer to assess the processes?

Continue to keep focused on the customer’s perspective.

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7Subprocess Mapping Techniques

Process flowchartAlternate path methodDeployment or cross-functional map/flowchart

There are a number of ways to draw a subprocess map. Your team can choose the approach or approaches most appropriate (or comfortable) for your use. Whatever type of subprocess map is chosen, make sure that it accurately reflects your process as it currently exists.

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8Process Mapping Symbols

These symbols represent the standard symbols for process mapping.

Most projects use the simplified symbol sets shown on the following page.

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9Process Flowchart

Key:

Task Review OrDecision Direction

StartStartEndEnd

AutomatedSystem

AnswersCriteria

Met?Yes

No

CustomerCustomerCallsCalls

CustomerChooses RoutingOption

Prepare Loan Offer

CallCallEndsEnds

Touch-Tone

Phone

Yes Rep Answers Phone

Call Gets Routed To

Voice-Activated System

Call Placed In Que, On

Hold

Customer Waits?

No

The business process map most people are familiar with uses four simple symbols: oval, rectangle, diamond, and arrow.

It is generally used when the process is fairly small and simple, or when documenting the work done by a single person or group.

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10Alternate Path Flowchart

Key:

DirectionPercentagesTask

40

60

AutomatedSystem

AnswersCriteria

Met?

80Yes

20No

CustomerCustomerCallsCalls

CustomerChooses RoutingOption

Prepare Loan Offer

CallCallEndsEnds

Touch-Tone

Phone

85Yes Rep

Answers Phone

Call Gets Routed To

Voice-Activated System

Call Placed In Que, On

Hold

Customer Waits?

15No

Decision

The “alternate path” process map method arose from reengineering efforts, where the mapping of very large processes made “decision diamonds” more of a hindrance than a help.

In this technique, diverging or alternate “paths” are noted by split arrows. Teams can then note relative percentages of times/incidences the process follows each path.

Process mapping software tools also make it easier to add “icons” showing the tools or methods employed at different points in the process.

Showing the alternate path allows us to identify sources of variation which maybe adding complexity to our process.

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11Deployment Or Cross-Functional Flowchart

Customer

ContractAdmin.

Attorney

Dealer

Who PROCESS FLOW

InitiateCall

InitiateCall

NegotiateNegotiate

ReviewContractReview

Contract

ReviseContractRevise

Contract

WriteContract

WriteContract

NegotiateNegotiate

ReviewContractReview

Contract

ReviseContractRevise

Contract

SignContract

SignContract

FileContract

FileContract

FileContract

FileContract

FileContract

FileContract

This approach to process mapping emphasizes who performs which tasks and which steps are done concurrently.

It provides a clear visual perspective of the hand-offs and relationships between groups involved in the process. (Note: Either of the mapping techniques described on the previous pages can be placed on this type of map.)

Always include the process customer and key suppliers as “bands” on this type of map. (Because customers are visible at the top, some people refer to this as a “Service Blueprint.”)

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12Steps In Deployment Mapping

1. Identify the participants of the process from start-to-top point. Place the customer at the upper left corner.

2. Identify the “trigger” or initial step andidentify the “final” step

3. Identify who receives the output of theinitial step and what activity they perform

4. Repeat by identifying who receives the output from the second step and what activity they perform

5. Continue identifying steps and align vertically with participants

For Your Process/Subprocess:

1. Identify the participants involved in the process, write their names on cards, and pin or tape the cards in a vertical column on the wall with the customer at the top of the column.

2. Identify the action that initiates the process, write it on a card, and place it next to the appropriate participant card. In many instances,the process is initiated by the customer but it is not always the case. Also, identify the final step in the process and place in the appropriate row at the end of the map. Here again, the last step may be the customer’s action.

3. Next, identify who receives the output of the second step and what activity they perform. Write this activity on a card and place it to the right of the second step on the same row as the participant performing the activity.

4. Identify who receives the output of this activity and what activities that participant performs.

5. Continue to create cards and position them in the same manner until the process is complete (i.e., the customer receives the final process output).

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13Tips In Subprocess Mapping

Involve people who know (focus on) the “as is”Clarify process boundariesBrainstorm steps–write on Post-its®

– Use verb-noun format (e.g., Prepare contract, not contracting ) – Don’t include “Who” in step description

Combine, eliminate duplicates, clarify stepsOrganize steps into proper “flow” and add arrows

Respect the boundaries

Don’t start “problem-solving”

Validate and refine before analyzing

Here are some guidelines on building a subprocess map. These are not absolute–but they should help you avoid some of the pitfalls of process mapping.

Focus on “As Is”–To find out why problems are occurring in a process, you need to concentrate on how it’s working now.Clarify Boundaries–If you’re working from a well-done high-level map, this should be easy. If not, you’ll need to clarify start and stop points. Brainstorm Steps–It’s usually much easier to identify the steps before you try to build the map. Starting each step description with a verb (e.g., “Collate Orders”; “Review Credit Data”) helps you focus on action in the process. Who does the step is best left in parentheses (or left out) –you want to avoid equating a person with the process step.

Combine and Clarify–Make sure brainstormed steps are clear and don’t overlap.

Organize in “Flow”–Creating the map is last. With all steps visible, it’s typically much easier to create a meaningful map without getting stuck on one or two minor issues.

Is the customer involved in your subprocess step? If so, how?

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14Verifying CTQ Elements For Process Mapping

Using Process Mapping in the Measure phase allows us to:Select an upstream step that is generating defectsDetermine where to collect the dataDefine the output measure (a good place to begin looking is a “No Exit” out of Decision Diamonds)

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Subprocess Mapping–Breakout Activity (20 minutes) 15

Desired Outcome: Practice creating a subprocess map

19 mins.AllPrepare the subprocess map for your own project

Brainstorm the challenges of subprocess mapping on your own projects

PrepareSubprocessMap

30 secs.AllChoose a subprocess to reportyour results

Close Exercise

30 secs.AllChoose a facilitator, timekeeper, scribe and/or notetaker

TeamPreparation

TimingWhoHowWhat

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16Cause & Effect Diagrams–CTQ Tool #2

A visual tool used by an improvement team to brainstorm and logically organize possible causes for a specific problem or effect.

ProblemProblemStatementStatement

Machines Methods Materials

Measurement Mother Nature People

Potential High-Level Causes

Procedure:

1. Draw a blank diagram on a flip chart.

2. Define your problem statement.

3. Label branches with categories appropriate to your problem. The categories shown are often used, but any categories can be used.

4. Brainstorm possible causes and attach them to appropriate branch.

5. For each cause ask, “Why does this happen?”

6. Analyze results; do any causes repeat?

7. As a team, determine the three to five most likely causes.

8. Determine which likely causes you will need to verify with data.

Alternative procedure:

Brainstorm causes independent of categories.

Use the Affinity Diagram and brainstorm items into categories.

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17Cause & Effect Diagrams–Example

timely?deliveries notWhy are the

Capital TruckCapital Driver

or3rd Party Carrier

orCapital Truck

Lease DriverNew employees

Freightliner Trucks

Mack Trucks

Volvo Trucks

48' trailers

52' trailers

Drop off & Hook up

Unload Delivery

Overnight Delivery

Distance

Weight of freight

Dock Clock

Watches

Computer Tracking

Precipitation

Temperature

People

MachinesMethods

Measurements

Environment

Cause & Effect for Capital LogisticsExample Of A CTQ

The C&E answers the question of “What am I going to measure?” I can now focus on weight of freight or distance or temperature, etc. (This is the output characteristic.)

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18FMEA–CTQ Tool #3

An FMEA is a structured approach to:Identifying the ways in which a process can fail to meet critical customer requirements Estimating the risk of specific causes with regard to these failuresEvaluating the current control plan for preventing these failures from occurringPrioritizing the actions that should be taken to improve the process

Identify Ways The Product Or Process Can Fail, Then Plan To Prevent Those Failures

Identify Ways The Product Or Process Can Fail, Then Plan To Prevent Those Failures

Purpose & Benefits of FMEAImproves the quality, reliability, and safety of productsHelps to increase customer satisfactionReduces product development timing and costDocuments and tracks actions taken to reduce risk.

Types of FMEASystem FMEA: is used to analyze systems and subsystems in the early concept and design stages. Focuses potential failure modes associated with the functions of a system caused by design.Design FMEA: is used to analyze products before they are released to productionProcess FMEA: is used to analyze manufacturing, assembly and transactional processes

FMEA’s will be covered in detail during the Improve phase of the CD Rom. This section is a brief introduction.

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19Potential Failure Modes and Effects AnalysisWorksheet

Process/Product:FMEA Team:

Black Belt:

FMEA Date: (Original)(Revised)

Page: of

FMEA Process Action Results

Item/ProcessStep

PotentialFailure Mode

PotentialEffect(s) Of

Failure Seve

rity Potential

Cause(s) OfFailure O

ccur

renc

e

Det

ectio

n

RPN Recommended

Action

ResponsibilityAnd TargetCompletion

Date

Total Risk Priority Number Resulting Risk Priority Number

ActionTaken

Seve

rity

Occ

urre

nce

Det

ectio

n

RPNCurrent

Controls

InvoicingInvoice Process Mgnt. TeamE. Jones

10/15/965/25/97

1 1

EnterAmtOwed

Inaccurate

Missing

Delayed

Overbill

Underbill

No Payment

Delay

Late Bill

No Bill

8

5

6

3

3

6

Wrong CtWrong Price

Wrong CtWrong Price

Sale ErrorDe ErrorDe ErrorSale ErrorDe ErrorDe ErrorSale “Too Busy”System Down

Sales BusySystem Down

Rare“

Rare“

Reviewed“

Reviewed“

Measured

“

Measured“

85

85

57

57

7

3

73

99

99

33

33

4

4

44

576360

360225

90126

4563

84

36

16872

DMAIC Teamto InvestigateRoot Causes of Count & Price Accessories

E. Jones5/15/97

All DMAIC Tasks Complete

8 4 2 648 3 2 48

5 1 2 105 1 3 15

6 5 3 906 7 3 126

3 5 3 453 7 3 63

3 7 4 84

3 3 4 36

6 7 4 1686 3 4 72

8212,205

In this example,the “Wrong Ct” component of billing accuracy becomes the highest priority defect type.

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20Failure Mode And Effects Analysis

FunctionPart/Process

Failure Mode

Effects

Causes

ControlsSeverity(1-10)

Occurrence(1-10)

Detectability(1-10)

RPNRisk Priority Number

RPN = S x O x D = 1 to 1000

RPNRisk Priority Number

RPN = S x O x D = 1 to 1000

How it Works

Review the product, service, or processDetermine failure modesList one or more potential effects for each failure mode. Answer the question: “If the failure occurs, what are the consequences?”Identify potential causesList current controls

Assign Severity, Occurrence, and Detection FactorsCalculate RPN.Prioritize RPNs from high to low.Identify the top issues, those with high RPN’s.Determine preventive or remedial actions, especially for high-priority issues.Recalculate RPN after actions have been implemented

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21FMEA: Calculating Risk Priority Number (RPN)

RPN = Severity x Occurrence x Detection

Good

BadInjure a customer or employeeBe illegalRender product or service unfit for useCause extreme customer dissatisfactionResult in partial malfunctionCause a loss of performance which is likely to result in a complaintCause minor performance lossCause a minor nuisance, but be overcome with no performance lossBe unnoticed and have only minor effect on performanceBe unnoticed and not affect the performance

Occurrence Scale

More than once per dayOnce every 3-4 daysOnce per weekOnce per monthOnce every 3 monthsOnce every 6 monthsOnce per yearOnce every 1-3 yearsOnce every 3-6 yearsOnce every 6-100 years

10987654321

Rating Time Period> 30%≤ 30%≤ 5%≤ 1%

≤ .03%≤ 1 Per 10,000

≤ 6 Per 100,000≤ 6 Per Million

≤ 3 Per 10 Million≤ 2 Per Billion

Probability

Severity Scale

10

Rating Criteria – A Failure Could:

9

65

43

2

87

1

Detection Scale

Defect caused by failure is not detectableOccasional units are checked for defectUnits are systematically sampled and inspectedAll units are manually inspectedUnits are manually inspected with mistake-proofing modificationsProcess is monitored (SPC) and manually inspectedSPC is used with an immediate reaction to out-of-control conditionsSPC as above with 100% inspection surrounding out -of-control conditionsAll units are automatically inspectedDefect is obvious and can be kept from affecting the customer

Rating Definition109

54

3

2

7

1

6

8

Total RPN is determined by multiplying all of the individual scores.

Note: Occurrence, detection and severity are independent estimates of risk.

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22Using A FMEA In The Measure Phase

Helps to prioritize Project Y’sHelps to identify where and how a process may fail to meet a CTQ (defects)

In this process, you may uncover an issue where you need to contain a problem (e.g., regulatory, non compliance, legal). If this occurs, it raises the priority.

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23Pareto Charts–CTQ Tool #4

Is there a defect that occurs frequently?

Segment data to look for a significant factor that influences the process

Frequency

C A E D BCategory of Defect

The Pareto chart is a bar chart with the bars (segmentation levels) arranged in descending order. It is an essential tool to help prioritize improvement targets by identifying the 20% of the problems that cause 80% of the poor performance (Pareto principle).

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24Pareto Charts (continued)

Freq

uenc

y

Cum

ulat

ive

Perc

enta

ge

100

90

80

70

60

50

40

30

20

10

Number Of Units Investigated: 5,000

April 1 – June 30

D10550.550.5

B4019.269.7

F209.679,3

A104.884.1

C52.486.5

E31.588.0

Other*2512.0100.0

0

20

40

60

80

100

120

140

160

180

200

Cumulative Summation Line(Cum Sum line)

*f = frequency

Approximately 80% of Defects from Defects D + B + F

f* of D

f* of D+B

f* of D+B+F

A: IllegibleB: Bank Info IncompleteC: Missing SignatureD: Personal Information

IncompleteE: Employment History

IncompleteF: Address Incomplete

LEGEND

Example

Total208100

Defect Type# Defects% DefectsCum %

A fully documented Pareto chart will include the “Cumulative Summation line”, or Cum Sum line, which depicts the running total of the frequency of each subsequent bar (segmentation factor). The right-hand axis on the graph will show the cumulative percent of defects. By reading the Cum Sum line against the cumulative percentage, your team can determine which of the segmentation levels comprise 80% of the total for the problem, and direct their attention to those levels.

In this example, I would likely focus on the ‘D” segment, and this would become my project Y.

You should also create a Pareto showing $’s. This may cause your focus to change.

* Other- Try to keep this category as small as possible. Find out what is in “other”.

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25Using Pareto Charts In The Measure Phase

Quantitative tool use to determine segmented areas of focusGraphically displays most frequent occurrence of outcomes (little y’s)Helps you get from Big Y to little y

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26QFD–CTQ Tool #5

Definition of QFD (Quality Function Deployment)

Structured Methodology to Identifyand Translate Customer Needs

and Wants Into MeasurableFeatures and Characteristics of a Product or Service

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27QFD Flowdown–Product Application

Functional Requirements Part Characteristics

GEProcessesHouse

ofQuality

#1House

ofQuality

#2 Houseof

Quality#3

Houseof

Quality#4

Key PartCharacteristics

KeyManufacturing

ProcessesKey

Process Variables

(HOW’s)ProcessVariables

Y

X

Func

tiona

lR

equi

rem

ents

(WH

AT’s

)

Cus

tom

erR

equi

rem

ents

(WH

AT’s

)

Part

C

hara

cter

istic

s(W

HAT

’s)

GE

Proc

esse

s(W

HAT

’s)

Y

Key Functional Requirements

(HOW’s)(HOW’s)

(HOW’s)

Product application of QFD links functional requirements to key process variables.

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28QFD Flowdown–Services Application

ServiceFunctions/Processes

(HOW’s)

Houseof

Quality#1 House

ofQuality

#2 Houseof

Quality#3

Service Requirements

(HOW’s)

Process Controls(HOW’s)

Serv

ice

Req

uire

men

ts(W

HA

T’s)

Cus

tom

er W

ants

(WH

AT’

s)

Serv

ice

Func

tions

/Pro

cese

s(W

HA

T’s)

Critical-to-QualityCharacteristics

(CTQ’s) KeyService

Processes KeyProcess Variables

Y

X

Services application of QFD links project deliverables to key process tasks.

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29House Of Quality Summary

4. RelationshipsH Strong 9M Medium 3L Weak 1

4. RelationshipsH Strong 9M Medium 3L Weak 1

H

H

H

H

L

M

M

M

MM

M L

L L

L

L

Importance RatingsImportance Ratings

6. Target values of HOW's (units)6. Target values of HOW's (units)

1a. CustomerNeeds

WHAT'SWhat does the

customer want?

Voice of the Customer

1a. CustomerNeeds

WHAT'SWhat does the

customer want?

Voice of the Customer

3.Characteristics/measuresHOW'S

How do you satisfy the wants ?

3.Characteristics/measuresHOW'S

How do you satisfy the wants ?

1b. Customer Importance

How important are the customer

wants to the customer?

1b. Customer Importance

How important are the customer

wants to the customer?

Roof Correlation

ConflictResolution

Roof Correlation

ConflictResolution

Cur

rent

Rat

ing

Com

petit

or #

1

Com

petit

or #

2

2. Competitive Assessment

Where are we and competitors relative to customer importance?

2. Competitive Assessment

Where are we and competitors relative to customer importance?

5. Competitive Benchmarks

How do competitors perform relative to each

HOW?

5. Competitive Benchmarks

How do competitors perform relative to each

HOW?

Target DirectionTarget

Direction

It is not necessary to develop every room for every house of quality you build.Room 1aCustomer Needs (in their language)High-level wants identified by the customerRoom 1bCustomer ImportanceCustomer ranking of the wants. A typical score is 1-5.1–least important5–most importantRoom 2Competitive ComponentsCustomer’s view of how GE compares with the competitionRoom 3Characteristics/MeasuresMeasurable attributes that can be used to indicate how well the customer’s needs are met.Room 4RelationshipsStrengths of interrelation between the WHAT’S and theHOW’s. H–Strong (9)

M–Medium (3)L–Weak (1)

To what extent will a HOW impact a WHAT? Using a 9, 3, and 1 scale forces a wider spread between the most important and least important items.Room 5Competitive BenchmarksHow the competition performs relative to the measures/characteristics.Room 6Target and SpecificationsTarget values for the HOW’S. Setting measurable targets allows the team to define what is required to achieve customer satisfaction.RoofRelationshipImpact of the HOW’S on each other.++ Strong positive+ Positive- Negative-- Strong Negative

Importance Ratings (IR)IR = Σ (Customer Importance X Strength Of Relationship)

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House Of Quality Example–Lunch Selection 30

Lunch QFD

O = HOLD CONSTANT

Prod

uct R

equi

rem

ent

Customer NeedsIm

porta

nce

Wei

ght o

f por

tion

Perc

ent n

utrit

ion

prov

ided

Perc

ent c

arbo

hydr

ate

prov

ided

Tim

e to

pre

pare

Num

ber o

f dis

hes

used

Cos

t of i

ngre

dien

ts

Num

ber o

f mea

sure

d in

gred

ient

s

PB&J

San

dwic

h

Inst

ant S

oup

Fast

Foo

d

Direction for improvementFills us up 5 H M M 2 3 4Is nutritious 4 M H L L 3 3 2Tastes good 3 H L 2 3 4Is easy to make 4 H H 2 1 4Is easy to clean up 2 M H 2 3 5Sticks with us 4 H M 2 2 4Is inexpensive 1 L L L M 4 3 1Is clean 2 M M H 2 3 4

Importance Rating 94* 52 59 48 60 10 18Target (Obtained from VOC) 16 33 25 3 1 0.50 0PB&J 2 33 25 3 1 0.25 0Instant Soup 8 15 10 5 3 0.50 1

Fast Food 16 40 73 10 0 3.00 0

Units Of Measure (Obtained from VOC) oz % % min $

KeyH=9

M=3

L=1*Importance Rating For “Weight Of Portion” = 5(9) + 4(3) + 4(9) + 1(1) = 94

Roof Relationship Symbols indicate if the quality goals of the CTQ’s are conflicting. For example, if I chose to focus on“Weight of Portion” I need to be concerned about the negative impact on the “Number of Measured Ingredients”

RelationshipHigh PositivePositiveHigh NegativeNegative

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31Analyzing A House Of Quality

Empty rows in Room 3 -Unaddressed customer want would be a major

problem

Empty rows in Room 3 -Unaddressed customer want would be a major

problem

H

H

L

M

M

M

MM

L

L L

L

L

Low competitive benchmarks - Poor long-term market performanceLow competitive benchmarks - Poor long-term market performance

Low score on competitive comparison, but high score on competitive benchmarks -Market technical advantages to improve

customer perception

Low score on competitive comparison, but high score on competitive benchmarks -Market technical advantages to improve

customer perception

Empty columns in Room 3 - Perhaps an

unnecessary measure

characteristic signaling it does not

affect customer wants

Empty columns in Room 3 - Perhaps an

unnecessary measure

characteristic signaling it does not

affect customer wants

Strong negative relationship in roof –Identify trade-offs

Strong negative relationship in roof –Identify trade-offs

Cur

rent

Rat

ing

Com

petit

or #

1

Com

petit

or #

2

Highest score on competitive

comparison - Able to lead the market with

existing product/service

Highest score on competitive

comparison - Able to lead the market with

existing product/service

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D M A I CMeasure 1–Select CTQ Characteristics

CTQ And Performance Standard Worksheet 32

ALunch Portion

ALunch Portion

Define AOutput UnitOutput Unit





SpecificationLimits*


Target*Target*

Defect *Defect *


Per Unit


Per Unit 11

Measure 2

< 14 oz. Or > 18 oz.< 14 oz. Or > 18 oz.

Measure 2

16 oz.16 oz.

Measure 2

LSL=14 oz.USL=18 oz.

LSL=14 oz.USL=18 oz.

Measure 2

WeightWeight

Measure 1

Total WeightIn Ounces Per Serving

Total WeightIn Ounces Per Serving

Measure 1

Healthy LunchHealthy Lunch

Define A

CTQCTQPreparedLunchPreparedLunch

High-Level Need (VOC)

You may not know Spec, Target or Defect at this time (in Step 1). If you know it now, write it down. This information will come from the VOC.

Here’s our next step:

Project Y Measure

Project Y Measure

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D M A I CMethodology Step: Measure 1–Select CTQ Characteristics









Target*Target*

Defect *Defect *


Per Unit


Per Unit

ALunch Portion

ALunch Portion

Define A

11

Measure 2

< 20%< 20%

Measure 2

25%25%

Measure 2

> 20%> 20%

Measure 2

% Carbohydrate Content% Carbohydrate Content

Measure 1

% CarbohydratePer Serving Per USDA

% CarbohydratePer Serving Per USDA

Measure 1

HealthyLunch

HealthyLunch

Define A

CTQCTQPreparedLunchPreparedLunch



Project Y Measure

Project Y Measure

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34Another Example

What are your needs for this class?

15375359Importance Rating

39112

Apply This Material To Project

11934

Pass The Exam

13395

Learn The Material

Customer Needs

KeyHigh = 9Medium = 3Low = 1

Impo

rtanc

e

Know

ledg

e As

sess

men

t Sc

ore

Exam

Pas

s R

ate

# To

ols

Use

d In

Pro

ject

# C

ompl

eted

Pr

ojec

t Per

Q

uarte

r

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35Points To Remember

The process may look simple, but requires effortMany entries look obvious–after they’re written downIf there are NO “tough spots” the first time– It probably isn’t being done right!

Focus on the end-user customerCharts are not the objective. Charts are the means for achieving the objective.QFD is a perishable document. It has a shelf life and must be updated.QFD is a valuable decision support tool, not a decision-maker

QFD is a valuable decision support tool (assigning numbers to H-M-L does not make the numbers and cut-off’s absolute decision points).

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Target*Target*

Defect *Defect *


Per Unit


Per Unit

KnowledgeAssessment

KnowledgeAssessment

Define A

11

Measure 2

< 80%< 80%

Measure 2

85%85%

Measure 2

≥ 80%≥ 80%

Measure 2

Knowledge Assessment Score(Percentage Correct)

Knowledge Assessment Score(Percentage Correct)

Measure 1

% Correct = Total Correct Questions Divided By 100

% Correct = Total Correct Questions Divided By 100

Measure 1

GB KnowledgeLevel

GB KnowledgeLevel

Define A

CTQCTQLearn Six SigmaLearn Six Sigma



Project Y Measure

Project Y Measure

Methodology Step: Measure 1–Select CTQ Characteristics

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37Common QFD Pitfalls

QFD on everything– Set the “right” granularity– Don’t apply to every last project

Lack of teamwork– Wrong participants– Lack of team skills– Lack of support or commitment

Too much “chart focus”“Hurry up and get done”Failure to integrate and implement QFD

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38QFD Activity

Background:Capital Logistics has established a customer help desk to handlecustomer inquiries regarding deliverables. However, customers are dissatisfied with the help desk.

A team consisting of Capital Logistics customer service representatives and Capital Logistics customers has been assembled. The team’s objective is to use QFD to identify the sub-processes that will be the focus of DMAIC improvement projects.

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QFD–Breakout Activity (20 minutes) 39

Desired Outcome: Practice constructing a House Of Quality

10 mins.AllReview the partially completed House Of Quality on the next page

Complete the relationship room of the house

CompleteRelationships

5 mins.AllCalculate the “How” importanceratings

Which “How” is most important to satisfy the customer?

Calculate “How” Importance Ratings

5 mins.AllChoose a facilitator, scribe and timekeeper

Preparation

TimingWhoHowWhat

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40QFD Activity

Quick problem resolution

Available when needed

100

Units

Importance rating

Target

% Hrs.

<3

Hrs.days

24x7

%

100

Courteous Service

Service Characteristics

% p

robl

ems

res o

lved

on

first

ca l

l

Cyc

le ti

me

t o

res o

lve

prob

lem

s

Num

b er o

f ho u

rs i n

th

e da

y he

lpde

s k i s

a v

a ila

ble

% c

usto

mer

s ra

t ing

Cus

tom

er S

ervi

c e

Rep

( CS R

) ex c

e lle

n t

o r g

ood

o n c

u sto

me r

s u

r ve y

of (

CS R

) . c o

u rte

o us n

e ss

Cus

tom

e r W

a nts

Imp o

r tanc

e

5

4

3

WH

ATS

HOWS

To what extent will the “How’s” impact the “What”?

Use L=1M=3H=9

Add one more service characteristic (CTQ) and place rating on the CTQ.

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41CTQ Tools: Summary

There are a variety of tools available to identify the CTQ characteristic for your project (Project Y)Select the tool that is most appropriate for your project

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2.1 Develop operational definition for process to be measured2.2 Identify target performance2.3 Set specification limit(s)2.4 Define unit, defect and defect opportunity




What does it mean to Define Performance Standards?A performance standard defines the process to be measured, how it will be measured, and how much variance will be tolerated. In step 1 of Measure, you determined the specific subprocess that is now the subject of your Green Belt project. In step 2, you’ll create a standard for the performance of that process. This is the point when you determine the best way to turn what the customer wants into a numeric measurement. This measurement will later be compared to the measurement of your current process in order to see how well you’re meeting the customer’s need.

Why is it important to Define Performance Standards?The performance standard translates the customer need into a clearly defined measure for which performance data can be collected. Once you know what constitutes acceptable and unacceptable performance for your process, you can define a defect. What you define as a defect becomes the basis for determining performance capability and improvement goals for the project.

What are the project tasks for completing Measure 2?2.1 Develop operational definition for process to be measured2.2 Identify target performance2.3 Set specification limit(s)2.4 Define unit, defect and defect opportunity

Measure 2–Define Performance Standards 1

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2Operational Definitions

Purpose

Definition An operational definition is a clear, concise description of a measurement and the process by which it is to be collected

To remove ambiguityEveryone has a consistent understanding

To provide a clear way to measure the characteristic

Identifies what to measure

Identifies how to measure it

Makes sure that no matter who does the measuring, the results are consistent

Defining The Measure

Always Pilot Your Operational DefinitionsAlways Pilot Your Operational Definitions

Operational definitions guide what properties will be measured and how they will be measured.

There is no single right way to write an operational definition. There is only what people agree to for a specific purpose. The critical factor is that any two people using the operational definition will be measuring the same thing.

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3Operational Definitions For Output Measures

FeaturesWhat: Must have specific and concrete criteriaHow: Must have a method to measure criteriaMust be useful to both you and the customer(the “wing-to-wing” concept)

Example: Loan Application Cycle TimeWhat: Loan application cycle time is the number of hours from

receipt of a loan application, to successful notification of decision for the loan application

How: The clock starts when the computer attaches the time of application receipt at data entry

The clock stops when the phone caller notes time of completed application decision notification in desk log

Example:

If a team were measuring “length of lines” at a bank, they would need to know whom to include in a count of people in line–do children count, or a spouse or friends waiting with someone?

Must Be Useful To Both You And The Customer

The operational definition makes it possible to make process improvements that are important to the customer and measurable for you. The definition should relate to issues that are important to both you and your customer.

Example:

Are customers really concerned with the length of a line, or just the length of time they must spend in line? It is important to include the customer’s perspective when developing operational definitions.

Must Have Specific And Concrete CriteriaEveryone has the same understanding of the definition. Different people can use the definition and know that their data will be measured in the same way.

Example:If a team were studying long wait lines at a bank, they would agree on what to measure (e.g., length of the lines, how long people wait) and agree on a way to measure it.

Must Have A Method To Measure CriteriaThe definition tells you how to get a value (either a number or yes/no). The definition clearly states how to get a measurement.

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4Why Start Our Measurement Work With The Project Y Metric?

The Project Y is the key metric for the project and is defined from the customer’s perspective

A customer-focused Project Y measure allows us to assess the process from the customer’s perspective

Changes in the values of a good Project Y measure will predict changes in the degree to which the process meets the customer CTQ’s

A Project Y measure expresses the “voice of the process”–changes in input or process conditions drive changes in true output measures

Project Y data is the first key to understanding process performance and the starting point for understanding how to control process output.

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5Define Performance Standards

Customer waits on hold too long

Customer Need

Timely Call Pick-up (Output characteristic) Established in Define, Step A

Established in Measure, Step 1



CTQ


A CTQ appliesTo each individualoutput unit

Hold Time (Project Y Measure)

10 seconds or less(Target)

Not greater than 20 seconds (specification/ tolerance limit)

Any response taking More than 20 seconds (Defect)

CTQ Elements (Performance Standards)–5 Major Elements ONLY

CTQ’s Are The Bridge Between Our Process Output And Customer Satisfaction

CTQ’s Are The Bridge Between Our Process Output And Customer Satisfaction

In Measure, Step 2, we are completing our CTQ Element Tree. Use the template on the next page or the one in your GB Workbook.

Definitions:Characteristic: a word or phrase that describe some aspect of the product or service.

Project Y: a definition of how the product/service’s characteristic is to be quantified. The key metric for the project.

Target: where we “aim” our product/service. If there were no variation in the product/service, this is the value we would always achieve.

Specification: the variation around the target the customer will accept.

Defect: failure to meet specification. Anything that results in customer dissatisfaction.

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CTQCTQCTQCustomer waitson Hold too Long

Customer waitson Hold too Long






SpecificationLimits

SpecificationLimits

TargetTarget

Defect Defect


Per Unit


Per UnitFMEA 1Process Map

FMEA 1Process Map

Measure 2

FMEA > 20 SecondsC&E

FMEA > 20 SecondsC&E

Measure 2

QFDPareto 10 SecondsVOC

QFDPareto 10 SecondsVOC

Measure 2

VOC USL=20 SecondsQFD

VOC USL=20 SecondsQFD

Measure 2

QFDProcess Map HOLD TIME C&EPareto

QFDProcess Map HOLD TIME C&EPareto

Measure 1

Process MapQFD C&E Time From CallC-O-P-I-S Placement to Pareto Customer Service

Pick-Up In Secs.

Process MapQFD C&E Time From CallC-O-P-I-S Placement to Pareto Customer Service

Pick-Up In Secs.

Measure 1

C-O-P-I-SA Call

C-O-P-I-SA Call

Define A

Timely Call Pick-upC-O-P-I-S

Timely Call Pick-upC-O-P-I-S

Define A

Project Y Measure

Project Y Measure

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7Establishing A Performance Standard

A performance standard translates customer needs into quantified requirements for our product or process Output

CharacteristicOutput

Characteristic

Project YProject Y

Specification/tolerance

limit(s) (USL/USL)

Specification/Specification/tolerancetolerance

limit(s) (USL/USL)limit(s) (USL/USL)

TargetTargetTarget 5 Minutes or less

Not Greater Than 60

Minutes (USL)

Timely Resolutionof a Call

Total time to resolve inquiry minus initiation

time of inquiry

CTQCTQCTQQuick AnswerQuick Quick AnswerAnswer

Specific Needs Statement

DefectDefectDefect Any Response Taking More Than

60 Minutes

Output Characteristic: A word or phrase that describes some aspect of the product or service. Comes from the Product/Process Drill-down tree.Project Y: A definition of how the product/process’s characteristic is to be quantified. State as a formula if possible (Operational Definition) and state the metric (Project Y Measure)Target Value: Where we will “aim” our product/process. If there were no variations in the product/process, this is the value we would always achieve.Specification Limits: How much variation is the customer willing to “tolerate” in the delivery of our product or process?Defect: An output which is unacceptable to the customer. Anything that results in customer dissatisfaction.

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8Identify Project CTQ’sTranslating Needs into CTQ’s: Example 1–Pizza

Characteristic: temperature of pizzaProject Y metric: temperature (degrees F) of Pizza at customer door stepTarget: 160 degreesSpecification: LSL=140 degrees and USL=180 degreesDefect: any pizza temperature falling outside of the specifications

Translating Needs into CTQ’s: Example 2–Customer ServiceCharacteristic: CSA Knowledge levelProject Y: training test scoreTarget: 100 pointsSpecification: LSL= 90 pointsDefect: any score less than 90 points

Translating Needs into CTQ’s: Example 3–InformationCharacteristic: Time to find informationProject Y: maximum time to find any piece of dataTarget: 1 minuteSpecification: USL=1.5 minutesDefect: any time greater than 1.5 minutes

Need = Hot Pizza

Need = Hot Pizza

Need = Problem

Solved on First Call

Need = Problem

Solved on First Call

Need = I want to find all info without effort

Need = I want to find all info without effort

LSL=Lower Specification LimitUSL= Upper Specification Limit

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9Specify Target And Specification Limits For Project Y

Once the Project Y metric has been established, the target and specification limits can be established.



Project Y Project Y

Specification/tolerance

limit(s)

Specification/Specification/tolerancetolerance

limit(s)limit(s)

TargetTargetTarget Customer request date

Variance not greater than

one day

Timely response

Variance between customer request and

actual delivery

CTQCTQCTQCustomer

receives approval on customer request date

CustomerCustomerreceives approval receives approval

on customer on customer request daterequest date

Specific Needs Statement

DefectDefectDefect Any response greater than

1 day

Target/Nominal ValueOptimal value for YSpecification/Tolerance Limit(s)Window or range of acceptable output values for YAlso called “performance standards”Information about where to set target and specification limits comes from the customer. This information can be collected not only from VOC but also from:– Contractual agreements– Industry standards– Customer observations– Process data

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10Project Y

Six Sigma Performance Definitions

Unit: The item produced or processed relative to the Project Y as reviewed by the customer

Defect: Any Project Y measurement value that does not meet the Y performance standards

Defect Opportunity: Any Y measurement event which provides a chance of not meeting the performance standard

Defective: A unit with one or more defects

The definitions listed above are based on the Project Y and performance standards and will be used later in the Measure phase to calculate Process Sigma or capability.The “defective” terminology is used when there is more than one defect opportunity per unit. A single unit could have more than one defect-the total number of defects is important because it represents the overall magnitude of the problem. It only takes one defect per unit to represent a problem from a customer’s perspective so looking at the percent of units with at least one defect gives us a perspective of how the customer sees the overall process performance. Notice that if units contain a number of defects, it is possible to reduce the overall total number of defects without having much impact on the percent of defective units. We need to be aware of both the total number of defects and the percent of units containing defects.

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11Project Y Alignment

Business Big Y’s

Project Y

Process Y’s

ManagementManagementManagement

PROCESSPROCESSPROCESSYY

YY

Key output metrics that are aligned with strategic

goals/objectives of the business. Big Y’s provide a direct measure of business

performance.

Key output metrics that summarize process

performance

Key project metric defined from the customer’s

perspective

Any parameters that influence the Y

X1 X2 X3

Does Your Project Y Pass The Alignment Test?All quality projects should be aligned to a Big Y and CTQ for the business. This ensures that project activity is organized and targeted to impact specific CTQ’s that the customer will feel.Not all Y’s are useful measures of business performance or customer impact. Your Project Y should be correlated to a higher level Business Big Y or CTQ.You should be able to describe the link between your Project Y and the related Business Big Y or CTQ in specific terms.

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6σ Performance Standards Definitions–Breakout Activity (5 minutes) 12

Desired OutcomePractice defining units and defect for your CTQ

AllChoose a spokesperson to report your results

Close exercise

5 mins.FacilitatorFor your process output, agree on the unit and defect for your Project Y. Use the worksheet on page 17 of your GB Workbook.

Define units and defect

AllChoose a facilitatorTeam Preparation

TimingWhoHowWhat

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1Minitab and Graphical Analysis Module Objectives

Understand the structure of Minitab*Understand data entry and correct data structure for analysis inMinitab Review variationBe able to create and interpret basic graphs in Minitab

In this module, you will focus on learning how to use Minitab and how to perform basic graphical analysis of data. We are stepping away from the DMAIC Flow for a moment.

If you’ve been given some historical data, you can start to view the data graphically. We will use Minitab to help us view this data.

In order to be fully effective in the Analyze phase, we need to expose you to Minitab’s capabilities now. This will help you think about the best way to collect data in Measure Step 3.

*Note: For another tutorial, the student can go to:www.minitab.com

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2Minitab Windows

Graph WindowGraph Window

Menu BarMenu Bar

Session Window:• Analytical Output

Session Window:• Analytical Output

Data Window:• A Worksheet, not a

Spreadsheet

Data Window:• A Worksheet, not a

Spreadsheet

Data Window–Stores data to be used for analysis. Discussed in more detail on next page.

Session Window–Stores numeric output and character graphs that result from executing a statistics command.

Graph Window–Generated whenever you run a command that results in a graphical output.

Info Window–Stores synopsis of your data (not shown) window.

History Window–Stores all commands initiated (not shown) from either the menus or the session window (not shown).

You can move through the windows using Ctrl-Tab, the windows menu, or the following shortcuts.

Data Window Crtl+ASession Window Crtl+MInfo Window Crtl+IHistory Window Crtl+H

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Data window is a worksheet, not a spreadsheet.Variables are usually entered in columns, observations in rows.Each column has a title area which is 31-characters or less and this title must be unique.Everything in a column is considered to be the same variable.Column names are above the column, not in the first row.Minitab cells contain values only, not formulas, like Excel.To perform mathematical functions, use Calc > Calculator.The orientation of the data arrow determines whether the enter key will take you to the next row or the next column.

If the value you enter into the first row is something other than a number or date, Minitab assumes that the entire column will be text (T).

3Data Window

Minimizes the Window Closes the Window

Maximizesthe Window

Scroll Bars

Data Entry Arrow

Column NamesAre Entered Here

Data is EnteredHere

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Notes on “Saving”:

Save Project As–When you save a project, you save all the worksheet, session, info, history and graph windows that are currently open. Minitab will use the file extension of .mpj.

Save Current Worksheet As–When you save as a worksheet, you save only the worksheet portion (you will lose session window and graphs). Minitab will use the file extension of .mtw.

Notes on “Opening”:

If you use the icon, only projects will be shown. You must use the file > open worksheet to view all Minitab worksheets.

*Six Sigma add-on in Minitab can be obtained via a link in support central.

4Minitab Menus–Summary

File Menu

Edit Menu

Manip. Menu

Calc Menu

Stat Menu

Graph Menu

Print and save the window that is currently activeFile menu changes depending on the window that is currently activeAllows open, close, and save

Similar to the edit menu in most standard Windows applications

Sort, code or manipulate data

Calculate or generate data

Basic statistics and quality toolsMost often used by Green Belts

Contains the commands that you will use to do graphical analysis during your project

Help Menu Minitab has a comprehensive Help system with detailed documentation of all features, complete with examples of how all the menu commands are used, and how to interpret graphical and statistical output which result from the use of the commands

Window Menu Allows you to manage multiple graphs on the screen

Six Sigma*Menu

Product & process report can be used for determining performance levels (Calculating Sigma)

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Command Parameters–Minitab sometimes calls these parameters:

X YFactor ResponseIndependent Dependent

Input variable

By variable variablesgraph variables

5Using Minitab: A Typical Session

1. Enter data2. Select menu command (for desired statistical/graphical

function)3. Enter command parameters in the dialog window4. View results in session window or graph window5. Copy output to another application6. Print output7. Save file

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Step 1: Minitab allows you to enter data in four different ways:

1. Open an existing Minitab worksheet2. Type data into the worksheet3. Import data files from other compatible software packages (such

as Excel)4. Paste data from other applications

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One way to enter data in Minitab is to type the data directly into the worksheet. For your Green Belt project, you will probably import or copy the data from Excel.


Enter Data Manually

Type data directly into worksheet

Only one row forheading

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14

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Importing Data From Excel

1.3 How to import an Excel data file:1. File > Open Worksheet2. Select Files of Type: Excel3. Highlight the file to be imported4. Double-click or click Open

Importing Data:

To determine whether a file can be opened by Minitab, choose Open Worksheet from the File menu. Notice that the area labeled Files of Type contains a drop-down menu. This is indicated by the arrow (triangle) at the right of the Files of Type selection box.

When you choose a file type from the drop-down list, only those files containing the chosen file extension are displayed in the file list. When you are importing files, it is important to choose the specific file type you are importing.

When importing from Excel, an Excel file can contain only one worksheet and the information contained in Row 1 will become the titles in Minitab.

Note: During import, Minitab will convert percentages, dollars, etc.

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Note: In order for this to work, youmust make all data non-format specificin Excel before you cut-paste.


Paste data from Excel1.In Excel:

Highlight Data (and Column Names) to be copiedUsing Your Mouse

2.Copy the Data to the Windows ClipboardEdit > Copy (or CTRL-C on Your Keyboard)

3.Go to Minitab:ALT > Tab

4. Position the Cursor where you want the data to fillSee example below.

5. Go to the Edit Menu:Edit > Paste/Insert Cells (or Ctrl-V on the keyboard)

Insertion point

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If you want to use a file in both Minitab and Excel, keep these points in mind.


Tips for moving data back and forth:

Structure the data so that each variable is in a single columnEach column must have a titleThe column title must have fewer than 31 characters and be on a single lineAll data must immediately follow the column namesDo not put empty rows between rows of dataColumns containing dollar signs or commas cannot be transferred to Minitab using Copy or Paste, but can be imported using the import command. Reformat these numbers to include only decimal points. After movement into Minitab, check column heading type (D vs. T.)

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Tables vs. Variable ColumnsTypical Excel Format:

The best format for analysis of data in Minitab is variable columns.

Sales Office January February March AprilCentral 387,980 45,700 456,789 349,050Southwest 578,990 600,987 456,789 456,798Northeast 435,800 542,700 345,988 564,050Southeast 497,050 827,900 456,789 687,050Northwest 613,242 61,689 456,789 434,567

Sales Office Revenue MonthCentral 387,980 JanuaryCentral 45,700 FebruaryCentral 456,789 MarchCentral 349,050 AprilSouthwest 578,990 JanuarySouthwest 600,987 FebruarySouthwest 456,789 MarchSouthwest 456,798 AprilNortheast 435,800 JanuaryNortheast 542,700 FebruaryNortheast 345,988 MarchNortheast 564,050 AprilSoutheast 497,050 JanuarySoutheast 827,900 FebruarySoutheast 456,789 MarchSoutheast 687,050 AprilNorthwest 613,242 JanuaryNorthwest 61,689 FebruaryNorthwest 456,789 MarchNorthwest 434,567 April

Format Needed For Minitab:

The format of data typically used in Excel is table format. The best format for analysis of data in Minitab is variable columns.

There are multiple ways to manipulate data. The major point is that Minitab likes to have the data in columns.

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Above is a set of data that has been captured and entered into an Excel spreadsheet. To make the data suitable for use in Minitab:

1. Reformat the data in Excel (hide columns, change dollar format to numeric) before copying and pasting the data into Minitab. Arrange the data in 3 columns as seen on the previous page.

2. Import the data directly into Minitab using Options and Preview in the Open Worksheet dialog box to customize the data structure.

Minitab also has several menu options that allow you to reorganize and restructure the data once you have imported it into Minitab. These options are available in theManip and Calc menus. You may want to first manipulate in Excel prior to exporting the data!


Tips For Importing Data Into Minitab–Let’s practice

What is wrong with the format of this data in terms of its suitability for use in Minitab?

Sales 1999Sales Office January February March April

Central $387,980.00 $45,700.00 $456,789.00 $349,050.00

Southwest $578,990.00 $600,987.00 $456,789.00 $456,798.00

Northwest $435,800.00 $542,700.00 $345,988.00 $564,050.00

Southeast $497,050.00 $827,900.00 $456,789.00 $687,050.00

Northwest $613,242.00 $61,689.00 $456,789.00 $434,567.00

Total $2,513,062.00 $2,078,976.00 $2,173,144.00 $2,318,658.00

File name: sales_data.xls

Note: For additional practice, see the Green Belt Training Support Central Site.

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Most of the commands you use in your Green Belt project are in the Stat and Graph menus.


Step 2: Select menu command

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Step 3: Enter parameters in dialog box

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Step 4: View results in session or graph window

Note: Sometimes there is only a session window. Therefore, check both the session window & the graph (if one exists).

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Note: You can also copy graphs from the window > manage graphs.


Step 5: Copy output to another application

Copying graphs:1. Make sure the graph window is active in Minitab2. Click right mouse button and select “Copy Graph”3. Open the application into which you want to copy the graph or table,

e.g., Microsoft Word4. Paste graph using Paste from the toolbar or Ctrl-V

Copying session window output:1. Highlight the text lines you want to copy2. Use the right mouse button to copy the text3. Open the application into which you want to copy the text4. Paste the text using Paste from the toolbar or Ctrl-V

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Steps 6 and 7: Print and Save

When you save a project, you can save the worksheet or session window individually, or save an entire project.

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18Recruitment Cycle Time Case Study

We will use the following case study to practice basic graphical analysis in Minitab.You are working on a project to reduce cycle time for filling temporary positions in the Information Technology department within the company. Currently, you work with one agency who finds temporary contractors to fill positions on request by the IT department. The performance standard for cycle time to fill these positions is 20 (working) days maximum. This is measured from the time the agency receives the request to the time the position is filled.

You have completed the Define and Measure phases. In the Measure phase, you collected cycle time data for a sample of positions filled within the last 6 months.

The data is contained in file fill_time.mtw. The column labels are as follows:C1: yrs exp–years experience of the person who filled the positionC2: agent–specifies the agent who processed the request and found the resource C3: site–specifies the company site from which the request originated (there are three sites in

the area who request temporary resources)C4: type of resource–specifies the type of resource requested (DBA, Programmer,

Systems Analyst)C5: cycle time–time to fill position (working) days

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19Graphical Analysis Of Data

Key Questions:How is my data distributed (variation)?What relationships exist between the Y variable and X variables?

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A fundamental principle of process improvement is the measurement, reduction, and control of variation. Variation is present in all processes, whether they are personal processes (getting to work, fixing dinner) or business processes (approval cycle time, order to delivery). The output of a process will vary as it is repeatedly performed. Although our customers may accept some variation, when variation is too extreme, our customers will be dissatisfied.

20Review–Variation

All repetitive activities have variation (fluctuation)Variation is a primary source of customer dissatisfactionIn order for our customers to “feel the quality” at GE, we must reduce variation

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Variation is a fact of life. There will always be fluctuations in our processes.

Graphically displaying measures provides a basic description of the variation and its sources.

Following any data collection effort, the first step toward understanding variation is to plot the data.

21Using Data To Understand Variation

Plot The Data Using Variation Tools

Mea

sure

men

tTime

Freq

uenc

y

Measurement

Histogram Run Chart

Study Variation For A Period Of Time Study Variation Over Time

– Histogram

– Box Plot

– Bar Chart– Pie Chart– Histogram

– Run Chart– Control Chart

– Control Charts– Run Chart

For Continuous Data For Discrete Data For Continuous Data For Discrete Data

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Continuous data holds several advantages over discrete data:– It gives us more information about our process.– Smaller sample sizes are required when we use

continuous data.

If you were the customer:– Which type of data would you want?– Which type of data shows what you see?

Consider this: If you were the process owner which would you prefer?– Simply how many applications were processed

within the customer specification?

OR–The exact time it took to process each application?

22Review–Continuous vs. Discrete Data

Reminder: Data Type Is Critical!Data type dictates how much variation we will see:

Continuous data–the most information about variation in the processDiscrete data–less information about variation in the process

Application Cycle TimeUpper Specification Limit = 30 Days

DiscreteY = late/on-time

No. Rec’d No. Late

30 2

Less variation information

ContinuousY = days to process

USL

The most variation information

28 23 13 34 24 29 21 16 24 11 49 21 21 25 26 27 27 29 30 29 30 20 10 30 12 11 27 23 24 28 17 9 30 29 29 28

Actual Times

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Machines–The various appliances used in the transformation from inputs into outputs. For example, a PC can turn various sources of information into an organized manual that then relates to a training service.

Methods–The procedures, formal or otherwise, that transform inputs into outputs. For example, there is a standard procedure for billing collections in the GE Capital businesses.

Materials–The components, tangible or otherwise, that are transformed from inputs into outputs. For example, paper stock and ink quality will affect a product brochure’s quality.

Measurements–The tools that monitor a process’sperformance. For example, a doctor’s blood pressure reading of a patient would determine subsequent activity related to treatment.

Mother Nature–The environmental elements within a process that influence a customer need or requirement.

In a training session, failure to regulate the thermostat can result in a non-conducive learning environment.

People–The staffing that influences customer needs and requirements. While often dominant in the service industry, this is an area still too often blamed for failure to meet or exceed customer requirements.

Sometimes in a service environment, the following categories are used:— Policies–Higher level decision rules or

management practices.— Procedures–The way in which tasks are performed.— Plant–The building, equipment, work space, and

environmental factors that affect performance.— People–The human element.— Parts–Systems, documents, and other supplies that

are needed to perform the service.

235 M’s & 1 P

Sources Of Variation

Machines

Methods

Materials

Measurements

Mother Nature

People

PROCESS

PROCESS

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There are two types of variation:Common causesSpecial causes

Common causes are characteristics of the process and exist as a result of the presence and interaction of different process variables. Common causes affect everyone working in the process, and affect all of the outcomes. Common causes are always present and thus are predictable within bounds.

Special causes are those causes that occur due to occasional extraordinary circumstances. Special causes are not always present, do not affect everyone working in the process, do not affect all of the outcomes, and are not predictable.

The distinction between common and special causes is important to determine the basic strategy for process improvement and control.

24Two Types Of Variation

Common Versus Special Causes

To distinguish between common and special causes variation, use display tools that study variation over time such as Run Charts and Control Charts.

Common Cause

Special Cause

Type of Variation Characteristics

Always PresentExpected

PredictableNormal

Not Always PresentUnexpected

UnpredictableNot Normal

Characteristics

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25Describing Variation For A Period Of Time: Data Distributions

Key Questions:What is the shape of the distribution–symmetrical, skewed, twin peaks, flat? What is the central tendency (“center”) of the distribution?What is the variation (“spread”) of the distribution–wide or narrow?

When describing variation, we usually focus on two things:

– Center– Spread

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26Statistics

Statistics is concerned with making inferences about general populations and about characteristics of general populationsWe study outcomes of random experiments If a particular outcome is not known in advance, then we do not know the exact value assigned to the variable of that outcome:– The number of invoices received weekly– The cost in dollars of reworking each part– The number of surfaces that are rough on a cast part– The number of calls received every Monday between the hours of 8-9

a.m.We call such a value a random variable

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27Some Distributions

A random variable can be expressed in terms of a distribution

Uniform DistributionSingle roll of a die

All permissible values P(X) are equally likely

Triangular DistributionSums of a pair of dice

Rapidly descending P(X), no tails

P(X)

X

P(X)

X

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Processes may have many differently shaped population distributions. The shapes may be uniform, symmetric, skewed, “ramped,” “camel-backed,” exponential, normal, and non-normal. The shapes may be mixtures of normal and non-normal distributions–or unmixed. Stable distributions can have many different shapes.

Why does the process, or product, result in a particular shape (distribution) and not some other shape? The answers to these questions may provide a better understanding of the process and how to improve it. The particular shape is not as important as why this shape and why not some other shape? Why this distribution, why not some other distribution?

28Distributions

Normal DistributionProcess/repair times

Error fluctuations about an operating point

Exponential DistributionTime between arrivals

Time between random (unrelated) failures

Events with no memory from one to the next

P(X)

X

P(X)

X

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The shape of a data set can be determined by examining a histogram, or, if testing the distribution for normality, using a “Normal Probability Plot.” There are many different shapes a data set may assume. The plots above illustrate three common shapes. The top left is a normal distribution, the middle is a bimodal distribution, and the top right plot is a skewed distribution.

Because of its predictive qualities, the normal distribution is of special interest.

29Shape

Shape is the distribution pattern exhibited by the dataAssess shape using a histogram, or more precisely with a Normal Probability Plot

12 13 14 15 16 17 18 19

01234567

Freq

uenc

y

Roughly Normal Distribution

0 10 20 30 40 50 60 70 80 900

10

20Skewed Distribution

Freq

uenc

y

7 9 11 13 15 17 19 21 230

1

2

345

6

Freq

uenc

y

Bimodal DistributionSpread Spread

Center

Center Center

Center

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The normal curve is a probability distribution that forms the basis for many decisions we will make about our processes. The curve is noted by its “bell-shaped” nature, where most of the values fall in the middle and fewer values fall in either direction. The curve has several important characteristics:

Infinity–The curve theoretically does not reach zero. It goes out to infinity in either direction.Symmetry–Roughly half of the values will be above the average, and half below.Centering–The peak of the curve tells us where the process is centered.Process Totality–The area under the curve represents virtually 100% of whatever we are measuring.

30The Normal Curve

Is The Data Distribution Normal?

Definition:A probability distribution is where the most frequently occurring value is in the middle and other probabilities tail off symmetrically in both directions.

Characteristics:The curve does not reach zeroThe curve can be divided in half with equal pieces falling either side of the most frequently occurring valueThe peak of the curve represents the center of the processThe area under the curve represents 100% of the product the process is capable of producing

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The normal curve can be divided into a series of segments. Each segment is mathematically called a standard deviation from the mean. It is also noted by the small s.

As you can see, the curve is first segmented into one standard deviation which represents approximately 34% of whatever you are measuring.

Because the curve is symmetrical, going one standard deviation in the other direction represents approximately 68% of whatever it is you are measuring. Going out +/– 2 standard deviations is equal to approximately 95% of whatever you are measuring and +/– 3 standard deviations is equal to 99.73% of whatever you are measuring.

Most common statistical terms and analysis tools are based on a normal data distribution. If we use these tools with a data set that is not normal, the accuracy of the tools may be compromised.

31The Normal Curve (continued)

Specific Characteristics

68.26% Fall Within +\- 1 Standard Deviation95.46% Fall Within +\- 2 Standard Deviation99.73% Fall Within +\- 3 Standard Deviation

-3s -2s -1s X +1s +2s +3s68.26%

95.46%

99.73%

34.13% 34.13%

13.60% 13.60%2.14% 2.14%

0.13% 0.13%

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What Is A Normality Test?

A normality test is a statistical process used to determine if a sample, or any group of data, fits a standard normal distribution. A normality test can be done mathematically or graphically.

A normality test can be thought of as a “litmus test” for determining if a distribution is a normal distribution.

The Y axis is the cumulative % of data points which fall below the value on the X axis.

Why Is A Normality Test Useful?

Many statistical tests (tests of means and tests of variances) assume that the data being tested is normally distributed. A normality test is used to determine if that assumption is valid.

When Should I Use A Normality Test?

There are two occasions when you should use a normality test:— When you are first trying to characterize raw data,

normality testing is used in conjunction with graphical tools such as histograms and box plots.

— When you are analyzing your data, and you need to calculate basic statistics such as Z values or to employ statistical tests that assume normality, such as t-Test and ANOVA.

Interpreting A Normal Probability Plot

— When plotted data follows a straight line, the Anderson-Darling p-value will exceed 0.05 and will increase, I have normally distributed data.

— Rule: p > .05 indicates data is normal.

32Normal Probability Plot

Average: 16.3921StDev: 5.61675N: 240

Anderson-Darling Normality TestA-Squared: 0.208P-Value: 0.864

2 12 22 32

.001

.01

.05

.20

.50

.80

.95

.99

.999

Prob

abilit

y

Cycle Time

Normal Probability Plot

Use this method to determine if distribution is normal

If p>0.05, then data is normal

We use a normal Probability Plot to determine if our data is normal

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33Normal Probability Plot (continued)

Normal Skewed Long-TailedBimodal curve

12 13 14 15 16 17 18 19

0

1

2

3

4

5

6

7

Freq

uenc

y

Roughly Normal Distribution

Perc

ent

Normal Probability Plot for a Normal Distribution

ML Estimates

Mean:

StDev:

0 10 20 30 40 50 60 70 80 90

0

10

20

Skewed Distribution

Freq

uenc

yPe

rcen

t

Normal Probability Plot for a Skewed Distribution

ML Estimates

Mean:

StDev:

15.0790

12.6232

Perc

ent

Normal Probability Plot for Long-Tailed Distribution

0 10 20 30

1

5

10

20

3040506070

80

90

95

99

7 9 11 13 15 17 19 21 23

0

1

2

3

4

5

6

Freq

uenc

y

Bimodal Distribution

0 10 20 30

1

5

10

20

304050607080

90

95

99

Perc

ent

Normal Probability Plot for aBimodal Distribution

ML Estimates

Mean:

StDev:

14.6382

5.47084

7 9 11 13 15 17 19 21 23

0

1

2

3

4

5

6

Freq

uenc

y

Long-Tailed Distribution

Distribution Type:

Straight line Two lines(Stable Operations)

“S” curveZig-zag

How Distribution Looks On Normality Curve:

The Normal Probability Plot is another way besides the histogram to plot data and look for normality. Normal data, when plotted with the data value on the X-axis and specially spaced percentiles of the normal distribution on the Y-axis, will fall on a straight line. 95% confidence limits are shown around the line.

In the top diagram on the left, we see that all of the data points roughly form a straight line and fall within the limits. We would conclude that there is no serious departure from normality in this data. In the other diagrams, we see that many of the data points fall outside the limits and do not form a straight line. We would therefore conclude that these data sets significantly depart from the normal distribution.

What types of process might result in data that follows a bimodal, skewed, and long-tailed distribution?

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If your data is non-normal, you may be able to proceed. It is important that you consult with your MBB before proceeding.

34

If you conclude that Y is non-normally distributed, there are two general approaches:

Approach 1: Variance-based Thinking (VBT) Methodology– possibly multiple processes embedded– segmentation and stratification– span reduction

Approach 2: Non-parametric techniques (beyond the scope of this course)

What If Your Data Is Not Normal?

Expectation: Green Belts Should Be Able To Do Approach 1

Expectation: Green Belts Should Be Able To Do Approach 1

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35Minitab–Histogram

0 10 20 30

0

10

20

30

Cycle Time

Freq

uenc

y

Datafile:Question:

Tool:

Data Type:

Data Structure:

To Make A Histogram:

Fill_time.mtwWhat does the distribution of cycle time to fill positions look like?

Histogram

Continuous. The X axis is cycle time, the Y axis is the number of times cycle time fell within the range of each bar or interval in the histogram. The Y axis is calculated for you.A single column of data for each histogram

Graph > HistogramVariable: Cycle TimeClick OK

Recruitment Cycle Time Case Study

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Since p > 0.05, the data is normal.

There are a few ways to determine normality. We have standardized on this Anderson-Darling normality test. We will discuss p-values later in the Analyze phase.

36Minitab–Normal Probability Plot

Average: 16.3921StDev: 5.61675N: 240


2 12 22 32

.001

.01

.05

.20

.50

.80

.95

.99

.999

Prob

abilit

y

Cycle Time


Datafile: Fill_time.mtw

Question: Are the cycle time data normally distributed?

Tool: Normality Test

Data Type: Continuous Y

Data Structure: A single column of data

To Make A Normal Stat > Basic Probability Plot: Statistics > Normality Test

Variable: Cycle TimeTest For Normality: Choose Anderson-DarlingClick OK


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A good guess of central tendency can be made by visually examining a histogram.

A more precise estimate of central tendency can be made using descriptive statistics such as the mean, median, or quartile values. The distribution shape dictates which metrics should be used.

37“Center” Or Central Tendency

Descriptive Statistics:Represents the nominal value of the process.

Mean ( ) Median (“middle” data point)Quartile Values (Q1, Q3)

x

Q1 Q3

Normal Distribution

Long-tailed Distribution

Skewed Distributions

X

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The Mean, sometimes called the average, is the most likely or expected value. The formula for the mean is:

Order the numbers from smallest to largest If the number of values (N) is odd, the median is the middle value. For example, if the ordered values are 3, 4, 6, 9, 20, the median is 6.If the number of values (N) is even, the median is the average of the two middle values. For example, if the ordered values are 1,5,8,9,12,18, the median is 8.5.

For very skewed data, we can describe the central tendency in terms of the quartile values, Q1 or Q3.Q1 is the data point that divides the lowest 25% of the data set from the remaining 75% and is used to describe performance when the data is skewed toward the right.Q3 is the data point that divides the highest 25% of the data set from the remaining 75% and is used to describe performance when the data is skewed toward the left.

“Center” Or Central Tendency (continued) 38

1. The sum of all data values2. Divide by number of data values

nX

X i∑=

:is median the gcalculatin for procedure The .X~ is median the for

symbol usedcommonly most The median. the than less is data the of 50% and median, the than greater is data the of 50% whereset

data the of middle theliterally is The Median

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39Variation

Descriptive StatisticsRepresents the variation ofthe process

Standard Deviation (s)SpanStability Factor (SF) = Q1/Q3

Q1

s

Q1Q3 Q3

Normal Distribution

Long-tailed Distribution

Skewed Distributions

p=.01 p=.99

A question to be answered in describing variation is “What is the spread of the data?” That is, how much variation exists in the data? By examining a histogram, a good guess of variation can be made.

A precise measure of variation is accomplished using basic descriptive statistics such as standard deviation, span, or stability factor.

Standard Deviation–measures average distance from the mean. Smaller is better.

Span–measures unusually low & high distance from the median. Smaller is better.

Stability Factor–ratio of first quartile and third quartile, 1.0 is best.

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Variation (continued) 40

Skewed Or Stable Ops Distributions:The stability factor (SF) is the ratio of the first quartile and third quartile values. The formula for Stability Factor is:

SF = Q1/Q3As Q1 and Q3 get closer together, their ratio decreases and the variation of the middle 50% decreases.

Long-tailed Distributions:Span is used to indicate the amount of variation in a long-tailed distribution. It is the distance between the two extremes of the data set. For example, in customer delivery span, it is the number of days between the earliest and latest delivery. Because we don’t want span to be determined by only one or two data points, we typically use P95 and P5 (although this changes depending upon sample size). The span is the difference between P95 and P5.The guidelines of what span to use varies with the sample size:

0 More Variation Less Variation 1

Q1

Q3

Q1

Q3

Q1Q3

0More

Variation

Q1Q3

1Less

Variation

Sample Size Span P

100-500 90%-10% P90, P10

501-2000 95%-5% P95, P5

2001-5000 98%-2% P98, P2

5001+ 99%-1% P99, P1

Normal Distributions:The standard deviation is the average distance, or deviation, that a given point is away from the mean. The formula for the standard deviation is:

Xi-X

B- square each difference

A- subtract each data value from the mean

D- divide by 1 less than the number of data values

E- take the square root of the result

Xi X

C- sum the squared differences

1n)XX( 2

i

−−∑

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The difference between population and sample:population has all the data points, Nsample only has a portion of the total data points, n < N

The divisor for the population variance is the population size N, whereas the divisor for the sample variance is the sample size minus one (n-1). The divisor (n-1) is used rather than N because this leads to an unbiased estimate for the population variance.

41The Computational Equations

PopulationMean

PopulationVariance

PopulationStandardDeviation

SampleMean

SampleVariance

SampleStandardDeviation

N

Xµ

N

1ii∑

==

( )N

µXσ

N

1i

2i∑

=−

=

( )N

µXσ

N

1i

2i2

∑=

−=

µ = = =∑

XX

n

ii

n

1

( )σ = =

−

−=∑

sX X

n

ii

n2

1

1

( )σ 2 2

2

1

1= =

−

−=∑

sX X

n

ii

n

∧∧

∧∧

∧∧

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Deviation = Measures Of Variation

A key concept is that the variance is the average SST for a population and a near average for a sample = SST/(n-1) = SST/df.

As the degrees of freedom (df) increase (which is the same as larger sample size (n)), the near average and average SST become essentially the same.

Finally, the standard deviation is the square root of the variance.

42Deviation = Measures Of Variation

Results & Take-Aways:

Deviation = measure of Variation, measure of Spread

SST = 8726.1 … large Deviations = large SST

Variance = “Average” SST = SST/df [df = deg. of freedom = n-1]

s2 = Sample Variance = SST/9 = 969.62 = Population Variance = SST/10 = 872.6

Standard Deviation = Square Root of Variance:

Sample StDev = s =

Population SD = =

Random data (“1” to “99”, n = 10 samples):n Xi Xbar Dev =(Xi-Xbar) (Xi-Xbar)^2

1 20 35.7 -15.70 246.49

2 1 35.7 -34.70 1204.09

3 6 35.7 -29.70 882.09

4 35 35.7 -0.70 0.49

5 54 35.7 18.30 334.89

6 67 35.7 31.30 979.69

7 43 35.7 7.30 53.29

8 99 35.7 63.30 4006.89

9 5 35.7 -30.70 942.49

10 27 35.7 -8.70 75.69----- ------ ---------- --------------357 0.0 8726.10

31.1 = 969.6

29.5 = 872.6

σ

σ

It’s All Variation… Deviation, SST, Variance, And Standard Deviation = Measures Of Spread

It’s All Variation… Deviation, SST, Variance, And Standard Deviation = Measures Of Spread

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Summary–Measures Of Variation:

Note that for any given set of numbers (Xis), the value for SST is fixed, unchanging. The only way to change SST is to change one or more of the numbers–which means that the spread around the mean will likely be changed.

43Summary–Measures Of Variation

Range = (Max - Min)Deviation = (Xi - Xbar) [Xbar = mean or mu]Sum-of-Squares (of the squared Deviations) = SSTVariance = Average SST = SST/df (df = degrees of freedom) Std Deviation = SqrRoot (Variance) andCoeff. of Variation = CV = (StDev/Xbar)* 100 i.e., ratio of StDev to Mean–expressed as %

SST is key concept in measuring variation.

The greater SST, the greater the variation.

SST is always conserved: given a set of numbers (data), it is fixed and unchanging.

SST can be allocated to different COMPONENTS OF VARIATION–i.e., within and between group.

Components Of Variation: The Key For Process Centering And ANOVA

Components Of Variation: The Key For Process Centering And ANOVA

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44Variation For A Period Of TimeDescriptive Statistics Summary

Shape Normality Plot Center Spread(central tendency) (variation)

normal

skewed

long-tailed

Quartile Q1 or Q3

Standard Deviation (s)

Stability Factor (SF)

Span

bimodal

Normal Probability Plot for a Normal Distribution

Perc

ent

ML EstimatesMean:StDev:

15.72241.74183

Normal Probability Plot for an Exponential Distribution

Perc

ent


15.079012.6232

Normal Probability Plot for a Long-Tailed Distribution

Normal Probability Plot for a Bimodal Distribution

0 10 20 301

510203040506070809095

99

Perc

ent


14.63825.47084

0 10 20 301

510203040506070809095

99

Perc

ent


14.63825.47084

The different processes must be stratified before descriptive statistics

can be calculated.

Mean ( ) X

Median ( ) X~

Q1= 25th PercentileQ2 = Median,, 50th PercentileQ3 = 75th PercentileRange = Maximum Value–Minimum ValueSpan = 99th Percentile–1st PercentileSF = Q1/Q3IQR = Inner Quartile Range = Q3-Q1 (middle 50th of data)

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After data is collected, it should be displayed graphically and described using basic statistical measures. The first graphical display used for describing variation is the histogram.

Histograms combined with basic descriptive statistics provide a clear picture of the current performance of a process.

45Displaying Variation For A Period Of Time

Histogram

Illustrates

Central tendency (center) of the dataVariation (spread) of the data

Shape (pattern) of the data

Measurements

10 11 12 13 14 15 16 17 18 19

0

5

10

Time Estimates (in seconds)

# of

Occ

urre

nces

Histogram of Time EstimatesGraphical Display

TimeEstimatesRound 1

16.4818.8913.1811.1114.6716.5314.7918.0614.4814.8915.6313.9513.7417.6710.2313.6711.3515.03

13.8413.5015.4114.3514.3714.6313.5814.7511.9514.3616.1715.1512.4814.1219.0013.8112.9714.19

TimeEstimatesRound 2

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Box Plots are graphical summaries of the patterns of variation in sets of data.

The horizontal lines at the top and bottom of the plot represent the highest and lowest values. The horizontal line in the middle of the solid box represents the median, and the solid box represents the middle 50% of the data, with 25% of the data on the top side of the box and 25% of the data on the bottom side of the box.

Points noted with an asterisk(*) represent extreme values or outliers.

Outlier calculationsHigh: Q3 + 1.5 (Q3-Q1)Low: Q1 - 1.5 (Q3-Q1)

46Displaying Variation For A Period Of Time (continued)

Box Plots

Highest Value

Third Quartile (75%) value Q3

Lowest Value

First Quartile (25%) value Q1

Median Q2

*

Each segment represents 25% of the data points

Outlier

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Box Plots and histograms provide similar information but in different graphical formats.

47Summary–Variation For A Period Of Time

10 11 12 13 14 15 16 17 18 19

0

5

10

28 23 13 34 24 29 21 16 24 11 49 21 21 25 26 27 27 29 30 29 30 20 10 30 12 11 27 23 24 28 17 9 30 29 29 28

Data

Histogram

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This graphical summary is one of the most widely used charts in Minitab.Useful Items:

Anderson-Darling normality TEST–We use the p-value to determine whether our distribution is normal or non-normal. If p > 0.05, the distribution is normal. (we will discuss p-value & hypothesis testing in Analyze, Step 6.)Mean–Average of the samples.StDev–Standard deviation of the samples.Variance–(Standard Deviation Squared.) A measure of how far the data are spread about the mean.

Skewness–A measure of asymmetry. A value more than or less than zero indicates skewness in the data. But, a zero does not necessarily indicate symmetry.Kurtosis–A measure of how different a distribution is from the normal distribution. A negative value typically indicates a distribution more peaked than the normal. A positive value typically indicates a distribution flatter than normal.N–sample size.Confidence Interval for Mu–Tells us the interval in which the true population mean lies (with 95% confidence.)

48Minitab–Graphical Summary

4 10 16 22 28

95% Confidence Interval for Mu

16.0 16.5 17.0 17.5

95% Confidence Interval for Median

Variable: Cycle Time

A-Squared:P-Value:

MeanStDevVarianceSkewnessKurtosisN

Minimum1st QuartileMedian3rd QuartileMaximum

15.6779

5.1552

15.7274

0.2080.864

16.39215.6167

31.54786.39E-02-2.4E-01

240

3.080012.406716.640020.306732.2667

17.1063

6.1698

17.3441

Anderson-Darling Normality Test


95% Confidence Interval for Sigma


Descriptive Statistics


Question: How can I examine the shape, central tendency, and variation (spread) of my data using one Minitab command?

Tool: Descriptive Statistics


To Make A Stat > Basic Statistics > Display Histogram: Descriptive Statistics:

Variable: Cycle TimeClick Graphs buttonSelect Graphical SummaryClick OK twice–once in each dialog box


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An important basic tool for understanding variation is the Run Chart. Run Charts are simple time-ordered plots of data. On these plots one can perform tests for certain patterns in the data. Presence of these patterns indicate special causes.

It is important to note that the data should be in time order for run charts to be valid.

49Variation Over Time

Run ChartA graphical tool to monitor the “stability of Project YAllows observation of time order properties such as trendShould be used before any detailed data analysis

Example of a Run Chart

Median

Is the process stable over time?

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Minitab Run Chart

The Minitab Run Chart tests for two kinds of Runs:(A) Consecutive points on the same side of the median. (Thus a new run starts when the median is crossed).(B) Consecutive points in the same direction up or down. (Thus, a new run starts when the direction is changed).

Mixture Pattern

A mixture represents more than expected number of runs of type A (above).

Cluster Pattern

A cluster represents fewer than expected number of runs of type (A).

Oscillating Pattern

Oscillation represents more than expected number of runs of type (B).

Trend Pattern

A trend represents less than expected number of runs of type (B).

At this point in time, our biggest concern is whether the process is stable or not. We use the above-mentioned checks to indicate stability. Minitab will do this for us.

50Run Charts–Special Cause Patterns

If p < 0.05, then there is significant statistical evidence to show that one of the trends below exists.

Cluster

Oscillating Trend

Mixture

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51Minitab–Run Chart


40 140 240

2

12

22

32

Observation

Cyc

le T

ime

Number of runs about median:Expected number of runs:Longest run about median:Approx P-Value for Clustering:Approx P-Value for Mixtures:

Number of runs up or dow n:Expected number of runs:Longest run up or dow n:Approx P-Value for Trends:Approx P-Value for Oscillation:

124.000121.000 9.000 0.651 0.349

151.000159.667 4.000 0.091 0.909

Run Chart for Cycle TimeDatafile: Fill_time.mtwQuestion: Does cycle time show any

patterned variation overtime?

Tool: Run Chart


Data Structure: A single column of data is all that is necessary. It is assumed that the data is entered in the order in which it is collected (time order).

To Make A Stat > Quality Tools > Run ChartRun Chart: Single Column: cycle time

Subgroup size: 1

The 4 p-values circled above indicate stability. Since p>0.05, there are no issues with Mixtures, Clusters, Oscillations or Trends. Therefore, our process appears stable (no special causes).

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For new process data, a Run Chart can be used to detect special cause situations. For processes that are already in statistical control, Control Charts are the preferred method. Control Charts are discussed in the Control phase of DMAIC training. But, here in the Measure and Analyze phase we suggest using the Run Chart to test for stability.

52Two Types Of Variation

Investigating Common vs. Special CausesFor new process data, use a Run Chart to look for special causes

Investigate special cause points for positive quick-fixesCommon cause variation requires systematic improvement effort

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Why is it important to know the source of variation and treat itaccording to the appropriate strategy? Because not reacting appropriately to the type of variation present in a process can seriously impact customer satisfaction and the amount of variation and defects, and it can increase costs.

When interpreting variation, you can make two types of mistakes:

Treating common causes as special causesTreating special causes as common causes

Treating common causes as special causes is essentially over-reacting to individual data points and is often referred to as “tampering.” The problem with making this type of mistake is that it typically leads to increased variation, costs, and defects. It’s like a novice driver who over-reacts to “slop” in the steering of a car. The result is more variation in the path of the car.

Treating special causes as common causes is essentially under-reacting to individual data points. The problem with making this type of mistake is missing an opportunity to prevent defects and reduce process variation. An example of this type of mistake would be failing to correct the steering on a car heading for a ditch, and ending up in the ditch.

Appropriately reacting to the source of variation in a process provides the correct economic balance between over-reacting and under-reacting to variation from a process.

53Two Types Of Variation (continued)

Reacting To Common vs. Special CausesHow you interpret variation . . .Common Causes Special Causes

Common

Causes

SpecialCauses

Mistake 1Tampering

(increases variation)

Focus on systematicprocess change

Mistake 2Under-reacting

(missed prevention)

Investigatespecial causes for possible quick-fixes

Truevariationtype...

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54Graphical Analysis Tools

Continuous Y Discrete YBoxplot

Pareto ChartScatterplot

Looking For Patterns In Data

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55Box Plots

What differences do you see between the output from the different shifts?

Shift 6Shift 5

Shift 4Shift 3Shift 2

Shift 1

60

30

10

Mea

sure

Box plots can be used to identify differences in variation between subgroups that exist in your data.

Look for 2 major items here:Center–are the medians similar?Spread–do the boxes and the “Whiskers”have similar heights?

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56Minitab–Box Plots

1 2 3 4

0

10

20

30

Agent

Cyc

le T

ime



Question: Is there a difference in variation in cycle time between agents?

Tool: Box Plot

Data Type: Continuous Y, Discrete X

To Make: Graph > Box plotA Boxplot Graph variables: Y Cycle time

X AgentClick OK

Additional Questions: Is there a difference in variation in cycle time between sites? Between types of resource?

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A Scatter Diagram is an important graphical tool for exploring the relationship between two continuous variables.

Here, it appears that size of Loan and Cycle Time have a relationship (Larger Loans take longer to process–positive relationship).

57Scatter Diagrams–Analyzing Relationships

Use Scatter Diagrams To Study The Relationship Between Two Variables.

Cyc

le T

ime

(Day

s) (Y

)

Size Of Loan (X)

40

30

25

20

15

10

5

35

1K 2K 3K 4K 5K 6K 7K 8K 9K 10K

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This is a plot of the population of Oldenburg at the end of each year against the number of storks observed in that year, 1930-1936.

Even strong correlations do not imply causation. (For example, there will likely be a positive correlation–but not causation–between the occurrence of vaporlocks in automobiles and the use of public swimming pools.)

58Warning! Correlation Does Not Imply Causation

Correlation Between Number Of Storks And Human Population

Number Of Storks

50100

80

70

60

200 30050

80

70

60

100 200 300

Source: Box, Hunter, Hunter. Statistics For Experimenters. New York, NY: John Wiley & Sons. 1978

Population(In Thousands)

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One of the most common mistakes that occurs with Scatter Diagrams is mixing up the X and Y variables.

The X variable is the potential cause and is plotted on the horizontal axis.

The Y variable is the effect and is plotted on the vertical axis.

59Common Construction Mistakes

Examples

Problem Variable Axis Variable

Bank Errors

Loan Delays

Computers Are Too Slow

Delays Unloading Airline Baggage

Size Of Loan

Length Of Time To Approve Loan

Computer’s Response Time

# Of People On Plane

# Of Errors In Closing Cost

Estimate

# Of Changes

Computer’s System Load

Time To Unload Baggage

Axis

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Common Patterns In The DataSee whether the potential cause variable and the effect variable are related to one another.

Range Of The Predictor Variable (X’s)The range is the difference between the largest and smallest values.Check that the range of the potential cause variable is wide enough to show possible relationships with the effect variable.

Irregularities In The Data PatternCheck whether the data pattern indicates possible problems in the data.

60Interpretation Of A Scatter Diagram

Look For:Common patterns in the dataRange of the predictor variable (X)Irregularities in the data pattern

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Interpretation Of Patterns:Positive Relationship: X Increases/Y Increases

Graphs 1 and 2–as X increases, Y increasesGraph 1–Strong, positive relationship between X and Y– Not much scatter– Points form a line with a positive slopeGraph 2–Weaker, positive relationship between X and Y– Scatter is wider– Points still form a line with a positive

slopeAs trainer experience increases, participant satisfaction also increases.Negative Relationship: X Increases/Y Decreases

Graphs 2 and 3–as X increases, Y decreasesGraph 3–strong negative relationship between X and Y– Not much scatter– Points form a line with a negative slopeGraph 4–weaker negative relationship between X and Y– Scatter is wider

As trainer experience increases, participant satisfaction decreasesNo Relationship: For any value of X, there are many values of Y

Graph 5–there is no relationship between X and YNo one line best describes the dataThere is no relationship between trainer experience and participant satisfaction

Non-Linear Relationship–The relationship between X and Y is complex and cannot be summarized with a straight line.

Graph 6–Inverted uAs trainer experience increases, participant satisfaction also increases until a critical threshold is reached, at which point participant satisfaction decreases. This is not a linear relationship.

61Interpreting A Scatter Diagram

Look For Patterns

No Correlation

Positive Correlation

Strong Positive Correlation

Other PatternNegative Correlation

Strong Negative Correlation

11

22

33

44

55

66

For all charts: Y = Participant satisfaction (scale: 1 – worst to 100 – best)X = Trainer experience (# of hours)

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62Minitab–Scatter Plot

0 5 10 15 20 25

0

10

20

30

Yrs Exp

Cyc

le T

ime


Question: Is there an association between cycle time and years experience?

Tool: Plot

Data Type: Continuous Y, Continuous X

To Make A Graph > PlotScatter Plot: Y Cycle time

X Years

Experience Click OK


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63Pairs Exercise–Analyze Patterns

With A Partner:Review scatter diagrams on following pages as assignedDetermine the type of relationship you observe (e.g., negative, positive, strong, weak, etc.)Describe an example from your business of this type of relationship

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Plot +/- Other Strong, Weak, Other Example

Potential Cause

Effe

ct

1

Potential Cause

Effe

ct

3

2

Potential Cause

Effe

ct

Common Scatter Diagram Patterns (continued) 64

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Potential Cause

Effe

ct

4

Potential Cause

Effe

ct

5

Potential Cause

Effe

ct

6



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Potential Cause

Effe

ct

7

Potential Cause

Effe

ct

8

Potential Cause

Effe

ct

9



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Potential Cause

Effe

ct

10

Potential Cause

Effe

ct

11

Potential Cause

Effe

ct

12



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We were introduced to Pareto charts in the CTQ tools module.

68Pareto Charts

Is There A Defect That Occurs Frequently?

C A E D B

Frequency

Category of Defect

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To find out which site has the most defects: Follow steps above except, place “Site” in “Chart Defects Data In” Box.

Alternate Method (Splitting A Worksheet)

MANIP > SPLIT WORKSHEETBy variable: Cycle_Time_DefectClick: OKNow you have 2 worksheets-one with “N” transactions and one with “Y” transactionsActivate the correct worksheet and then follow the steps in the slide above

Alternate method (subsetting a worksheet)MANIP > SUBSET WORKSHEET

Name: No TransactionsInclude or Exclude: CLICK ON “Specify which rows to include”Specify which rows to include: CLICK ON “Rows that Match”CLICK ON “Condition” ButtonCondition: Double Click on C6 then = “N”(‘cycle_time_defect’) = “N”Click “OK” twiceNow you have a worksheet with “N” transactions

69Minitab–Pareto Chart

Datafile: Fill_time.mtwQuestion: Which agent has the most cycle

time defects?Tool: Pareto ChartData Structure: A single column where the

defect categories are recorded ORA tally table in two columns. One column contains the Type of Defect, the second column contains the frequency of the defect.

To Make A Stat>Quality Tools>Pareto ChartPareto Chart: Chart Defects Data In: Agent

By Variable: Cycle _Time_DefectChoose: One Chart Per Page, Independent Ordering of BarsClick: OK

Additional Which site has the most cycleQuestions: time defects? Which type of

resource has the most cycle time defects?


4 1 2 3

35 12 8 756.5 19.4 12.9 11.3

56.5 75.8 88.7 100.0

0

2040

6080

100

120140

160180

020406080100

Defect

CountPercentCum %

Y

Perc

ent

Cou

nt

Pareto Chart for Agent

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3.1 Develop a plan to collect data3.2 Validate the measurement system3.3 Collect data per plan




What does it mean to Establish A Data Collection Plan, Validate the Measurement System, and Collect Data?A project data collection plan is a written strategy for collecting the data you will use in your project. A validated measurement system is one that has been shown to provide reliable data that represents the process output.

Why is it important to Establish A Data Collection Plan, Validate the Measurement System, and Collect Data?A project data collection plan and a validated measurement system are important because they define a clear strategy for collecting reliable data efficiently.The data collection plan helps ensure that resources are used effectively to collect only data that is critical to the success of the project. A validated measurement system is important because it ensures that the collected data accurately represents the true nature of your process. Data collection is costly; therefore, you need to make sure that both the data collection plan and the measurement system are sound.

What are the project tasks for completing Measure 3?3.1 Develop a plan to collect data3.2 Validate the measurement system3.3 Collect data per plan

Measure 3–Plan Data Collection And Collect Data 1

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D M A I CMeasure 3–Plan data collection, validate measurement

system, and collect data

Data collection purpose:

Sampling Plan (Scheme, Frequency, Size)

Measurement Procedure

Measure (Name)

Data Type(Discrete)/

(Continuous)Range Of

Values

How to measure:

Refer to more detailed documentation, if necessary.

What to measure (output measure and segmentation factors)

Measure Type (Y, X)

OperationalDefinition

Data Collection Plan Worksheet 2

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Type of Gage R&R Conducted (Check One):Gage R&R (Continuous Data)

Gage R&R Results1) Two-Way ANOVA Significant?

Part p-value Y NOper p-value Y NOper & Part p-value Y N

Pass?2) % Tolerance [ <30% ] Y N3) % Contribution [ <8% ] Y N4) % Study [ <30% ] Y N5) # Distinct Categories [ >4 ] Y N

Graphical Output OK?1) Effective Resolution [ >50% ] Y N2) Stability [R Chart] Y N3) Consistency Between Xbar consistency Y N

Between Oper4) Systematic Shift [Oper/Part Inter. Plot] Y N

Attribute Gage R&R1) Repeatability [ >90% ]2) % Reproducibility [ >90% ]3) % Accuracy [ >90% ]_______________________________________________________________1) Gage R&R Pass? Y N, If NO:

Plan for improvement:______________________________________________________________________________________________________________________________

Date Conducted:

Measurement System Analysis (MSA) Worksheet 3

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1Plan For Data Collection

Ensure DataConsistencyAnd Stability

EstablishData CollectionGoals

Develop OperationalDefinitions AndProcedures

Clarify purpose of data collectionIdentify what data to collect

Test and validate measurement systems

Write and pilot operational definitions

Develop and pilot data collection forms and procedures

Establish a sampling plan

Collect DataAnd MonitorConsistency

Train data collectors

Pilot process and make adjustments

Collect data

Monitor data accuracy and consistency

1 432

Data Collection Is The First Step To Understanding The Variation The Customer Feels

Data Collection Is The First Step To Understanding The Variation The Customer Feels

Data collection occurs multiple times throughout DMAIC. The data collection plan described here can be used as the guide for data collection regardless of where you are in DMAIC or what type of data you are collecting. Using this model will help ensure that you collect useful, accurate data that is needed to answer your process questions.

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2Step 1: Establish Data Collection Goals

In order to establish your data collection goals you must:State the purpose of the data collectionIdentify what data is required

Asking these questions may help you clarify your goals:What do I need to know about my process?What data do I need?What is the plan for analysis once the data is collected?What data is already available?

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3Preparing For The Analyze Phase

Segmentation:– An analysis technique that involves temporarily dividing a large group of

data into smaller logical categories to look for areas of very good vs. very poor performance

– Can be used to understand which X’s drive variation of the Project YCollect Project Y data to identify patterns and performance trends and establish current baseline defect rateCollect segmentation factor data to be used for later analysis

Segmentation Helps Us Understand Variation In Project Y

Segmentation Helps Us Understand Variation In Project Y

Think ahead about how you plan to analyze the data. Collect additional information corresponding to the Project Y that may be helpful in subsequent analysis.

– Include possible external factors that may be useful for segmenting the total Y data set.

– Consider how to collect continuous data instead of discrete data.

Thinking about segmentation factors now allows you to gather these conditions along with data on your Project Y so they don’t have to be reconstructed after the measurement is completed.Segmentation factors include external variables outside our control that may explain patterns in the Project Y measures.

For example, in deal businesses where the Project Y is the cycle time of closing the deal, a potential segmentation factor is client size (large, medium, or small)..

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4Common Segmentation Factors

Segmenting by external factors will help us identify the drivers of variation in the processPossible categories:

CustomerProductMarketTimeGeographySize of accountDegree of dissatisfaction

What Data Is Needed?Project Y data, collected over X time periodExamples:1. Y = Application cycle timeObjective:

Understand cycle time performance of credit approvals process.Identify potential sources of poor or irregular performances.

Data Required:Physical cycle time data (collect several business cycles) for individual credit applications.Data on possible segmentation factors external to the process (e.g., customer information, time/date applications received with product type, processing center).

2. Y = On-time delivery of servicesObjective:

Measure on-time delivery performance for customer service centerIdentify possible sources of poor or irregular performance.

Data Required:Deviations from target date/time for individual orders (minutes/hours, early or late)Data for segmenting factors [e.g., customer, market, geography, time (day, month, hour), request type]

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Other Categories

Factor Example

What type Complaints, defects, problems

When Year, month, week, day

Where Country, region, city, work site

Who Business, department, individual, customer type, market segment

Tip: Begin with factors “outside” the process box–often these are factors that were not considered when the process was first designed

In service-related processes, “When” elements to pay special attention to include: relationship to deadline (e.g., end of quarter), time/number in queue, or timing versus systems changes.

Note: Your team will need to segment the data in several different ways in order to uncover where the most significant differences occur.

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6How To Collect Data For Segmentation

Identify the factors for segmentation before you start collecting dataMake sure the segmentation factors can be measured reliably Record the segmentation factors for each Y data point collectedSegmentation factors are typically easy to collect, so collectmore segmentation factors rather than fewer

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7

Determine Segmentation Method

For your Project Y:– Brainstorm a list of segmentation factors– Remember to also segment on “unlikely” parameters

5 Minutes

Step 1: Breakout Activity (5 Minutes)

InstructionsInstructions

ObjectiveObjective

TimeTime

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8Step 2: Develop Operation Definitions and Procedures

Clearly specify variables to be collected:Operational definitions for all metricsSpecific descriptions of how to take the measurement

Specify the details of the data collection process:How to collect the dataHow to record the dataThe period of time for data collectionThe sampling plan to be followed

To help ensure consistency, clearly define each metric and the process for collecting it. Attention to these details will help ensure that the data you collect will give you an accurate picture of the variation in your process.

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9Operational Definitions

PurposePurpose

An operational definition is a clear, concise description of a measurement and the process by which it is to be collected

To remove ambiguity– Everyone has a consistent understanding

To provide a clear way to measure the characteristic– Identifies what to measure

– Identifies how to measure it

– Makes sure that no matter who does the measuring, the results are consistent

DefinitionDefinition

Defining The Measure

Always Pilot Your Operational DefinitionsAlways Pilot Your Operational Definitions

Operational definitions guide what properties will be measured and how they will be measured.There is no single right way to write an operational definition. There is only what people agree to for a specific purpose. The critical factor is that any two people using the operational definition will be measuring the same thing.

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10Operational Definitions–Scale Of Scrutiny

Choosing The Level Of MeasurementMeasure one scale or level smaller than what your customer measuresFor Example:

If your customer measures cycle time in days, your scale of scrutiny would be hoursIf your customer measures cycle time in hours, your scale of scrutiny would be in minutesScale of scrutiny may expose larger true variation

The scale of scrutiny is how finely you measure your process. Measuring one level smaller than your customer allows you to more fully understand and capture the variation in the process.

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1Sampling

Sampling is the process of:Collecting only a portion of the data that is available or could be available, and drawing conclusions about the total population (statistical inference)

Population Sample

xx

x

xxx

x

x

x

xx

x x

x

x

xx

x

xxx

x

N = 5,000 n = 100

From the sample, we infer that the average resolution time ( ) is 1.2 days

What is the average resolution time?

Sampling is the process of collecting a portion or subset of the total data that may be available. All of the data available is often referred to as a population (N). The purpose of sampling is to draw conclusions about the population using the sample (n). This is know as statistical inference.

In the example above, the population is all of the written inquiries received at a processing center last month (5,000). The manager of the process wants to know the average resolution time for the inquiries received last month. Measuring the resolution time for each inquiry is too expensive; therefore, a decision is made to take a sample.

A random sample of 100 inquiries is made and the average resolution is estimated.

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2When To Sample

When to sampleCollecting all the data is impractical or too costlyData collection can be a destructive processWhen measuring a high-volume process

When not to sampleA subset of data may not accurately depict the process, leading to a wrong conclusion (every unit is unique – e.g., structured deals)

Statistically Sound Conclusions Can Often Be Drawn From A Subset Of The Total Available Data

Statistically Sound Conclusions Can Often Be Drawn From A Subset Of The Total Available Data

One of the first questions to ask is ‘Do I need to sample?” The major reason sampling is done is for efficiency reasons-it is often too costly or time consuming to measure all of the data. Sampling provides a good alternative to collect data in an effective and efficient manner.

If the circumstances surrounding the data collection plan do not justify sampling, then sampling should not be done. This is often the case in low volume processes (e.g., deal processes).

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3Goal Of A Useful Sample

Representative SamplesRepresentative sample:

All parts of the target population are represented (i.e., selected for measurement) equallyThe customer’s view is captured

How to guarantee a representative sample:Design a sampling strategyUnderstand special characteristics of the population before sampling

Regardless of the situation, a sample must be “representative” of the population.

For practical purposes a sample is representative if it accurately represents the target population. Consideration that may hinder collection of a representative sample include:

The cost and ease of obtaining samplesTime constraintsUnknown characteristics of the population

Samples that are not representative of a target population are called biased samples. Often, the biases are not recognized until the collected data has been analyzed.

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4Sample Size For Continuous Data

How Do I Determine Sample Size?Sample size (n) depends on three things

Level of confidence required for the result, “How confident I am that the result represents the true population”

– Level of confidence increases as sample size increasesPrecision or accuracy (∆) required in the result, “The error bars or uncertainty in my result”

– Precision increases as sample size increasesStandard deviation of the population (σ), “How much variation is in thetotal data population”

– An estimate of standard deviation is needed to startAs standard deviation increases, a larger sample size is needed to obtainreliable results

In this equation, “1.96” represents a 95% confidence level

296.1n

∆σ×=

Consider the following example:We want to estimate average call length in handling customer inquiries, and we want our estimate to be accurate to within + 1 minute.

Based on a small random sample of 30 inquiries we know that the variation in call length, as measured by a statistic called the standard deviation, is 5 minutes.

We want to have 95% confidence that the estimate will be in the range of specified accuracy – i.e., + 1 minute.

Therefore, from the statistical theory we can answer according to the formula:

Where n = sample size, u = standard deviation and ∆ = degree of precision required. In our example, the required sample size is:

n = [(1.96x5)/1] 2 = 96.04or 96 samples

296.1n

∆σ×=

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Other Categories

Factor Example

What type Complaints, defects, problems

When Year, month, week, day

Where Country, region, city, work site

Who Business, department, individual, customer type, market segment

Tip: Begin with factors “outside” the process box–often these are factors that were not considered when the process was first designed

In service-related processes, “When” elements to pay special attention to include: relationship to deadline (e.g., end of quarter), time/number in queue, or timing versus systems changes.

Note: Your team will need to segment the data in several different ways in order to uncover where the most significant differences occur.

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6Calculating A Sample Size

( )Zα /2 *σ2∆

Z α /2 *σ

=

=

=n

Standard error–

Zα /2σn ∆

∆

∆n

Zα/2σn X

X ±

±CI X– *–

Solve for n

Given

Continuous Data To Derive Sample Size Formula

n = sample size∆ = precision of the estimate. How much error is ok? The smaller ∆, larger the sample size. May be a business decision.CI = Confidence IntervalZα/2 = Z score we usually set at 1.96 for 96% confidence.σ = estimated standard deviation

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7How To Estimate Standard Deviation When It Is Unknown

Use an existing Xbar or R chartwhere d2 is control chart factor

Collect a small pre-sample & calculate s (n = 30)Ask subject matter experts to take an educated guess at the plausible range of data

2/dRσ =ˆ

( ) /3XUCLσ −=ˆ

( )/6value known Lowest-value known Highestσ =ˆ

3 Ways To Estimate σ

Control Chart Factor d2

Range or moving range chart should be in statistical control (stable) to use this estimate of σ

n

2

3

4

5

6

d2

1.128

1.693

2.059

2.326

2.534

2/dRσ =ˆ

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8Sample Size For Continuous Data (continued)

What Is The Performance For Delivery Time?

Calculate sample size (n) based on:Precision (∆)95% confidence Level (1.96)Standard deviation (σ)

Y = DeliveryTime

(Days)

nValues

Conclusion:

I know with 95% confidence that the population mean is ⌧ + ∆

Calculate average (⌧)

Population

Sample

⌧ - ∆ ⌧ + ∆⌧

∆ ∆

296.1n

∆σ×=

Whenever samples are taken to estimate a population there will be differences between the “true” population values and the sample values.

Through statistical theory we can determine the amount of variation we can expect in our estimates. This is known as a confidence interval. Confidence intervals are stated in terms of an interval and a confidence level.

For example, when estimating average inquiry resolution time from samples, we may obtain a 95% confidence interval for the average 1.2 - 2.3 days. This means that if repeated samples were taken from the same population, 95 times out of 100 we would expect the sample average to be between 1.2 and 2.3 days.

Confidence intervals are important when precise estimates of populations are required, and the degree of precision in the estimate needs to be known.

For those statistically inclined, an important statistical theory supporting confidence intervals is the “central limits theorem”. The central limit theorem states that regardless the shape of the population, sample averages will always be “normally” distributed and inversely proportioned to the square root of the sample size.

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9Finite Population Correction

If You Have A Finite Population1. Calculate sample size (n)

2. If n/N > .05 OR

If n > N…

3. Calculate n finite nfinite = n/(1+n/N)

Where n = sample size;N = population size

Operational definitions guide what properties will be measured and how they will be measured.There is no single right way to write an operational definition. There is only what people agree to for a specific purpose. The critical factor is that any two people using the operational definition will be measuring the same thing.

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10Sample Size For Discrete Data

How Do I Determine Sample Size?Sample size (n) depends on three things:

Level of confidence required for the result, “How confident I amthat the result represents the true population”– Level of confidence increases as sample size increases

Precision or accuracy (∆) required in the result, “The error bars or uncertainty inmy result”– Precision increases as sample size increases

Estimated proportion defective of the population (P) – An estimate at P is needed to start– Sample size is maximized at P = 0.5

In this equation, “1.96” represents a 95% confidence interval

( )P1P96.1n2

−

∆=

You need to know the approximate proportion defective for the population to be sampled to calculate the sample size. For example:

P ∆ n.05 .02 456.50 .02 2400.95 .02 456

This calculation procedure is based on the binomial model and should only be used when nP > 5.

As for continuous measurements, if the sample size (n) is more than 5% of the population size (N), the finite population correction should be used n (finite) = n/(1 + n/N) and n (finite) should be used as the sample size.

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11Sample Size For Discrete Data (continued)

What Is The Defect Rate (P) Of A Process?

Y = ProportionDefective

nValues

Conclusion:I know with 95% confidence that the population

proportion defective is P + ∆Calculate Proportion

Defective (P)

Population

Sample

Recalculate n* based on the calculated P. If the new required sample size (n*) is more than the number of samples taken, take (n*-n) samples and recalculate P based on the full sample size. If it is not practical to take more samples, then use the actual n and P to recalculate the actual precision (∆).

Calculate sample size (n) based on:Precision (∆)95% confidence Level (2)Estimated proportion defective (P)

( )P1P96.1n2

−

∆=

Minimum Sample Size

ExampleWe want to estimate the defect rate (P) within + 0.02 (I.e., ∆ = 0.02). We expect P to be approximately 0.05.

( )P1P96.1n2

−

∆=

( ) 45605.0105.02.0

96.1n2

=−

=

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12How To Estimate P and ∆

( )n

P1PxΖ∆ α/2−=

Estimate PTake a small pre-sample of data (n = 100) and calculate PUse X from an existing control chartSet P = .5 as a worst case (largest n)

Estimate ∆See estimation of ∆ for continuous dataTo determine ∆ for a given sample size

Sample Size & P

0 .5 1

n

P

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13Sample Size Considerations

Beyond The Formulas…The formulas give an approximate sample sizeDon’t forget these important factors:– Is the population homogeneous?

If not, you will need to segment before sampling– What is the opportunity for bias?

Plan ahead to make sure your data is representative of the true population

What Is The Impact On The Customer If Your Sample Size Is Not Representative Of The Process?

What Is The Impact On The Customer If Your Sample Size Is Not Representative Of The Process?

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14Sampling Exercise

Apply Sample-Size Formulas

1. In your table-team, answer the assigned questions and be prepared to report your answers. Assume confidence level of 95%.

2. Determine the sample size needed if the following is known. P = 0.20, ∆ = 0.0784

3. Give an estimated proportion defective guessed to be 5%, how many observations should we take to estimate the proportion defective within 2%?

4. We want to estimate the average cycle time within 2 days. A preliminary estimate of the population standard deviation is 8 days. How many observations should we take?

5. We want to estimate average hold time at one of our cost centers within ± 2 seconds. We will assume hold time standard deviation is 10 seconds. How many calls do we need to sample?

10 Minutes


ObjectiveObjective

TimeTime

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1Measurement System Analysis–Objectives

Recognize that observed variation of a product/process includes the true variation of the product/process & the variation due to the measurement systemIdentify & describe possible sources of variation in a measurement processDescribe the importance of a validated measurement systemDescribe the terms precision, accuracy & resolution in relation to MSAUse appropriate tools to validate measurement system, analyze, and interpret results– Gage R&R for continuous data– Attribute R&R for discrete data

One of the objectives of the Measure Phase is to validate your measurement system. A Gage R&R Study will help us do this!

The focus of this module is to review the methodology and tools to validate your measurement system.

MSA = Measurement System Analysis

Gage R&R = Gage Repeatability & Reproducubility

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2Possible Sources Of Variation

Long-term Process Variation

Actual Process Variation

Accuracy (Bias)

Accuracy (Bias)

Measurement Process Variation

Measurement Process Variation

Observed Process Variation

Short-term

Process Variation

Variation due to gage

Variation due to gage

Variation due to

operator

Variation due to

operator

“Other” sources

(Environment, etc.)

“Other” sources

(Environment, etc.)

Precision (Measureme

nt Error)

Precision (Measureme

nt Error)

Discrimination

(Resolution)

Discrimination

(Resolution)

ObservationsMeasurementsData

Process Outputs MeasurementProcess

OutputsInputs Inputs

To Address Actual Process Variability; The Variation Due To The Measurement System Must First Be Identified And

Separated From That Of The Process

To Address Actual Process Variability; The Variation Due To The Measurement System Must First Be Identified And

Separated From That Of The Process

Measurement System Variation

We will be evaluating the variation in our measurement systems. We will include the variation due to the operator and gage (Accuracy, Precision and Discrimination).

When collecting data, we are seeing the process through the lens of our measurement system. We never really see the actual process variation-instead, we see the actual process variation and the measurement process variation. Therefore, the total observed variation can be broken down into 2 parts: the actual process variation and the variation (or measurement error) created by the measurement process.

Why is MSA important?

Data is only as good as the process that measures itMSA identifies how much variation is present in the measurement processUnderstanding measurement variation is necessary for identifying “true” process variation and maximizing true Y improvementsWithout MSA, you run the risk of making decisions based on an inaccurate picture of your processMSA helps direct efforts aimed at decreasing measurement variationExcessive measurement variation distorts our understanding of what the customer feels

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3Measurement Error vs. Process Variation

Call Taking Y= Time to Respond (Response Time)– Process Variation: Time to answer a question varies for different

operators, locations, etc.– Measurement Error: Error in capturing the time measurement due to

vague definition of when to stop.Application Processing Y= Time to Decision– Process Variation: Different types of applications vary in time to

complete. Associates vary in their productivity.– Measurement Error: Error in measurement time. Time stamp

inconsistencies or application arrival times not recorded accurately.Deal Approval Y = Time to Complete– Process Variation: Differing cycle times. Clients are treated differently.– Measurement Error: Inconsistencies in start-up or set-up definitions.

Deal Approval Y = Agreeable Terms and Conditions– Process Variation: Deal value variation (net income generated).– Measurement Error: Errors in recording net income.

Measurement Error vs Process Variation

When conducting a Gage R&R, you will be looking at the Measurement Error and determining if it is at an acceptable level. We want to minimize the measurement error (or measurement process variation). By conducting a Gage R&R, you will know how much of the total variation is due to the measurement process itself. In other words, by knowing the Measurement Error, we can assume that the variation we are observing in the process is mainly due to the process variation and not due to the measurement error. If the measurement error is found to be unacceptable, the measurement process must be fixed prior to collecting and/or analyzing data and trying to

make process improvements. The Minitab results obtained from your Gage R&R will indicate where the largest sources of measurement variation are hiding. Your goal will be to fix or reduce this variation and then to re-run the Gage R&R. You cannot collect and/or use your data until the Gage R&R passes.

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4Planning Your MSA

Questions to ask:What are you measuring?Who is measuring?What do you use to measure (gage)?How are you measuring? Do you always use the same procedure?Under what conditions are you measuring (6 m’s)?What is the resolution of your measurement system? Does the customer measure the same way?Which analysis will you use (continuous, Attribute and/or Destructive)?

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5Performing An MSA

An MSA can be conducted with Continuous or Discrete Data (we will review each method).When conducting the MSA, the following guidelines are suggested:– Choose 2-3 “operators” who normally perform the measurements.– For continuous data, choose 10 parts/samples (e.g., applications, calls,

deals, trucks, etc) to measure. The parts should be as dissimilar as possible (within the normal measurement range). These same, ten parts will be used throughout the entire MSA study.

– For discrete data, choose 30-40 parts/samples (higher is better). – The parts must be labeled with a number. The part numbers will remain

constant throughout the MSA.– Each operator will measure the parts 2-3 times. A blank data collection

form should be used for each trial.– The Gage should be “calibrated” as per the calibration procedure prior to

conducting the MSA.

Choosing Parts for your Study: The “Parts” are NOT randomly chosen. They should be chosen specifically for the study. For example, you need to choose parts that vary from one another (in size, weight, length of time, etc.) because one output in the MSA tells you if your measurement system can distinguish between parts.

Measuring the Parts: The operators should measure each of the 10 parts and record them on a data collection form. On their second round of measurement, they should have a new blank form. Never allow the operator to see previous measurements or measurements from other operators.

Analyzing the Results: After all the data is collected, you will run the MSA in Minitab (for Continuous data) or in Excel (for Discrete data). The remaining pages in this section explain the MSA output.

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6Measurement System Analysis

Five Components Of An MSA:

Accuracy–the differences between observed average measurement and a standard

Repeatability–variation when one person repeatedly measures the same unit with the same measuring equipment

Reproducibility–variation when two or more people measure the same unit with the same measuring equipment

Stability–variation obtained when the same person measures the same unit with the same equipment over an extended period of time

Linearity–the consistency of the accuracy across the entire range of the measurement system

Think in terms of shooting at a target.

Accuracy: How well do you hit the target? Do you hit where you are aiming?

Repeatability: Can you keep hitting the target in the same place?

Reproducibility: Can another person with the same gun hit the target in the same place?

Stability: If you come back to shoot at other times are you still able to shoot as accurately (consistency over time)?

Linearity: Are you as accurate at 50 meters as you are at 250 meters?

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7

For Attribute R&R:

90% matches for each Repeatability, Reproducibility,and Accuracy analysis.

Process Flow For MSA (Measurement System Analysis)

Conduct MSA

Continue ProcessImprovement

Take Preventive AndCorrective Actions OK?

No

Yes

Examples of Corrective Actions:Review data and decisionsInstitute stopgap measures

Examples of Preventive Actions:Correct mechanical or definitional errorsInstitute or upgrade training

Examples of Process Improvement:Measure gage over time to address stabilityStudy linearity of gage

Note: Attribute = Discrete

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8Attribute Data AR&R’s

With Discrete Data, we will look at these things:– Repeatability: Do repeated measures match within an operator?– Reproducibility: Do repeated measures match between operators?– Accuracy: Do the measures match the standard value?

An MSA helps us determine if our measurement system must be improved, and if so, gives guidance as to how

Although it has been emphasized that it is best to find a Y that is associated with continuous data, this is not always possible. In some cases, the response will be discrete. The measurement system must still be validated.

Attribute = Discrete

AR&R = Attribute Repeatability and Reproducibilityis the method we’ll use to analyze Discrete Data.

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9AR&R Guidelines For Evaluation

Repeatability: 90% of repeated measures within an operator matchReproducibility: 90% of the repeated measures across operators match Accuracy: 90% of the individual measures match the standard

Guidelines for determining how to design an AR&R study:1. For accuracy: The sample size is the total number

of measurements. (40 parts x 3 repeated measures x 3 operators = 360 measures.)

2. For repeatability: The more repeated measures on the same unit, the better the sensitivity. Increasing the number of units has a minimal effect on sensitivity. (Rather than measure 40 parts 3 times, measure 10 parts 12 times.)

3. For reproducibility: The more operators, the better the sensitivity. More units have a minimal effect on sensitivity. (Rather than measure 40 parts with 3 operators, measure 10 parts with 12 operators.)

The examples that follow balance all three characteristics of an AR&R study.

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10How To Determine Sample Size In The AR&R

How many samples should I take for an AR&R Study?Typically, 30-40 samples should give you a good indication of your measurement systemTen samples may be enough if running 30-40 samples would be too costly or time consuming. Use your “Business Sense” and learn from the study. Always ensure you choose samples that represent typical measures in your process.

For example, if your process requires a Customer Service Representative to code customer complaints as “A-K” categories, you would need to ensure your samples represented each of those codes. You also should choose samples that clearly fit that category and also ones that may fall within a “gray” area. (if such samples exist.) Therefore, the AR&R study will show whether your current measurement system is adequate.

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11AR&R Data Sheet

'True' Operator 1 Operator 2 Operator 3Sample Answer Trial1 Trial2 Trial3 Trial1 Trial2 Trial3 Trial1 Trial2 Trial3

1 N N N N N N N N N N2 N N N N N N N N N N3 N N N N N N N D N N4 D D D D D D D D D D5 D D D D D D D D N D6 N N N N N N N N N N7 D N D N D D D D D D8 N N N N D N D N N N9 N N N N N N N N N N10 N N N N N N N D N D11 D D D D D D D D D D12 D N N N D D D D D D13 D D D D D D D D D D14 N N N N N N N N N N15 D D D D D D D D D D16 N D D D N N N N N N17 N N N N N N N N N N18 N N N N N N N N N N19 N N N N D D D N N N20 N N N N N N N D D N21 D D D D D D D D D N22 N N N N D D D N N N23 N N N N D D D N N N24 N N N N N N N D D D25 N N N N N N N N N N26 D D D D D D D D D D27 N N N N N N N N N N28 N N N N N N N N N N29 N N N N N N N N N N30 D N D N D D D D D D31 D D D D D D D D D D32 N N N N N N N N N N33 N D N N D D N N N N34 N N N N N N N N N N35 N N N N N N N N D N36 D D D D D D D D D D37 N N N N N N N D N N38 N N N N N N N N N D39 N N N N N N N N N N40 N N N N D D D N N N

This data sheet uses 3 operators, 3 trials, and 40 units to measure repeatability, reproducibility and accuracy.

Repeatability of the measurement system is assessed by determining the proportion of times each operator matches on (e.g., three) repeated measures of one unit. For this example, there are 120 opportunities for a repeatability match.Reproducibility of the measurement system is assessed by determining the proportion of times all operators match on (e.g., nine) repeated measures of one unit. For this example, there are 40 opportunities for a reproducibility match.Accuracy of the measurement system is assessed by

determining the number of times each individual measure matches a standard. For this example, there are 360 opportunities for an accuracy match.

An extra column is added to define the true state of the standard according to a subject matter expert. In this example, N = Non-defective and D = Defective.

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12AR&R Example: Repeatability

Operator 1 Operator 2 Operator 3Sample Tr1 Tr2 TR3 Match? Tr1 Tr2 Tr3 Match? Tr1 Tr2 Tr3 Match?

1 N N N Y N N N Y N N N Y2 N N N Y N N N Y N N N Y3 N N N Y N N N Y D N N N4 D D D Y D D D Y D D D Y5 D D D Y D D D Y D N D N6 N N N Y N N N Y N N N Y7 N D N N D D D Y D D D Y8 N N N Y D N D N N N N Y9 N N N Y N N N Y N N N Y10 N N N Y N N N Y D N D N11 D D D Y D D D Y D D D Y12 N N N Y D D D Y D D D Y13 D D D Y D D D Y D D D Y14 N N N Y N N N Y N N N Y15 D D D Y D D D Y D D D Y16 D D D Y N N N Y N N N Y17 N N N Y N N N Y N N N Y18 N N N Y N N N Y N N N Y19 N N N Y D D D Y N N N Y20 N N N Y N N N Y D D N N21 D D D Y D D D Y D D N N22 N N N Y D D D Y N N N Y23 N N N Y D D D Y N N N Y24 N N N Y N N N Y D D D Y25 N N N Y N N N Y N N N Y26 D D D Y D D D Y D D D Y27 N N N Y N N N Y N N N Y28 N N N Y N N N Y N N N Y29 N N N Y N N N Y N N N Y30 N D N N D D D Y D D D Y31 D D D Y D D D Y D D D Y32 N N N Y N N N Y N N N Y33 D N N N D D N N N N N Y34 N N N Y N N N Y N N N Y35 N N N Y N N N Y N D N N36 D D D Y D D D Y D D D Y37 N N N Y N N N Y D N N N38 N N N Y N N N Y N N D N39 N N N Y N N N Y N N N Y40 N N N Y D D D Y N N N Y

0.925 0.950 0.800Operator 1 Operator 2 Operator 3

Repeatability of the measurement system is assessed by determining the number of times each operator matches on (e.g., three) repeated measures of one unit.In this example: – A Y in the “Match?” column indicates a match, and

an N indicates a non-match. On Unit 2, operator 2, for example, all three measures matched, while on Unit 3, Operator 3, only trials 2 and 3 matched.

– There are 40 samples *3 operators which yield 120 opportunities for a defect. Subtract (number of non-matches/120) from 1 and multiply by 100% to get the percent match for repeatability. 13/120 = .1083 did not match.

– The percent matched = 100 (1- .1083) = 89.17%– Since 89.17% matched is very close to 90%

matched, gage repeatability technically fails but is practically acceptable.

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13AR&R Example: Reproducibility

Operator 1 Operator 2 Operator 3Sample Tr1 Tr2 TR3 Tr1 Tr2 Tr3 Tr1 Tr2 Tr3 Match?

1 N N N N N N N N N Y2 N N N N N N N N N Y3 N N N N N N D N N N4 D D D D D D D D D Y5 D D D D D D D N D N6 N N N N N N N N N Y7 N D N D D D D D D N8 N N N D N D N N N N9 N N N N N N N N N Y10 N N N N N N D N D N11 D D D D D D D D D Y12 N N N D D D D D D N13 D D D D D D D D D Y14 N N N N N N N N N Y15 D D D D D D D D D Y16 D D D N N N N N N N17 N N N N N N N N N Y18 N N N N N N N N N Y19 N N N D D D N N N N20 N N N N N N D D N N21 D D D D D D D D N N22 N N N D D D N N N N23 N N N D D D N N N N24 N N N N N N D D D N25 N N N N N N N N N Y26 D D D D D D D D D Y27 N N N N N N N N N Y28 N N N N N N N N N Y29 N N N N N N N N N Y30 N D N D D D D D D N31 D D D D D D D D D Y32 N N N N N N N N N Y33 D N N D D N N N N N34 N N N N N N N N N Y35 N N N N N N N D N N36 D D D D D D D D D Y37 N N N N N N D N N N38 N N N N N N N N D N39 N N N N N N N N N Y40 N N N D D D N N N N

0.525Operator 1 Operator 2 Operator 3

Reproducibility (plus repeatability) of the measurement system is assessed by determining the number of times operators match on the same unit.In this example: – A Y in the “Match?” column indicates a match, and

an N indicates a non-match. On Unit 1, for example, all three operators matched, while on Unit 3, only Operators 1 and 2 matched.

– There are 40 samples or 40 opportunities for a defect in reproducibility. 19/40 = .475 did not match.

– The percent matched = 100 (1-.475) = 52.50% matched.

– Since 52.50% matched is lower than 90% matched, gage reproducibility is not acceptable.

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14AR&R Example: Accuracy

Std Operator 1 Operator 2 Operator 3 NotSample Value Tr1 Tr2 Tr3 Tr1 Tr2 Tr3 Tr1 Tr2 Tr3 Match?

1 N N N N N N N N N N 02 N N N N N N N N N N 03 N N N N N N N D N N 14 D D D D D D D D D D 05 D D D D D D D D N D 16 N N N N N N N N N N 07 D N D N D D D D D D 28 N N N N D N D N N N 29 N N N N N N N N N N 010 N N N N N N N D N D 211 D D D D D D D D D D 012 D N N N D D D D D D 313 D D D D D D D D D D 014 N N N N N N N N N N 015 D D D D D D D D D D 016 N D D D N N N N N N 317 N N N N N N N N N N 018 N N N N N N N N N N 019 N N N N D D D N N N 320 N N N N N N N D D N 221 D D D D D D D D D N 122 N N N N D D D N N N 323 N N N N D D D N N N 324 N N N N N N N D D D 325 N N N N N N N N N N 026 D D D D D D D D D D 027 N N N N N N N N N N 028 N N N N N N N N N N 029 N N N N N N N N N N 030 D N D N D D D D D D 231 D D D D D D D D D D 032 N N N N N N N N N N 033 N D N N D D N N N N 334 N N N N N N N N N N 035 N N N N N N N N D N 136 D D D D D D D D D D 037 N N N N N N N D N N 138 N N N N N N N N N D 139 N N N N N N N N N N 040 N N N N D D D N N N 3

# of N 5 2 4 6 5 5 5 4 4 40

Accuracy of the measurement system is assessed by determining the number of non-matches to the standard for each individual measureIn this example, – The “Non-Match?” column contains a count of non-

matches to the standard value (std value) for the unit (row). For example, all operators matched the standard for unit 2, so the number of non-matches is 0. For unit 3, operator 3 failed to match the standard on trial 1, so the number of non-matches is 1.

– There are the 40 units *9 repeated measures, or 360 individual measurements. 40/360 = .1111 did not match.

– The percent matched = 100 (1-.1111) = 88.89% matched.

– Since 88.89% matched is very close to 90% matched, gage accuracy technically fails but is practically acceptable.

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15AR&R Analysis Example: Accuracy (continued)

To summarize the AR&R MSARepeatability: 13/120 non-matched = 100 (1-.1083) = 89.17% (Fail–But Close!)Reproducibility: 19/40 non-matched = 100 (1-.475) = 52.50% matched (Fail)Accuracy: 40/360 non-matched = 100 (1-.1111) = 88.89% matched (Fail–But Close!)

Note: For Repeatability, 89.17% (and Accuracy 88.89%) we considered both of these as “Passing” due to the closeness to 90%. Use your judgment. If an improvement can be made, feel free to improve the measurement system. The 90% rate is an approximation not a “hard” limit.

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Gage R&R Results

1) Two-Way ANOVA Significant?Part p-value Y NOper p-value Y NOper & Part p-value Y N

Pass?2) % Tolerance [ <30% ] Y N3) % Contribution [ <8% ] Y N4) % Study [ <30% ] Y N5) # Distinct Categories [ >4 ] Y N



Attribute Gage R&R1) % Repeatability [ >90% ] OK2) % Reproducibility [ >90% ] Need to improve. See plan below3) % Accuracy [ >90% ] OKGage R&R Pass? Y N, If NO:Plan for improvement: Will work on Reproducibility problem by conducting a team meeting

with the 3 operators and discussing the differences in their measurements. Suspect that additional training is needed for less experienced operators because the data showed less experienced operators answering differently. Will also investigate if there is anything unique with each of the samples where reproducibility was an issue.

Date Conducted: 1/2/01

89.17%52.5%

88.89%

√

√

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17Causes Of Measurement System Variation

If you fail the Gage R&R, here are some factors that could cause measurement process variation (measurement error).

RepeatabilityOperational definitionsMaintain stability

ReproducibilityOperational definitionsConsistent use of gageTrainingVarying work environmentAUDIT-follow-up on trainingHuman/physical characteristicsPerformance measuresUnclear requirements

If the Gage R&R fails, you need to improve the measurement system before moving on. Use these factors above as places to begin looking for areas of variation in your measurement system. By improving some of these factors, your measurement system variation should be reduced (or brought to an acceptable level).

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18Causes Of Measurement System Variation (continued)

AccuracyError in masterInstrument used improperly by appraiserOperational definitionStandard not understood

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19Other Considerations

Temporal EffectsGage R&R depends upon our ability to measure things multiple timesIf the item is an event, it may not happen the same way twice. For this reason, Gage R&R may be impossible.If the event is recorded, it may be possible to conduct a Gage R&R studyIf the event cannot be recorded, but multiple judges can observe at once, reproducibility can be estimated, but repeatability cannot

Video cameras or audio voice recordings can allow a Gage R&R to be conducted. Use today’s technology to help you in validating your measurement system.

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Temporal Effects Example 1Many Olympic sports are judged based on a numerical score sheet filled out by a judge. The difference among different judge’s readings of one live event is a measure of reproducibility.

For this same case, repeatability can be estimated only if the competition is taped. A random sample of 10 performances shown to five judges, two times each, would allow estimates of both repeatability and reproducibility.

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Temporal Effects Example 2Call centers field service calls from around the world at centralized locations. Call duration and call quality are both recorded and tracked very closely.

Call quality is calculated based on a scoring sheet filled out by a quality monitor. Calls are scored on a continuous scale from 1-100 and can be assumed to be continuous for the purposes of a Gage R&R calculation.

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Temporal Effects Example 2 (continued)In one monitoring scenario, monitors listen in live and score the calls. For a “live listen” it is impossible to calculate repeatability, but if two monitors listen at the same time, it is possible to calculate reproducibility.

In another monitoring scenario, calls are recorded at random and scored at a later date. For this recorded scenario, both repeatability and reproducibility may be calculated.

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23Continuous Data MSA, First Step

Test-Retest Study

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24Test–Retest Study

Best Practice Hint: Do Test-Retest before Gage R&R–a quick look at the situation.

Why: Determine the precision of the system, instrument, device, or gage–where Precision = Measurement Error = Repeatability

How:Repeatedly measure the same itemSame conditions, operator, device, and location on item–same, same, sameCompletely mount and dismount item for each measurement–exercise gage through full range of normal use

Data: Twenty (20) or more measurements is an adequate sample size. Ifmeasurements are difficult or expensive, then 10-15 may be OK. More is better. Calculate the sample mean ( ) and standard deviation (s) of the repeated measurements.

Χ

Test–Retest studies are sometimes called Calibration Tests. This study is done prior to a Gage R&R.

A Test–Retest Study will indicate if you have either a precision or accuracy problem.

A Test–Retest Study is typically run using a certified or working “Standard.” The same item is measured repeatedly.

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25Test–Retest Study Guidelines

Device precision should be less than 1/10 of the tolerance:

s < 1/10 x tolerance*

If s exceeds 1/10 x tolerance*, then the measurement system is unacceptable because it lacks precision. Action is required to find and remove the sources of this error, including the replacement of the device.

Device accuracy may be estimated if you know the true value of the test unit:

Inaccuracy = Bias = - True ValueX

Precision is a term used to describe the amount of measurement error (repeatability error) in a measurement system.

Precision is also used to describe the term ∆ (delta) in confidence intervals. There it indicates ½ width of a confidence interval.

If your gage lacks precision or accuracy, you may need to remove or replace the measurement device. Perhaps a better or updated device can be used.

*For a one-sided specification you can: (1) Use the mean minus the tolerance. Note: the new formula would be: (½) S ≤ 1/10 (USL – X) or (½) S ≤ 1/10 ( X-LSL). (2) use the natural boundary (for example, use 0 for a cycle time measurement) as the other spec. (Tolerance = USL-0).

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26Process Flow For MSA (Measurement System Analysis)

For continuous data we’ll look at these major items: %Tolerance,% Contribution, % Study and # Distinct Categories.

Conduct MSA

Continue ProcessImprovement

Take Preventive AndCorrective Actions OK?

No

Yes

MSA is a set of methods for estimating the current amount of variation in the Measurement System.

Examples of Corrective Actions:Review data and decisionsInstitute stopgap measures

Examples of Preventive Actions:Correct mechanical or definitional errorsInstitute or upgrade training

Examples of Process Improvement:Measure gage over time to address stability Study linearity of gage

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27Precision & Accuracy

Target Analogy

I. Precise, not accurate

==

True Value = Bull's Eye

Xbar

II. Accurate, not precise

==

True Value

Xbar

III. Precise and accurate

==

True Value

Xbar

Precision: What kind of repeatability does the whole system have? What is the scatter? (standard deviation)

Accuracy: Does the average reading agree with the actual size of the part? (mean)

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28Measurement System

Product Variation

(Actual variation)

MeasurementVariation

Total Variation(Observed variation)

Measurement System Variability

- Investigated through “R&R

Study”

σ 2Actual (Part) + σ 2

Meas. System = σ 2Observed (Total)

ObservationsMeasurementsDataProcess

Outputs MeasurementProcess

OutputsInputs Inputs

Example

#1

Example

#2

The measurement system will also contribute some variation to the overall total observed variation.

Here are two examples of the effect of measurement variation. This variation comes from both the gage and the operator.

In a Gage R&R Study, we will determine how large the measurement variation contributes to the overall variation we’re observing in our process. The key will be to minimize the measurement variation so that we are mainly seeing process variation.

σ 2= variance

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29Types Of Variation Estimated By The Gage R&R

Equipment Variation (EV)(Repeatability)

(Sources of variation from within the process)Within Gage–Within Operator–Within Part/Process–Etc.

The variation introduced into the measurement process from within one or more elements of the measurement process–such as: within operator variation–within gage variation–within part variation–within method variation.

Appraiser Variation (AV)(Reproducibility)

(Source of variation from across the process) Across Gages–Across Operators–

Across Parts/Process–Etc.The variation introduced into the measurement process by effects going across the measurement process–such as

different appraisers–different part configurations–different checking methods.

Equipment variation–variation within a sample group.

Appraiser variation–variation between sample groups.

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30Relationship Between EV, AV And R&R

R&R is the Reproducibility (AV) and Repeatability (EV) of the Measurement System. It represents the total variation in the Measurement System.

σ 2Equipment + σ 2

Appraiser = σ 2Total (R&R)

R&R

EV AV

EV = Equipment Variation

AV = Appraiser Variation

The variation due to the equipment and appraiser do not directly add up to determine the total (R&R) variation. There is an overlap between EV and AV. You can use the Pythagorean theorem (right angles) to add to the influence of each EV and AV to calculate the total variation.

Repeatability: variation when one person repeatedly measures the same unit with the same measuring equipment.

Reproducibility: variation when two or more people measure the same unit with the same measuring equipment.

σ 2= variance

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31Relating R&R To Specification Window

How much of the tolerance is used up by the Measurement System variation?

Lower Spec. Limit Upper Spec. Limit

Specification Window (tolerance)

About 50% Of The Tolerance In This Example Is Used Up By The Measurement System Variation This Leaves Only 50%

For The Process Variation

About 50% Of The Tolerance In This Example Is Used Up By The Measurement System Variation This Leaves Only 50%

For The Process Variation

99%

R&R(5.15σ)

We’re interested in how this variation compares to the tolerance with which we are working.

If the measurement system takes up lots of variation, we don’t have any room for process variation. Minitab calls this variation % Tolerance. This is one or our 4 key metrics in the Gage R&R Study.

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32Gage R&R For Continuous Data: Example

GB Case Study: On Time Delivery of Shipments to Customers

Background: The dispatchers for “Capital Logistics” keep a record of the time when truck drivers radio in to report delivery of the shipment was made to the customer (this is a requirement from the customers). Since there are 3 dispatchers recording the delivery time and 10 truck drivers calling in, the Green Belt needs to validate these delivery times for repeatability, reproducibility & accuracy.

First, we will walk through the process to conduct a Gage R&R Study in Minitab, analyze the results and draw conclusions. We will use Capital Logistics’ study of the delivery of shipments to customers.

Then, you will do an activity to conduct a Gage R&R Study in Minitab with a new set of data from the same Capital Logistics’ study.

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33Gage Reproducibility & Repeatability (GR&R) Study: Steps

1. Set up a Minitab Worksheet2. Perform study–collect & enter Data. (use file: “Gage

R&R-Continuous Data.mtw)3. Perform calculations & prepare Charts.

– Perform Gage R&R Study–ANOVA method (ANOVA = Analysis of Variance)

4. Analyze–interpret & draw conclusions.5. Investigate variation in measurement system, take action, make

recommendations–keep, improve, or replace the measurement system.If measurement system is changed, repeat above steps to validate accuracy, repeatability & reproducibility of new measurement.

We have standardized on using the “ANOVA” method in Minitab. ANOVA simply stands for Analysis Of Variance. Minitab will partition the total variation and allocate this variation to gage variation or process variation. In the Gage R&R Study, we analyze the gage variation and want to understand how much gage variation is present. If we have too much measurement variation, we’ll need to fix our measurement system prior to collecting any data. We want to ensure the variation we are observing is mainly process variation.

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34Case Study Setup

Does my measurement system provide me a clear view of my process...

…or does it cloud what I see?

To help answer this question the GB established the following analysis:

1. The GB developed a master matrix which listed the times each truck was supposed to arrive at the customer. The GB gave a copy of the matrix to each of the three dispatchers.

2. The GB had each of the truck drivers radio a message from a radio truck, identifying himself as one of the 10 units listed in the matrix..

3. So that the GB could get repeatability & reproducibility data, the GB had the message recorded and then sent to the dispatchers throughout a 3 day period. The GB was able to program the phone system to deliver the messages precisely at the same time both days. The dispatchers were able to hear the call-in simultaneously via speakerphone.

4. Therefore, both days, the dispatchers, all in the same room at the same time, would receive the radio message and record the difference in minutes, from the target time listed onthe matrix. At the end of the day, the GB would collect the data collection sheets from each dispatcher and give them a blank form for the following day. This procedure was then repeated the second day.

5. The GB then consolidated the data into a single Minitab file for analysis. (Gage R&R–continuous data.mtw).

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35Gage R&R For Continuous Data: Example

Step 1: Set up Minitab data sheet.GB asked 3 dispatchers to record the truck driver call-in time for the 10 different truck drivers.Data sheet for recording the data was set up in Minitab to keep track of the 10 trucks (Part/Truck), 3 dispatchers (Oper), 2 runs (Trial) and the “Y” of Difference from Target (Meas).Open the File: Gage R&R–Continuous Data.mtw

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36Gage R&R For Continuous Data: Example (continued)

Step 2: Perform Study–Collect & Enter Data.Truckers called in to report delivery and dispatchers recorded the difference from target time.The data was collected and recorded on a data sheet and was input into Minitab (see Data column).

Minitab File: Gage R&R – Continuous Data.mtw

Use Minitab file: Gage R&R–Continuous Data.mtw Columns 1-3 in the Minitab worksheet represent the data collected by the dispatchers as each truck driver called on their delivery times.

1. Part/Truck–indicates which of the 10 trucks

2. Oper–indicates which one of the 3 dispatchers

3. Meas–indicates the difference, in minutes, from the target time

4. Trial–indicates the trial number when the operator took the measurement.

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Step 3: Perform Calculations & Prepare ChartsPerform Gage R&R Study–ANOVA method

Now let’s perform the Gage R&R study on this dispatching process example.

ANOVA is the best method–it breaks down the overall variation into three categories:

part-to-partrepeatabilityreproducibility

and….it breaks down reproducibility further into its components:

operatoroperator by part

The standard value for a 2-sided specification is 5.15. This is the number of standard deviations needed to capture 99% of your process measurements. If you only have a 1-sided spec, you would use 2.575 (half of 5.15).

In Minitab:

Click on STAT > Quality Tools > Gage R&R StudyIn the Gage R&R Study dialog box:

1. Select Columns for part, operator & measurement.

2. Select the ANOVA method

3. Select Options: Enter Tolerance width (note: Tolerance was set to 20 minutes here). The customer wanted the delivery within +/- 10 minutes of the target time.

4. Click “OK”, twice.

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Minitab Output will generate the following items which we will use to determine if our measurement system is acceptable:1. Graphical Summary2. Two-Way ANOVA Table with Interaction (p-values)3. % Comparisons Table (% Contribution)4. % Comparisons Table (% Tolerance)5. % Comparisons Table (% Study)6. Discrimination Index

We will cover each of these 6 outputs in this section.

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39The Central Question In A Gage R&R Study

There are 2 ways to (1) FUTURE STATUS: (2) PRESENT STATUS:answer the question Will my measurement Is my measurement“Is my measurement variation be too large variation too large right

variation too big?” when I reach the 6-Sigma now, compared to agoal (i.e., with small process realistic estimate of current

spread, good capability)? process spread (which may be narrow next year)?

Red

Yello

wG

reen

CAUTION:The magnitude of these

%’s are exaggerations

10%10% 2%2% 1010

30%30% 30%30%448%8%

R&R %Tolerance

R&R %Tolerance

R&R %Contribution(Ratio of Variances)

R&R %Contribution(Ratio of Variances)

Number of Distinct

Categories(Discrimination

Index)

Number of Distinct

Categories(Discrimination

Index)

R&R % Study Variation

(Ratio of StdDev’s -- AIAG)

R&R % Study Variation

(Ratio of StdDev’s -- AIAG)

15%15%

If the Gage R&R (as a percent of tolerance) is less than 10%, the MS is green, or acceptable; if Gage R&R is 10-30% , the MS is yellow, or marginal; if Gage R&R is greater than 30%, the MS is red, or unacceptable. This estimate may be appropriate for evaluating how well the measurement system can perform with respect to specifications. We can use it to look into the future and ask “Will my measurement system variation be too large when I reach the 6 Sigma goal (with small process spread, good capability)?”If Gage R&R (as a percent contribution) is less than 2%, the MS is green, or acceptable; if the Gage R&R is 2-8%, the MS is yellow, or marginal; if Gage R&R is greater than 8%, the MS is red, or unacceptable.

If the discrimination index (number of distinct categories) is greater than 10, the measurement system (MS) is green, or acceptable; if the discrimination index is 4-10, the MS is yellow, or marginal; if the discrimination index is less than 4, the MS is red, or unacceptable. The discrimination index is just a transformation of %R&R contribution (for ease of interpretation.) It addresses the same issues and contains the same information.If Gage R&R (as a percent study) is less than 15%, the MS is green, or acceptable; if Gage R&R is 15-30%, the MS is yellow, or marginal; if Gage R&R is greater than 30%, the MS is red, or unacceptable.

Note: the limits shown above can be derived from one another. Some rounding was done for ease of interpretation.

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40Rules Of Thumb–Acceptable Ranges

Step 4: Analyzing Gage R&R Results

A. R&R% of Tolerance1. R&R less than 10%–Measurement System “acceptable”

2. R&R 10% to 30%–May be acceptable–make decision based on classification of Characteristic, Application, Customer Input, etc.

3. R&R over 30%–Not acceptable. Find problem, re-visit the Fishbone Diagram, remove Root Causes. Is there a better gage on the market, is it worth the additional cost?

RULES OF THUMB:

1. Less than 10% = Good

2. 10% to 30% = Fair–improvements possible; look to find opportunities in process and training.

3. Over 30% = Problem–measurement system not acceptable; fix problem with training, improved instruments, correct measuring process, and/or improved operational definitions for data collection. The gage is not adequate for Product/Process Acceptance decisions.

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41Rules Of Thumb (continued)

B. % Contribution (or Gage R&R StdDev):GR&R Variance should be “small” compared to Part-to-Part Variance–applies in cases where Tolerance Width is not meaningful, and %Tolerance is unavailable–such as one sided specs.

1. % Contribution < 2%–Measurement System “acceptable”

2. % Contribution 2%-8%–Measurement System “marginal”

3. % Contribution > 8%–Measurement System “unacceptable”

Questions to ask for validating the measurement system:Are we capturing the correct data? Does the data reflect what is happening in the process?How big is the measurement error?Can we detect process improvement if and when it happens?What are the sources of measurement error?Are the measurements being made with measurement units which are small enough to properly reflect the variation present?Is the Measurement System stable over timeIs the Measurement System “capable” for this study?How much uncertainty should be attached to a measurement when interpreting it?How do we improve the measurement system?

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42Rules Of Thumb (continued)

C. Number of Distinct CategoriesA “Signal-to-Noise” Ratio = (StdDevparts/process/StdDevGR&R) x 1.41 and roundedGuidelines:< 2 =>no value for process control, parts all “look” the same= 2 =>can see two groups–high/low, good/bad= 3 =>can see three groups–high/mid/low≥ 4 =>acceptable measurement system (higher is better)

D. R&R % Study1. % Study less than 15%–measurement system acceptable.2. % Study 15% to 30%–may be acceptable (marginal)3. % Study over 30%–not acceptable

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43Minitab Gage R&R–Session Window Analysis

Here are the Results:% Comparison Table–Found in our Minitab Session Window

Source %Contribution %Study Var %Tolerance

Total Gage R&R 10.67 Fails! 32.66 Fails! 171.53 Fails! Repeatability 3.10 17.62 92.54 Reproducibility 7.56 27.50 144.43Oper 2.19 14.81 77.76Oper*Part/Truck 5.37 23.17 121.70 Part-To-Part 89.33 94.52 496.41 Total Variation 100.00 100.00 525.21

Number of distinct categories = 4 pass!

We fail the Gage R&R!

% Tolerance is 171.53% which fails, based on our criteria.This shows us the % of the Tolerance which is being taken up by the gage. In this case, 171.53% of our tolerance is taken up by the variation of the gage. Note: You must put in the tolerance in Minitab in order to get this data. If you do not enter a tolerance, these figures will not appear. If you do not have a tolerance, then % Contribution would be more important in your analysis

.% Contribution is 10.67% which fails our criteria. % Contribution is based on overall measure of gage variation (regardless of the specification).

% Study, probably the least important, (because % contribution tell us roughly the same thing) also fails based on our criteria. This gives us a measure of gage variation compared to 99% of a normal distribution.

Number of distinct categories passes! This tells us the number of divisions the measurement system can accurately measure across the seen process variation.

For a more detailed explanation of output, refer to the end of this section.

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44Minitab Gage R&R–Graphical Analysis

Now Let’s Review the Graphical Summary:

Gage name:Date of study :Reported by :Tolerance:Misc:

030405060708090

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Xbar Chart by Oper

Sam

ple

Mea

n

X=80.753.0SL=87.96-3.0SL=73.54

0

0

5

10

15 1 2 3

R Chart by Oper

Sam

ple

Ran

ge

R=3.833

3.0SL=12.52

-3.0SL=0.00E+00

1 2 3 4 5 6 7 8 9 10405060708090

100110

Part/Truck

OperOper*Part/Truck Interaction

Aver

age

123

1 2 3405060708090

100110

Oper

By Oper

1 2 3 4 5 6 7 8 9 10405060708090

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Part/Truck

By Part/Truck%Total Var%Study Var%Toler

Gage R&R Repeat Reprod Part-to-Part0

100

200

300

400

500

Components of Variation

Perc

ent

Gage R&R (ANOVA) for Meas

1

2

3

4

5

6

Chart 4:The chart shows the 10 parts and the average measurement of those parts broken-out by operator. Ideally, all 3 lines should be on top of each other. We can see that there is some measurement variation in parts 4, 8 and 10. We should investigate why.

Note: For more detailed explanation, refer to the end of this section

Chart 5:This chart shows the average reading for all parts by operator. The red circle is the average. This could show us if one operator is measuring higher/lower (on average) than the others.

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45Next Steps For The Green Belt

Sit down with your BB and/or Mentor to ensure proper analysisAfter an initial look at the Gage R&R Results for this example, the Green Belt will investigate the following:– Look at the feasibility of changing the gage to a digital clock– Talk with the operators to find out why they are measuring differently– Can a spreadsheet be developed to calculate time automatically?– Can we implement a driver call-in procedure to reduce variation?– Why was it harder to measure parts 4, 8 and 10?

Continue on to see the GB’s Next Steps…Continue on to see the GB’s Next Steps…

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If you fail the Gage R&R, here are some factors that could cause measurement process variation (measurement error).Repeatability

Operational definitionsCalibrating too oftenGranularity of the measure (e.g., nearest hour, minute, second)Maintain stability

ReproducibilityOperational definitionsConsistent use of gageTrainingVarying work environmentAUDIT–follow-up on trainingHuman/physical characteristicsPerformance measuresUnclear requirements

If the Gage R&R fails, you need to improve the measurement system before moving on. Use these factors above as places to begin looking for areas of variation in your measurement system. By improving some of these factors, your measurement system variation should be reduced, (or brought to an acceptable level).

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47Causes Of Measurement System Variation (continued)

AccuracyError in masterInstrument not calibratedWorn components/trend or drift in masterInstrument used improperly by appraiserCalibrating too oftenOperational definitionRange of the master

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LinearityInstrument calibrated incorrectlyError in masterWorn instrument

StabilityError in masterWorn instrumentInstrument measuring wrong characteristicInstrument not calibrated properlyInstrument used improperly by appraiser

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49Gage R&R Action Plan

Step 5: Investigate sources of variation in the measurement system and make recommendations–keep, improve or replace the measurement system.

After completing the analysis of the measurement system, the Green Belt investigated the sources of variation. By observing the process, the GB found:

The % Tolerance is the largest issue (171.53%). With the current gage and measurement process in place, the gage is not acceptable. To address this issue the GB has done the following:– Changed the Gage– Implemented a standardized call-in procedure– Implemented a new spreadsheet

Explanation of Bullets:The Dispatchers are using a clock on the wall that is not digital. Therefore, the GB implemented a new procedure to use the computer clock. All computers were synchronized and a procedure was implemented to have the system automatically synchronize clocks each day with the Atomic Clock.The GB also found that the Truck Drivers were inconsistent in calling in their arrival times. After going into the field and interviewing some truck drivers, the GB found that a new call-in process needed to be implemented. Part of the problem was not with the gage but with “when” the truck driver called in the delivery time. In many cases, the truck driver was within the 10 minute window but had forgotten to call in the arrival. A standardized process was implemented to address this issue.

The GB also noticed that all the data was positive, (indicating that the deliveries were always late). Upon investigation, the GB found that the dispatchers did not know that they should enter both positive and negative numbers. A new spreadsheet was created to fix this issue

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50Gage R&R Action Plan

Step 5 (continued)The % Contribution also failed (10.67%). From the Minitab data, the GB found Reproducibility to be the larger issue and the interaction between certain trucks and certain operators was the issue. To address these issues, the GB has done the following:– The data indicates that the measuring of the arrival time for trucks 4 & 10 seem to

vary from operator to operator. By going back and reviewing the data and talking to the operators, the following was found:

There was a typo on the recording of time from Operator 1 on truck 4. He accidentally typed in the wrong number. To address this problem, a new spreadsheet was developed and now the Dispatcher is asked to verify his data prior to saving it in the spreadsheet. For Truck 10, the Operators had a very difficult time hearing the recording because the Truck Driver was using a cell phone with a poor connection. The GB changed the procedure so that each Dispatcher was now required to repeat-back the time given by the truck driver. The Truck Driver then confirms that the correct time is being recorded.

– The data also indicated that Operator 2 seems to measure slightly lower than Operators 1 & 3. The GB found that Operator 2 was sitting on an angle and when he read the clock his time was distorted. By converting to the computer clock, this issue should be resolved.

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Desired Outcome: Determine if the improved measurement system utilized by the Capital Logistics dispatchers is “acceptable” or not

10 mins.TeamComplete 5 steps for a Gage R&R study and record results

Use File: Gage R&R–ContinuousData.mtw and use columns C6-C9

ConductMSA

5 mins.TeamComplete Report Summary

Present findings to class (seenext page for report summary)

Are there any additional itemsthe GB should consider toimprove the MSA even further?

ReportOut

Choose a facilitator, scribePreparation

TimingWhoHowWhat

Gage R&R For Continuous Data–Activity (15 minutes) 51

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Gage R&R Results


Pass?2) % Tolerance [≤ 30%] Y N3) % Contribution [≤ 8%] Y N4) % Study [≤ 30%] Y N5) # Distinct Categories [≥ 4] Y N



Attribute Gage R&R1) Repeatability [>90%]2) % Reproducibility [>90%]3) % Accuracy [>90%]Gage R&R Pass? Y N, IF NO:Plan for improvement:__________________________________________________________________________________________________


Date Conducted:

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53Analyzing The Gage R&R Results

Rules of Thumb1. R&R (% Tolerance)

Less than 10%–Measurement System is acceptable10% to 30%–maybe acceptable–make decision based on classification of characteristic, hardware application, customer input, etc.Over 30%–Measurement System is not acceptable. Find problem, re-visit the fishbone diagram, remove root causes. Validate Measurement System again

2. % Contribution (or Gage R&R StdDev) :GR&R Variance should be “small” compared to Part-to-Part Variance–applies in cases where Tolerance Width is not meaningful, and % Tolerance is unavailable–Such as one-sided specs.1.% Contribution < 2%-Measurement System “acceptable”2.% Contribution 2%-8%-Measurement System “marginal”3.% Contribution > 8%-Measurement System “unacceptable”

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54Analyzing The Gage R&R Results (continued)

3. Number of Distinct Categories = a “Signal-To-Noise” Ratio = (StdDevparts/StdDevGR&R) X 1.41 and rounded

Guidelines:< 2–no value for process control, parts all “look” the same= 2–can see two groups–high/low, good/bad= 3–can see three groups–high/mid/low> 4–acceptable measurement system (higher is better)

4. R&R % Study1. % Study less than 15%–measurement system acceptable2. % Study 15% to 30%–may be acceptable (marginal)3. % Study over 30%–not acceptable

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55Summary–Measurement System Analysis

Variation in the measurement system will contribute to the observed variation in a processThe resolution is the ability of the gage to see the variation in the process – The gage should be accurate: mean close to the true mean of the

process, and precise: small variation.Minimize the measurement process variationUse MSA (Gage R&R for Continuous Data or Attribute R&R for Discrete Data) to identify the amount of measurement system variation and process variationUnderstand how measurement error impacts your customerMeasurement error is always a bigger deal than you think!

Make Sure Your MSA Is Examining The Actual Measurement System Itself

Make Sure Your MSA Is Examining The Actual Measurement System Itself

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Measure Step 3–Green Belt Project Activity (30 minutes) 56

Desired Outcome: Outline of a Data Collection Plan and MSA for your GB project

15 mins.2 . MSA*

Develop an MSA for your project Ydata

List factors that might cause measurement system variation andhow you would reduce the impactof those factors

15 mins.1. Data Collection plan*

Review and finalize your DataCollection Plan for your GB project

Have you answered:

What data will you need tocollect?

How will you collect it? Fromwhere?

Who will collect the data?

(can refer to the data collectionworksheet)

Your Individual GB Project

TimingHowWhat

*Refer to the Self-Paced Workbook pp 43-49.

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57Gage R&R Details–Optional Information

Pages 58-69 contain Optional/Additional information that will not be covered in

the 3-Day Workshop

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58Full Gage R&R Details–Optional Information

Graphical Output


030405060708090

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Xbar Chart by Oper

Sam

ple

Mea

n

X=80.753.0SL=87.96-3.0SL=73.54

0

0

5

10

15 1 2 3

R Chart by Oper

Sam

ple

Ran

ge

R=3.833

3.0SL=12.52

-3.0SL=0.00E+00

1 2 3 4 5 6 7 8 9 10405060708090

100110

Part/Truck


Aver

age

123

1 2 3405060708090

100110

Oper

By Oper

1 2 3 4 5 6 7 8 9 10405060708090

100110

Part/Truck



100

200

300

400

500


Perc

ent


•ANOVA simply stands for “ Analysis of Variance”

•It is a tool used to analyze the total variability among different sources.

•It partitions the total variation into “buckets”, and then allocates each bucket to each source (part, operator, oper*part interaction).

•ANOVA simply stands for “ Analysis of Variance”

•It is a tool used to analyze the total variability among different sources.

•It partitions the total variation into “buckets”, and then allocates each bucket to each source (part, operator, oper*part interaction).

1

2

3

4

5

6

What do the graphs tell you about the measurement system? Is it acceptable?

1 > 50% of points should be outside control limits.

2 Range of measures by operator should be in control (this is showing repeatability.)

3 “D” should be largest, then A, B & C approximately equal.

4 Parallel lines will show no problems with certain parts (trucks.)

5 Scatter of individual measures should be equal by operator.

6 Scatter of individual measures should be equal by part (truck.)

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59Minitab Gage R&R ANOVA Graphical Output


030405060708090

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Xbar Chart by Oper

Sam

ple

Mea

n

X=80.753.0SL=87.96-3.0SL=73.54

0

0

5

10

15 1 2 3

R Chart by Oper

Sam

ple

Ran

ge

R=3.833

3.0SL=12.52

-3.0SL=0.00E+00

1 2 3 4 5 6 7 8 9 10405060708090

100110

Part/Truck


Aver

age

123

1 2 3405060708090

100110

Oper

By Oper

1 2 3 4 5 6 7 8 9 10405060708090

100110

Part/Truck



100

200

300

400

500


Perc

ent


Average of 2 measurements taken by operator 1.

Oper 1 Oper 2 Oper 3

Range of 2 measurements taken by operator 1.

Xbar chart by Operator: Plots the average for each part measured by each operator (average of 2-3 #’s). In our example, it is the average of 2 measurements.

We want the parts to be “out of control” If they are not out of control, we can’t tell one part from another! Remember , we’ve chosen parts that are different from each other. Usually, we want 50% of our points to be outside the control limits.

In this example, the Xbar chart looks OK (more than 50% of the points are outside the control limits.)

R Chart by Operator:Plots the range of each average point in the Xbar chart. This is the difference between the highest and lowest measurement for all 10 parts for each operator.

We want the R chart to be “in control”. If it is not, then this may be an indication that repeatability is poor. Our data in our session window will confirm if we have a Repeatability issue. At this point, make a mental note. Look for any points outside the Upper Control Limit (verify the measurement is not a typo!)

In this case, the R Chart looks OK. The chart is in control indicating that Repeatability is probably not an issue.

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60Minitab Gage R&R ANOVA Graphical OutputGage name:Date of study :Reported by :Tolerance:Misc:

030405060708090

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Xbar Chart by Oper

Sam

ple

Mea

n

X=80.753.0SL=87.96-3.0SL=73.54

0

0

5

10

15 1 2 3

R Chart by Oper

Sam

ple

Ran

ge

R=3.833

3.0SL=12.52

-3.0SL=0.00E+00

1 2 3 4 5 6 7 8 9 10405060708090

100110

Part/Truck


Aver

age

123

1 2 3405060708090

100110

Oper

By Oper

1 2 3 4 5 6 7 8 9 10405060708090

100110

Part/Truck



100

200

300

400

500


Perc

ent


A B C D

Graphical Display MSA Indicators by Components of Variation:

This is a graphical display of the components of variation. You can view the actual data in the session window.% Total Var ==> same as saying % Contribution % Toler ==> % Tolerance

Remember, we want the variation in the parts (Part-to-Part) to be the major piece of variation and we want the variation from the gage itself to be small. Therefore, we want “A-C” to be small and “D” to be largest.

In this case, the total variation of the parts is contributing 89.33% and the variation in the gage is contributing 10.67% (can be found in the session window). We’ll learn more later on % Contribution and % Tolerance.

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61Minitab Gage R&R ANOVA Graphical Output


030405060708090

100110 1 2 3

Xbar Chart by Oper

Sam

ple

Mea

n

X=80.753.0SL=87.96-3.0SL=73.54

0

0

5

10

15 1 2 3

R Chart by Oper

Sam

ple

Ran

ge

R=3.833

3.0SL=12.52

-3.0SL=0.00E+00

1 2 3 4 5 6 7 8 9 10405060708090

100110

Part/Truck


Aver

age

123

1 2 3405060708090

100110

Oper

By Oper

1 2 3 4 5 6 7 8 9 10405060708090

100110

Part/Truck



100

200

300

400

500


Perc

ent


Operator by Part Interaction: Shows interaction between the operator and the part

We want the lines to be on top of each other. Crossed lines could indicate the potential for interaction. Confirm suspected interactions with the p-value in ANOVA Table. We want all operators measuring the parts the very similarly (ie, getting the same measurement). Use this chart to help you look at particular parts which operators may be measuring differently. By reviewing this chart, we notice that the operators are measuring Part 4 & Part 10 differently. We would want to investigate why. This chart would also show us if one operator measures higher or lower than the others. It may indicate a Reproducibility issue. It appears that Operator 2 is measuring slightly lower than Operators 1 & 3. The Minitab Session Window can also tell us more.

By Operator: Main effect plot for Operator

We want a flat horizontal line. This would indicate that it is unlikely the operator is having an effect...confirm with the p-value from ANOVA. This chart shows the measurements, by operator. Some dots may be on top of each other. Visually, you can see each operator’s measurements.

By Part: Main effect plot for Part.

We want to see lots of changes in slope. This would indicate that it is likely that the parts are having an effect. Confirm with the p-value from Anova. (Remember, we set up our study this way. We wanted differences in the parts.) More importantly, look for parts that have varying measurements. For instance, part 10 shows more variation in measurement than some of the other parts.

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62Minitab Gage R&R ANOVA Table

ANOVA TABLE

P< 0.05 indicates statistically significant!

Are any of these “p-values” less than 0.05?

If so, their sources of variation can be considered statistically significant (i.e, Active, Influential).

For this gage... parts, operators and the interaction between parts & operators are statistically significant sources of variation!

Sources of

Variability

Two-Way ANOVA Table With Interaction

Source DF SS MS F P

Part/Truck 9 20587.1 2287.45 39.7178 0.00000Oper 2 480.0 240.00 4.1672 0.03256Oper*Part/Truck 18 036.7 7.59 4.4588 0.00016Repeatability 30 387.5 12.92 Total 59 22491.2

There are 4 major outputs other than the graphical summary. We will discuss each separately.

Explanation of output for ANOVA Table:

Part/Truck: p=0.00000; I would expect the parts to be significant because we chose truck travel routes that were really different from each other (short runs and long runs).

Oper: p=0.03256; This is telling us that the Operators are statistically significant. I need to look further to find out if it’s a repeatability or a reproducibility issue (Minitab does this for us in both the Comparisons Table and in the charts. We’ll show you later!)

Oper*Part/Truck: p=0.00016; This is the interaction between the operator and the parts (eg, when operators measure/record certain travel times). Since this is statistically significant, it is indicating that there may be some issues when some operators measure/record certain runs. We will look further into the Minitab output to find out which run and which operators.

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63Minitab Gage R&R % Tolerance

% Comparisons Table

“R&R as a % of Tolerance”


P/T Ratio(Precision-to-Tolerance Ratio)


% & ( . . )T o l e r a n c eT o l e r a n c e

R R M e a s S y s t=•

∗5 . 1 5 σ

1 0 0 %

Not Acceptable

QuestionableQuestionable

Acceptable

30%

10%

% Tolerance Acceptable Ranges

If you wanted to calculate %Tolerance by hand:


Total Gage R&R 10.67 32.66 171.53 Repeatability 3.10 17.62 92.54 Reproducibility 7.56 27.50 144.43Oper 2.19 14.81 77.76Oper*Part/Truck 5.37 23.17 121.70 Part-To-Part 89.33 94.52 496.41 Total Variation 100.00 100.00 525.21

This shows us the % of the Tolerance which is being taken up by the gage. For instance, in this case, 171.53% of our tolerance is taken up by the variation of the gage. Refer to the next page for a visual explanation of % Tolerance. Note: You must put in the tolerance in Minitab in order to get this data. If you do not enter a tolerance, these figures will not appear. If you do not have a tolerance, then % Contribution would be more important in your analysis.

% Tolerance = A good indicator for Future StatusFor this Gage: %Tolerance GRR = 171.53%This Gage Fails the Criteria for %Tolerance for the Total Gage RR Piece.

If % Tolerance is unacceptable now, then once you reach a Six Sigma Process, the measurement variation will be too large compared to the process variation.In this case, the gage fails % Tolerance.

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64Minitab Gage R&R % Tolerance Graphically

%Tolerance: Graphically

%Tolerance = 10%

%Tolerance = 30%

%Tolerance = 70%

LSL USL

Graphically, this shows the amount of the engineering tolerance used up just from the measurement system.

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65Minitab Gage R&R % Contribution

% Comparisons Table

“R&R as a % of Total Process Variation”

“R&R as a % of Total Process Variation”

%R&R Contribution (Total Variation)

%R&R Contribution (Total Variation)

% Contribution Acceptable Ranges

8.0%

2.0%

Not Acceptable

QuestionableQuestionable

Acceptable

Source %Contribution

Total Gage R&R 10.67Repeatability 3.10Reproducibility 7.56

Oper 2.19Oper*Part/Truck 5.37Part-To-Part 89.33Total Variation 100.00


Total Gage R&R 10.67 32.66 171.53 Repeatability 3.10 17.62 92.54 Reproducibility 7.56 27.50 144.43Oper 2.19 14.81 77.76Oper*Part/Truck 5.37 23.17 121.70 Part-To-Part 89.33 94.52 496.41 Total Variation 100.00 100.00 525.21

Variation due to the gage Variation due to the parts+ = 100%

Further Explanation:

3.10 + 7.56 = 10.67

Now, we know that Reproducibility is our bigger issue (contributing more than Repeatability).

2.19 + 5.37 = 7.56

Now, we know that of the Reproducibility, the Oper to Part/Truck interaction is our bigger issue than the Reproducibility of Operators. Check with the Oper*Part/Truck Interaction Graph to find out which parts may be the issue.

% Contribution = a good indicator for Present StatusThe measurement system (gage) is contributing to 10.67% of the total variation and the parts are contributing 89.33%.This Gage Fails the Criteria for % Contribution, but it is close to passing.

σ

σ

R RM e a s S y s t

T o t a l

&( . . )

2

2 1 0 0 %

×=% R&R

Contribution

Note: If you don’t have a tolerance, then, % Contribution becomes a very critical measurement for Gage R&R. It gives you a good indication of the measurement variation, now, compared to a realistic estimate of current process spread.

If you wanted to calculate %R&R Contribution by hand:

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66Minitab Gage R&R Discrimination Index

Discrimination Index

“Number of Distinct Categories”


Discrimination IndexDiscrimination Index

Discrimination Index:

•Provides the number of divisions that the Measurement System can accurately measure across the process variation.

•Indicates how well a gage can detect part-to-part variation -- process shifts and improvement.

Discrimination Index:

•Provides the number of divisions that the Measurement System can accurately measure across the process variation.

•Indicates how well a gage can detect part-to-part variation -- process shifts and improvement.

Discrimination Index Acceptable ValuesDiscrimination Index Acceptable Values

•Less than 2, inadequate •Equal to 2, equal to a go/nogo gauge. •Minimum acceptable value = 4. •Optimal = 10 or more.

For this gage: the Discrimination Index = 4

• This says that the gage has reached the minimum acceptable level.

Number of Distinct Categories = 4

D iscrim T ota l

R RM eas.S ys t

= •

−2 12

2

σσ &

( . )

Std Dev (Parts)

Std Dev (GRR)x 1.41

If you wanted to calculate

Discrimination Index by hand:

Discrimination Index will tell us how many categories or “buckets” the measurement device is able to see or discriminate. If you’ve chosen parts that are different (eg, in size, length, width, etc), the Discrimination Index will indicate how many distinct categories are present. In our example, Minitab is able to see 4 distinct categories. Note: If you’ve designed and ran your study with similar parts (on purpose), this reading would be meaningless to you.

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67Minitab Gage R&R Key Indices

3 Key Indices for Measurement System Capability 3 Key Indices for Measurement System Capability



11



“R&R as a % of Total Measure Variation”

“R&R as a % of Total Measure Variation”

22

%R&R Contribution%R&R Contribution



33

Discrimination IndexDiscrimination Index

%Tolerance GRR = 171.53% % R&R Contribution = 10.67% Discrimination Index = 4

The next question to be answered: What do I do now that the % Tolerance & % Contribution has failed?

Well, this is what we have learned so far about the break-down of % Tolerance and % Contribution:

For % Tolerance and % Contribution, we know the bigger issue is reproducibility. And, with Reproducibility, the bigger issue is the interaction between parts and operators. By looking at the graphical summary, it appears that trucks 4 and 10 may be the issue. Investigate why there is a difference. Is there something unique about those truck routes? Is it harder to measure the time for Trucks 4 & 10 due to time length? Should there be an Operational Definition or Procedure on how to measure? Was there a problem with calculating the time from target?

We also know that Operators and the Operator*Part/Truck Interaction is significant (from p-value). This is an indication that the operators are measuring differently. It also tells me there is some variation when certain operators measure certain trucks. Again, the graphs indicate which trucks and which operators.

I would investigate those areas mentioned above. Depending on your findings, you may need to implement a new training program with your operators on how to measure/record the time. You also may need to do something like having the computer measure the time when we measure parts similar to Parts 4 & 10. Once you’ve done those items, go back and re-run the Gage R&R using your implemented changes.

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68Gage R&R Acceptable Ranges

Acceptable Ranges–ANOVA METHODAcceptable Ranges–ANOVA METHOD

%Contribution

8.0%

2.0%

%Tolerance

30%

10%

% Discrimination Index

4

10

Not Acceptable

Questionable

Acceptable

This tells us how much variation the gage itself is contributing to the variation.

This tells us how much of the tolerance is being taken up by the variation the gage.

• Provides the number of divisions that the Measurement System can accurately measure across the process variation.

• Indicates how well a gage can detect part-to-part variation--process shifts and improvement.

30%

15%

This tells us the ratio of each component of variation (the standard deviation for each component divided by the total standard deviation).

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Gage R&R Results


Pass?2) % Tolerance [≤ 30%] Y N3) % Contribution [≤ 8%] Y N4) % Study [≤ 30%] Y N5) # Distinct Categories [≥ 4 ] Y N


Between Oper4) Systematic Shift [Oper/Part Inter. Plot] Y N_______________________________________________________________Gage R&R Pass? Y N, If NO:Plan for improvement:

Look at the gage and possibly change to a digital clock.Review/Implement a driver call-in procedure. Suspect there is variation between drivers.Review/develop a new spreadsheet for calculating the time.Talk with operators to determine why Oper 2 measures differently than Operators 1 & 3.Talk with customers about the right specification, if possible.Train all operators and truck drives on new procedures.Re-run Gage R&R to verify improvements.


Date Conducted: 1/2/02

171.53%10.67%32.66%

4

0.000000.032560.00016

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1Analyze Module Objectives

Learn and apply the tools and concepts in the Analyze phase

You will learn the concepts and tools for the Analyze phase during this classroom session. After the classroom session, you can use the Six Sigma training CD to review how the Analyze phase is applied.

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2Analyze Phase Flowchart

AD M I C

ANALYZE PHASE

OVERVIEW

Analyze 4:Establish Process Capability

Analyze 5:Define Performance Objectives

Analyze 6:Identify Variation Sources

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11



Control


9



10




Improve





5



4Analyze




3






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4Analyze Phase Overview

What is the Analyze phase?The Analyze phase is when your team:

Calculates baseline process capability for the processDefines the improvement goal for the projectAnalyzes historical data to identify the sources of variation

Why is the Analyze phase important?This phase is important because it clearly defines how well the process is currently performing and identifies how much the process will be improved.

Steps involved in the Analyze phaseAnalyze 4: Establish process capabilityAnalyze 5: Define performance objectivesAnalyze 6: Identify variation sources

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Root cause analysis



Practical Problem

Statistical Problem


Practical Solution

D M A I C




– Risk analysis

– Control plans




Collect data




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ANALYZE STEP OVERVIEW

4.1 Graphically analyze data for project Y (continuous data only)4.2 Calculate baseline sigma for project Y

Analyze 4:EstablishProcess Capability

Analyze 5:Define PerformanceObjectives

Analyze 6:Identify VariationSources

What does it mean to Establish Process Capability?Process capability refers to the ability of a process to produce a defect-free product or service. In this step, you will determine how consistently your product or process meets the performance standard for your project Y calculating the sigma level. The sigma level is calculated through statistical analysis of the collected data.

Why is it important to Establish Process Capability?You can’t set a measurable goal without a clear understanding of where you are. It is important to establish process capability in order to baseline your current process performance. This will be the starting point from which you will set your improvement goals.

What are the project tasks for completing Analyze 4?4.1 Graphically analyze data for project Y (continuous data only)4.2 Calculate baseline sigma for project Y

Analyze 4–Establish Process Capability 1

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2

Step 4.1: Graphically Analyze Data ForProject Y

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3Review: Describing Variation

Prior to Calculating Capability, we need to know:Key question #1–Stability–Variation over time (Run Chart)

How stable is the data?Key Question #2–Shape, Spread–Variation for a period of time: Data Distributions (Graphical Analysis)

What is the shape of the distribution–symmetrical, lopsided, twin peaks, long-tailed? (determination of normality)What is the central tendency (“center” or “average”) of the distribution?What is the variation (“spread”) of the distribution–wideor narrow?

These attributes of your data will help determine which statistical calculations are better descriptors of your data set.

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4Graphically Analyze Data

We can use the following example:Data set: Holdtime.MPJ1. First, look at Stability:

STAT > Quality Tools > Run Chart- Approx p-value for clustering = 0.1139- Approx p-value for mixtures = 0.8861- Approx p-value for trends = 0.2883- Approx p-value for oscillator = 0.7117

p ≥ 0.05 indicates stability. Therefore, data is stable.2. Secondly, look at Shape:

STAT > Basic Statistics > Normality Test Anderson-Darling p-value = 0.885p-value ≥ 0.05 indicates data is normal. Therefore, data is normal.

3. Third, look at Centering and Spread:STAT > Basic Statistics > Display Descriptive StatisticsAgain, p-value = 0.885. Data is normal.Mean = 8.5 and S = 0.10

p ≥ 0.05 indicates normal data. Therefore, will use mean and standard deviation to describe data.

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5

Steps 4.2: Calculate Baseline Sigma

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6What Is Process Capability?

A Measurement Scale Which Compares the Output of a Process to the Performance Standard

Process capability allows us to compare how “capable” the process is of meeting customer CTQ’s by looking at the probability that the process will produce a defect.

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7Common Metric For Comparison

Process PerformancePurchase Order 98% accuracyGenerationAccounts Receivable 33 days average agingCustomer Service 82% rated 4 or 5 on responsivenessSupplier Delivery 95% on-time delivery

Which process is performing best?

It’s difficult to compare processes with very different kinds of measure. By expressing process capability as a “sigma” value we can compare different types of processes.

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8Data Analysis Roundup

e.g Cycle Time, Length, Weight…

Discrete DataDiscrete Data Continuous Data

Continuous Data

Defects per Opportunity

Defects per Million Opportunities

Six Sigma Product Report

Six Sigma Process Report:

ZLong term

ZShort term = ZBench =

reported yield

ZShift

e.g Light On

Process Capability Tools and Terminology

e.g Light off

In this step you will learn how to calculate discrete and continuous data.

A note on terms to describe capability. All the following are synonyms:

ZLT = ZBenchLT = Sigma CapabilityLT (or, you may see capability written as σLT or SigmaLT. This is no longer standard usage to denote capability).

ZST = ZBenchST = Sigma CapabilityST = ZBench(σ or SigmaST is no longer recommended).

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9Process Capability Continuous Data

Verify we have a normal distributionCalculate ZLSL and/or ZUSLDetermine probability of a defectiveDetermine ZBench

We will look at how to do each of these steps in detail!

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10Calculating Z–Continuous Data

You can calculate a Z-value for any given value of x. Z is the number of standard deviations which will fit between the mean and the value of x. This is known as a Z-score.

µ 1σ 2σ 3σ 4σ

z

σµ−= XZ

The Z-score is a way to transform any normal distribution to the standard normal distribution. The standard normal distribution has a mean of 0 and a standard deviation of 1. This transformation allows us to compare two entirely different processes on a common scale-that of standard deviation units.

You must have a normal distribution: A stable process prior to using this method. If not, you’ll need to use the Discrete, DPMO method.

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ZUSL = Look up Z = 2.0 => 0.0228

LSL = Look up Z = 3 => 0.00135

Area Total = 0.0228 + 0.00135 = .02415

Yield = 1-.02415 = 0.97585 = 97.6%

Go to Memory Jogger (or Abridged Sigma Table) and look up a Yield of 97.6%

ZST = 3.4

11Calculating Capability

43210-1-2-3-4

8.98.88.78.68.58.48.38.28.1

Standard Deviations

Units of Measure

X = 8.5

s = 0.1

USLUSL Probability of a defect greater than USL

Probability of a defect greater than USLZUSL

ZUSL = USL - X = 8.7 - 8.5 = 0.2 = 2

s 0.1 0.1

LSLLSLProbability of a defect less than LSL

Probability of a defect less than LSL ZLSL

ZLSL = X - LSL = 8.5 - 8.2 = 0.3 = 3

s 0.1 0.1

xx

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12Reading The Z Table

0.20 .420740315 1.71 .043632958 3.22 .000640954 4.73 .0000011530.25 .401293634 1.76 .039203955 3.27 .000537758 4.78 .000000903

.382088486 1.81 .035147973 3.32 .000450127 4.83 .0000007051.86 .031442864 3.37 .000375899 4.88 .0000005501.911.962.012.062.112.162.212.262.312.36

.028066724 3.42 .000313179 4.93 .000000428

.024998022 3.47 .000260317 4.98 .000000332

.022215724 3.52 .000215873 5.03 .000000258

.019699396 3.57 .000178601 5.08 .000000199

.017429293 3.62 .000147419 5.13 .000000154

.015386434 3.67 .000121399 5.18 .000000118

.013552660 3.72 .000099739 5.23 .000000091

.011910681 3.77 .000081753 5.28 .000000070

.010444106 3.82 .000066855 5.33 .000000053

.009137469 3.87 .000054545 5.38 .0000000412.41 .007976235 3.92 .000044399 5.43 .0000000312.46 .006946800 3.97 .000036057 5.48 .0000000242.51 .006036485 4.02 .000029215 5.53 .0000000182.56 .005233515 4.07 .000023617 5.58 .0000000142.61 .004527002 4.12 .000019047 5.63 .0000000102.66 .003906912 4.172.71 .003364033 4.222.76 .002889938 4.272.81 .002476947 4.32

1.35 .088507862 2.86 .002118083 4.371.40 .080756531 2.91 .001807032 4.421.45 .073529141 2.96 .001538097 4.471.50 .066807100 3.01 .001306156 4.52

Units of Measure

SpecificationLimit

Table Of Area Under The Normal

Curve

Z = 1.91

ProbabilityOf A Defective

Example = .028066

To the right of the

Z-score you will note the tail area

Yield

Z-score

Yield = Probability of a non-defective

From the Z Table, we can get the probability of a defective. 1-Probability of defective = Yield.

This is what we’ll need to eventually calculate Process Capability.

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D M A I C z(Values of Z from 0.00 to 4.99)

Single–Tail Z Table 13

Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.00 5.00e-001 4.96e-001 4.92e-001 4.88e-001 4.84e-001 4.80e-001 4.76e-001 4.72e-001 4.68e-001 4.64e-0010.10 4.60e-001 4.56e-001 4.52e-001 4.48e-001 4.44e-001 4.40e-001 4.36e-001 4.33e-001 4.29e-001 4.25e-0010.20 4.21e-001 4.17e-001 4.13e-001 4.09e-001 4.05e-001 4.01e-001 3.97e-001 3.94e-001 3.90e-001 3.86e-0010.30 3.82e-001 3.78e-001 3.74e-001 3.71e-001 3.67e-001 3.63e-001 3.59e-001 3.56e-001 3.52e-001 3.48e-0010.40 3.45e-001 3.41e-001 3.37e-001 3.34e-001 3.30e-001 3.26e-001 3.23e-001 3.19e-001 3.16e-001 3.12e-0010.50 3.09e-001 3.05e-001 3.02e-001 2.98e-001 2.95e-001 2.91e-001 2.88e-001 2.84e-001 2.81e-001 2.78e-0010.60 2.74e-001 2.71e-001 2.68e-001 2.64e-001 2.61e-001 2.58e-001 2.55e-001 2.51e-001 2.48e-001 2.45e-0010.70 2.42e-001 2.39e-001 2.36e-001 2.33e-001 2.30e-001 2.27e-001 2.24e-001 2.21e-001 2.18e-001 2.15e-0010.80 2.12e-001 2.09e-001 2.06e-001 2.03e-001 2.00e-001 1.98e-001 1.95e-001 1.92e-001 1.89e-001 1.87e-0010.90 1.84e-001 1.81e-001 1.79e-001 1.76e-001 1.74e-001 1.71e-001 1.69e-001 1.66e-001 1.64e-001 1.61e-001





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D M A I C(Values of Z from 5.00 to 9.99)

z

Single–Tail Z Table 14

Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09






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3.458

1020304070100150230330480680960

1,3501,8602,5503,4604,6606,2108,19010,70013,90017,80022,70028,70035,90044,60054,80066,80080,80096,800

115,000135,000158,000184,000212,000242,000274,000308,000344,000382,000420,000460,000500,000540,000570,000610,000650,000690,000720,000750,000780,000810,000840,000860,000880,000900,000920,000

0.340.50.812347

10152333486896135186255346466621819

1,0701,3901,7802,2702,8703,5904,4605,4806,6808,0809,68011,50013,50015,80018,40021,20024,20027,40030,80034,40038,20042,00046,00050,00054,00057,00061,00065,00069,00072,00075,00078,00081,00084,00086,00088,00090,00092,000

0.0340.050.080.10.20.30.40.71.01.52.33.34.86.89.6

13.518.625.534.646.662.181.9107139178227287359446548668808968

1,1501,3501,5801,8402,1202,4202,7403,0803,4403,8204,2004,6005,0005,4005,7006,1006,5006,9007,2007,5007,8008,1008,4008,6008,8009,0009,200

0.00340.0050.0080.010.020.030.040.070.1

0.150.230.330.480.680.961.351.862.553.464.666.218.1910.713.917.822.728.735.944.654.866.880.896.8115135158184212242274308344382420460500540570610650690720750780810840860880900920

0.000340.00050.00080.0010.0020.0030.0040.0070.010.0150.0230.0330.0480.0680.0960.1350.1860.2550.3460.4660.6210.8191.071.391.782.272.873.594.465.486.688.089.6811.513.515.818.421.224.227.430.834.438.24246505457616569727578818486889092

99.99966%99.9995%99.9992%99.9990%99.9980%99.9970%99.9960%99.9930%99.9900%99.9850%99.9770%99.9670%99.9520%99.9320%99.9040%99.8650%99.8140%99.7450%99.6540%99.5340%99.3790%99.1810%98.930%98.610%98.220%97.730%97.130%96.410%95.540%94.520%93.320%91.920%90.320%88.50%86.50%84.20%81.60%78.80%75.80%72.60%69.20%65.60%61.80%58.00%54.00%

50%46%43%39%35%31%28%25%22%19%16%14%12%10%8%

6.05.95.85.75.65.55.45.35.25.15.04.94.84.74.64.54.44.34.24.14.03.93.83.73.63.53.43.33.23.13.02.92.82.72.62.52.42.32.22.12.01.91.81.71.61.51.41.31.21.11.00.90.80.70.60.50.40.30.20.1

Long-Term Yield ST Process Sigma

Defects Per 1,000,000

Defects Per 100,000

Defects Per 10,000

Defects Per 1,000

Defects Per 100

Note: Subtract1.5 to get long-termSigma level

Abridged Process Sigma Conversion Table 15

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How much variation we observe in a process is influenced by whether we are looking at long-term data or short-term data.

Long-Term:

Data collected over a long enough period of time and over diverse enough conditions such that it is likely to contain some process shifts and other special causes.

Short-Term:

Data collected over a short enough period of time so that shifts and other special causes are unlikely

For now, and as a default, treat all data as long-term data. The convention for Six Sigma is to report short-term, as you will see later.

Why do we report Short-Term Sigma?

We want to standardize reporting of the best a process can do, given its current capability. Therefore, Short-Term Sigma tells us this.

16Long-Term vs. Short-Term Data

Time

Y(Continuous)

Short-Term Data

Long-Term Data

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It is possible to calculate short-term, but for most Green Belt projects we do not attempt to do so; instead we use the 1.5 sigma shift rule.

In order to truly calculate short-term sigma, you have to use several rational subgroups. If you did not use a rational sub-grouping sampling scheme for data collection in the Measure phase, it will not be possible to calculate actual short-term sigma. (Therefore, add 1.5 to long-term sigma.)

Special Cause = Between subgroup variation due to assignable causes, non-random influences.

Common Cause = Within subgroup variation, inherent in a process, random influences.

To ensure you are sampling* properly, these 3 items must be true:

– Representative Data– Enough Data (at least 20 subgroups)– Measured with something that passes the Gage R&R

*Refer to the workbook for further details on sampling (Tools > Measure phase)

17Reporting Sigma Values

Short-Term Sigma = Long-Term Sigma + Sigma Shift If “Shift” is unknown, then assume 1.5Assume that sigma calculated from project data is long-term sigmaA rational subgrouping sampling scheme for data collection (in the Measurement Phase) must have been used if you are calculating a shift (other than using 1.5.)

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Rational subgrouping refers to grouping the data for analysis in a meaningful way to understand variation. Rational subgrouping attempts to select groups of data such that mainly common cause variation is within groups, and mainly special cause variation is between groups.

18Principles Of Rational Subgrouping

1. Never knowingly subgroup unlike things together2. Minimize variation within each subgroup

– Group homogeneous units, within a logic, within a reason3. Maximize variation between subgroups

– The Xbar shows differences between subgroups that are bigger than that shown within subgroups

4. Treat the chart in accordance with the use of the data– Subgroup frequency should reflect the process– Use individuals with limited data– Use subgroups when logical

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The 1.5 shift is used as a compensatory off-set in the mean to generally account for dynamic non-random variations in process centering. It represents the average amount of change in a typical process over many cycles of that process.

If the process is centered, then Six Sigma capability means that 6 standard deviations fit between the mean and the specification limit.

If the process center “shifts” by 1.5 sigma , then the average is 4.5 sigma from either the LSL or USL.

Six Sigma Short-Term Capability = 4.5 Sigma Long-Term Capability

Zero Sigma Short-Term Capability = -1.5 Sigma Long-Term Capability

19Generalizing The Correction

USLLSLLSL ± 6σ

.0005 ppm .0005 ppm

USLUSL

ProcessCapability

Six Sigma Centered

3.4 ppm

LSL USL4.5σ

TT

µµSix Sigma Shifted 1.5σ

TT

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Long-term is what is actually going on in the process.SL - m is the distance the specification is from the mean.

Short -term is the best the process can do.SL - T is the distance the specification is from the target.ZST is bigger than

LTLT σ

µSLZ −= The larger the ZShift , the greater the control problem.Typical ZShift = 1.5

STST σ

TSLZ −=

LTSTShift ZZZ −=

20The Universal Equation For Z

Z =

USLLSL

T (Target)µ (Mean)

st (short-term)lt (long-term) σ st

σ lt

λ = SL =

Z =SL - λ

σ. . . so what are the possibilities?

and how do we choose the right one?

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In Six Sigma, it is common to report out process capability using ZBench. As shown previously, ZBenchcorresponds to yield, i.e., we look at the chance of being outside the specification limit on either side. ZBench is calculated for both short and long-term. The difference between the two is ZShift.

21Z-Bench

Long-Term

Short-Term

LSL T USL_x

P(d)LSL P(d)USL

Zlt =SL -

σlt σZst = SL - T

st

ZLSL=T - LSL

σstZUSL=

USL- Tσst

P(d)USL = from Z table

P(d)LSL = from Z table

P(d)Total = P(d)USL + P(d)LSL

ZB-st = from Z table

ZLSL=-

σltZUSL=

USL-σlt

P(d)USL = from Z table

P(d)LSL = from Z table

P(d)Total = P(d)USL + P(d)LSL

ZB-lt = from Z table

Z-Bench-Long-Term Z-Bench-Short-Term

Z-Long-Term Z-Short-Term

LSL

µ

µ µ

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You can use the hand calculation or you can open the spreadsheet: SIGMACAL.xls.

Enter:

Xbar: 5

S: 2

USL: 9

LSL: (leave blank)

Note: This gives you ZST (the 1.5 shift was added to ZLT).

22Activity–Calculating Process Capability–Continuous Data

What is the process capability for a process that has:

Mean = 5Standard Deviation = 2Upper Spec. Limit = 9

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We always analyze the data this way:

1. Look at Stability–Is the process Stable?

2. Look at Shape–Do I have a normal distribution?

3. Look at the Spread–What measure of dispersion should I use?

Recall from our Case Study:

Time *(minutes early or late) = (Target Arrival Time) – (Actual Arrival Time)

Date 1 = Date of Shipment

* Spec. for time = ± 60 min.

Graphically Analyze Data–Breakout Activity (20 minutes) 23

Desired Outcome: Graphical Analysis of Capital Logistics Project Y Data Minitab File: GB Case Study.mtw

10 mins.AllUse the Normal Probability Plot inMinitab to analyze the shape of theproject Y data

Use the Descriptive Statistics tool inMinitab to analyze the shape,normality, central tendency andspread of the project Y data

Use the Minitab Six Sigma ProcessReport to calculate Process Sigma

Shape, Normality, Central Tendency And Spread

5 mins.AllYou can check your answers usingthe solution sheets on the followingpages

Solutions

5 mins.AllUse the Run Chart tool in Minitab toinvestigate the variation in theproject Y data over time

Run Chart

TimingWhoHowWhat

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First Step, Check Stability

Stat > Quality Tools > Run Chart

24Solution–Run Chart

Stability Calculations for Case study data.

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1. Double click on “C5”

3. Click ”OK”

2. Double click on “C1” Each Date is a sub-group

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By using the Run Chart, I’m looking for stability.

How do I analyze this chart?Look at p-values. P > .05 indicates stability. If the process is unstable, look for the most recent stable period and analyze with Minitab. If there is not a most recent stable time period, investigate & remove special causes.

Note: To manipulate data in Minitab:

MANIP > Subset worksheet > include/exclude row #’s


Each Date is a column of data points.

Spread

2 7 12 17

-100

0

100

Subgroup Number

time

Number of runs about median:Expected number of runs:Longest run about median:Approx P-Value for Clustering:Approx P-Value for Mixtures:

Number of runs up or dow n:Expected number of runs:Longest run up or dow n:Approx P-Value for Trends:Approx P-Value for Oscillation:

10.0000 9.4706 4.0000 0.6050 0.3950

9.000011.0000 4.0000 0.1118 0.8882

Run Chart for time

Median

Each column has it’s mean plotted as a red square

If these numbers had a value < .05, then the process is unstable.

This Run ChartThis Run Chart indicates that the process is stable over time.indicates that the process is stable over time.

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Second Step: Check Shape (Normality)

Stat > Basic Statistics > Normality Test (Variable = Time)

The results of the Anderson-Darling Normality Test tell you if the data is normal or not. A p-value of greater than or equal to 0.05 means the data is normal. A p-value of less than 0.05 means that the data is not normal. Step 6 will address p-values in more detail.

27Solution–Normality Testing

In Minitab, you can perform a Normality Test (Stat-Basic Statistics-Normality Test).Use the normality test to validate the shape of your data, when the shape is in question.

The data is Normal by this test method if the P-value is > = .05

Average: -4.40316StDev: 43.1714N: 506


-100 0 100

.001

.01

.05

.20

.50

.80

.95

.99

.999

Prob

abilit

y

time


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Third Step: Check Spread

The graphical summary of descriptive statistics (Stat–Basic Statistics–Descriptive.)

Stat > Basic Statistics > Display Descriptive Statistics

Variable = TimeClick on “Graphs” & choose “Graphical Summary”

Test p-value. Minitab will always display a normal curve based on the data’s mean and standard deviation –this may not be a fit to the actual distribution.

28Solution–Normality Testing (continued)

-100 -60 -20 20 60 100


-10 -5 0


Variable: time

A-Squared:P-Value:



-8.174

40.665

-9.369

0.1300.983

-4.4032 43.17141863.77

7.65E-02-1.2E-01

506

-114.021 -35.085 -4.956 23.421 120.046

-0.633

46.009

0.532





Descriptive StatisticsThis data isnormal.

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Now let’s look at how to calculate process capability for continuous data in Minitab, using the Six Sigma Process Report.

The subgroup size can be entered in two different ways:Size of each subgroup –10 (subgroup size must be constant)ID column–oper 50 (subgroup size may be constant or not)

Warning: If you choose to use a subgroup size of 1, the short-term values calculated in the Six Sigma Process Report will be invalid since there is not variation within the groups.

The Six Sigma Process Report is used to calculate the long-term and short-term z-values of your process. In order to be accurate in the calculation of the z-values, it is important that we enter all of the information available. If a target is available, then enter the target value for the calculation of the z-values. If the upper and lower specification limits are entered and the target is left blank, Minitab approximates the target value as the midpoint of the specific range. If only one specification limit is entered and the target is left blank, then Minitab approximates the target as the mean of the data. Hence, when the target is available, always input the given value to avoid approximations made by Minitab.

29Minitab Six Sigma Process Report

MINITAB FILE: GB case study.mtw

1. Double Click C5 time

2. Double click C1 to use Date1 as the Subgroup size

3. Type in Lower and Upper specs

4. Click OK

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Report 1 contains the essence:Sigma potential (ST) = ZBench-ST: if you were to use just one number to indicate the capability of your process, it is this one. If a firm XY claims to be a 5σcompany, they talk about this value. If you only see ZST, it means ZBench-ST. It is a convention to benchmark other companies using this value. However, it is a good practice to report out both ZBench values, for the short and long-term. Sigma actual (LT) = ZBench-LT: this value corresponds to the actual performance of your process, and is easier to comprehend with PPM. PPM actual = DPMO actual: the actual number of defects per million opportunities that the process produces. PPM potential (not so important): corresponds to ZBench-ST, not commonly used.

Upper graph: show short (dotted) and long-term (full line) distributions. By definition, the short-term distribution is shown to be on target. In this case, the long-term distribution is slightly below the target.Lower graph: shows cumulative PPM’s.

Note: When reporting ZST, determine if you will be using the shift calculated from your data or the standard 1.5 shift. If using the 1.5 shift, you will need to manually add the 1.5 to ZLT to get ZST. Minitab cannot accommodate a predetermined shift. (When in doubt, use the 1.5 shift and/or consult your BB/MBB).


Actual (LT) Potential (ST)

-100 0 100

Process Performance

USLLSL


1

10

100

1000

10,000

100,000

1,000,000

0 5 10 15


PPM

Sigma(Z.Bench)

Process Benchmarks

0.97

164350

0.98

166781

Process DemographicsDate:

Reported by:

Project:Department:

Process:

Characteristic:

Units:

Upper Spec:

Lower Spec:

Nominal:

Opportunity:

60

-60

Report 1: Executive Summary

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Report 2 is more detailed:The table to the right side contains all the details of the calculation of ZBench for short and long-term.The graphs to the left side are called control charts. This subject will be covered in the “control” session of your training. In order to use Minitab’s calculated shift (right column in the table), the “S” chart must be in control (minimize variation within subgroup) In this example, S chart is out-of-control (one point outside control limits). It does not meet the condition mentioned in the 2nd bullet, therefore, report ZLT = 0.9670. To get ZST: ZST = ZLT + ZShift

ZST = 0.9670 + 1.5 = 2.467Refer to the next 2 pages for rules on using this Process Capability Report.

Note: When reporting ZST, determine if you will be using the shift calculated from your data or the standard 1.5 shift. If using the 1.5 shift, you will need to manually add the 1.5 to ZLT to get ZST. Minitab cannot accommodate a predetermined shift. (When in doubt, use the 1.5 shift and/or consult your BB/MBB).


1020304050607080

S=42.70

3.0SL=61.28

-3.0SL=24.12

0 5 10 15

-50-40-30-20-10

010203040

Xbar and S Chart

Subgroup

X=-4.403

3.0SL=21.49

-3.0SL=-30.29

-60 60

-129.508 129.508

Potential (ST) CapabilityProcess Tolerance

Specifications

I I I

I I I

-60 60

-133.981 125.175

Actual (LT) CapabilityProcess Tolerance

Specifications

I I I

I I I

Ppk

Pp

Cpk

CpPPM

Yield

P.Total

P.LSL

P.USLZ.Shift

Z.Bench

Z.LSL

Z.USL

StDevMean

ST LT

Capability Indices

Data Source:Time Span:Data Trace:

0.000043.1471

1.3906

1.3906

0.9767

0.00980.082175

0.082175

0.164350

83.5650

1643500.46

0.43

-4.4032 43.1714

1.4918

1.2878

0.9670

0.00980.067876

0.098905

0.166781

83.3219

166781

0.46

0.43

Report 2: Process Capability for time

1. Between Subgroup Variation

2. Within Subgroup Variation

3. Because variation is not out of control, there is no LT Variation

4. This makes sense, we only have 1 month’s worth of data

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32Rules For Using The Six Sigma Process Report

Rules for Process Capability1. Ensure the process is stable (Run Chart). If not, remove

special causes first.2. Ensure normal distribution (if not, use DPMO method to

calculate capability)3. For continuous data: use Six Sigma Process Report. If

subgroup size > 1 and the S-chart is in-control, then both columns in the table are valid. If the S-chart is out-of control, only the LT column is valid. Add 1.5 to the ZBenchLT to get ZST.

4. If the subgroup size = 1, use LT column only in the Process Report

Use the Decision Flow on the next page to help you!Use the Decision Flow on the next page to help you!

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33Process Capability Decision Flow

Analyze for Special Causes-

Should not calculate process capability until the process is stable.

Unstable process data can only be used to describe

the capability of the current data set, not the future capability

of the process.

Six Sigma>Product Report, DPMO, L1 (Input D, U and O)

•Sigma Conversion Table gives ZST

•Z LT = Z ST - Z Shift (1.5)

•Product Report and L1 give Z Bench

•Z Bench = Z ST

•Z LT = Z Bench - Z Shift (1.5)

Note:Z ST = Z LT + ZshiftZ ST = Z Bench-STZ LT = Z Bench-LT

No

Yes

Do you have

RationalSubgroups?

Is the Distribution

Normal?

No

Is your Process

Stable (use Run Chart)?

Do you have

Continuous Data?

Yes

No

Yes

Use Z Bench-LT only and add 1.5 Shift to get Z Bench-ST

Use Six Sigma> Process Report (Input Data, Specification Limits

and Target as appropriate)

Yes

No Is the S-Chart in-control?

Z Bench-LT , Z Bench- ST & Z Shift all valid on

the Process Report

Yes

Use Z Bench-LT only and add 1.5 Shift to get Z Bench-ST

No

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34The Normal Curve And Capability

Poor Design Capability

High Probability of Defective

High Probability of Defective

LSL USL

Low Probability of Defective

Low Probabilityof Defective

Good Design Capability

LSL USL

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35Summary–Z-Value

Basic statistical summaries, histograms, dotplots, boxplots, and run charts are used to visualize data and better understand a processThe Z-score is a non-dimensional quantity that enables us to compare different processes–it represents the process capabilityThe Z-score is the number of standard deviations that will fit between the mean and the respective specification limit of a normal distribution The Z-score corresponds to yield, or the area under the curve inside the specification limits

Note on Capability:Capability can be described as any of the following:– ZBenchST = ZST = σST = Sigma CapabilityST =

SigmaST = ZBench– ZBenchLT = ZLT = σLT = Sigma CapabilityLT =

SigmaLT

In the new BOK, σST and σLT are not recommended ways to describe capability. σST = pooled standard deviation and σLT = standard deviation.

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36Summary–Continuous Data Process Capability

The Minitab Six Sigma Process Report is used to describe capability with continuous data

– Displays the actual capability relative to the target distribution– By rationally subgrouping (subgroup size >1), long-term capability, short-term

capability, and shift are calculated.Rational Subgrouping refers to grouping the data for analysis in a meaningful way to understand variation. Rational Subgroupingattempts to select groups of data such that mainly common cause variation is within groups, and mainly special cause variation is between groups.

– Special Cause = Between group variation, due to assignable causes, non-random influences

– Common Cause = Within group variation, inherent in a process, random influences

A subgroup that contains only common cause variation, or random variation, represents the short-term capability of the process or entitlement (ZBench)

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Classical Yield (YC) = Final Yield

Throughput Yield (YTP) = First Pass Yield

Rolled Throughput Yield (YRT)

37Process Capability & Yield–Discrete Data

Calculate the distribution of defects, defects per million opportunity (DPMO)Utilize Z tables to convert DPMO to yield or sigma levelUnderstand the difference between classical, Throughput Yield, and Rolled Throughput YieldCalculate submitted, observed, and escaping defect levels

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Note: Black dots indicate a defect.

ClarificationDefect–Any single non-conformance (defect=black dot)

Defective–A unit with 1 or more defects. (defective=any square with 1 or more black dots).

38Definitions

Unit (U)The number of parts, sub-assemblies, assemblies, or systems inspected or tested

– Squares: 4 unitsOpportunity (OP)

A characteristic you inspect or test– Circles: 5 opportunities per unit

Defect (D)Anything that results in customer dissatisfaction. Anything that results in a non-conformance.

– Black circles: 9 defects

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39Formulas

Defects per UnitDPU = D/U9/4 = 2.25

Total OpportunitiesTOP = U*OP4*5 = 20

Defects per Opportunity (Probability of a Defect)DPO = D/TOP9/20 = .45

Defects per Million OpportunitiesDPMO = DPO*1,000,000.45*1,000,000 = 450,000

Once we calculate DPMO, we go to the Abridged Sigma Table (next page) to get ZBenchST or ZBenchLT

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Converting DPMO To Z

To Calculate Process Sigma:Go to the Memory Jogger–Abridged Sigma Conversion Table (or use the table above)Look up the DPMO value and report Short Term Sigma value (always round to poorer performance if between values in the table.)

In our example, we calculated 450,000 DPMO. This value is not found in the table, therefore, we go to 460,000 and report 1.6 as the Short Term Sigma Value. We’re always conservative. Therefore, report the lower value for ZST or ZLT. And, you cannot interpolate, so choose the lower sigma value.

40Converting DPMO To ZST

ZST = Reported Sigma (Short-Term)

Abridged Process Sigma Conversion Table

Long term Actual ReportedDPMO Sigm a (long term ) Sigm a (short term )

500,000 0 1.5460,172 0.1 1.6420,740 0.2 1.7382,089 0.3 1.8344,578 0.4 1.9308,538 0.5 2274,253 0.6 2.1241,964 0.7 2.2211,855 0.8 2.3184,060 0.9 2.4158,655 1 2.5135,666 1.1 2.6115,070 1.2 2.7

96,801 1.3 2.880,757 1.4 2.966,807 1.5 354,799 1.6 3.144,565 1.7 3.235,930 1.8 3.328,716 1.9 3.422,750 2 3.517,864 2.1 3.613,903 2.2 3.710,724 2.3 3.8

8,198 2.4 3.96,210 2.5 44,661 2.6 4.13,467 2.7 4.22,555 2.8 4.31,866 2.9 4.41,350 3 4.5

968 3.1 4.6687 3.2 4.7483 3.3 4.8337 3.4 4.9233 3.5 5159 3.6 5.1108 3.7 5.2

72 3.8 5.348 3.9 5.432 4 5.521 4.1 5.613 4.2 5.7

9 4.3 5.85 4.4 5.9

3.4 4.5 6

2 308,5383 66,8074 6,2105 2336 3.4

ZSTZST DPMODPMO

ZST = 1.6 for 450,000 DPMO

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How would the customer measure the process performance?

First, determine the unit, defect opportunities per unit, and the number of defects from each perspective.

For this example, assume the process of reviewing and correcting invoices is 100% effective.

Use the worksheets on the following pages.

41DPMO Calculation

Example

Customer CTQsInvoice mailed on date specifiedInvoice is error free

– Correct address– Correct amount

Prepare Invoice

500 Preliminary Invoices

Review Invoice

Fix Errors

Mail Invoice

446 Accurate Invoices

470 Invoices Mailed On-Time

30 Invoices Mailed Late

Errors Detected28 – Wrong amount14 – Wrong address12 – Improper accounting code

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The unit in this case is an invoice. Hence, there are 500 units for this example.

Based on the CTQ’s listed for this example, there are 3 defect opportunities per unit–late, wrong amount, and wrong address.

Therefore, the total number of defects is 30 late, 28 wrong amount, and 14 wrong address for a total of 72.

Even though the errors on the accounting code were detected and corrected, they are not counted for this process. The CTQ’s stated here are for our external customers. They do not care if our accounting codes are correct; therefore, this “error” is not one of their CTQ’s. If we were to examine this from the perspective of our internal customer, the list of CTQ’s would be different..

Now calculate the DPMO and determine the capability.

42Calculating Process Sigma Discrete Data Method

1. Number of Units processed U = __________

2. Number of Defect Opportunities Per Unit OP = __________

3. Total number of Defects made D = __________ (include defects made and later fixed)

4. Solve for Defects Per Opportunity

= = 0.048

5. Convert DPO to DPMO

6. Look up Process Sigma in Abridged Process Sigma Conversion Table ZST = 3.1

( 72 )( 500 ) ( 3 )

DU∗ OPDPO =

DPMO = DPO ∗ 1,000,000 = 0.048 ∗ 1,000,000 = 48,000

500

3

72

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43Exercise–Calculating Process Sigma Discrete Data

1. Number of Units processed U = __________

2. Number of Defect Opportunities Per Unit OP = __________

3. Total number of Defects made D = __________

4. Solve for Defects Per Opportunity

= =

5. Convert DPO to DPMO

6. Look up Process Sigma in Abridged Process Sigma Conversion Table ZST =

( )( ) ( )

DU∗ OPDPO =

DPMO = DPO ∗ 1,000,000 = ( ) ∗ 1,000,000 =

500

3

30

Let’s verify our answer using Minitab’s Product Report.

1. First open a blank worksheet and enter 3 column headings and your data:

Defects Units Opportunities30 500 3

2. Six Sigma > Product ReportDefects = DefectsUnits = UnitsOpportunities = Opportunities

3. Click “OK”

4. Verify ZBench = ZST (from your calculations)

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44Activity–Calculating Process Capability–Discrete Data

Project: Billing Product ImprovementCTQ: Complete Billing InformationDefect: Information missing from billUnit: A billOpportunities for defect per unit: 3 (items of information that can be missing on each bill)Out of 50 bills, you find 20 defectsWhat is the sigma level of the process?

What is the DPMO value for this process?

Now let’s look at how to calculate process capability for discrete data in Minitab, using the Six Sigma Product Report.

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45Six Sigma Product Report


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46Discrete Data Examples

1. Select Defects, Units 2, & Opportunities

2. Select OK.

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47Six Sigma Product Report Output

Characteristic

1

Total

Defs

89

89

Units

506

Opps

1

TotOpps

506

506

DPU

0.176

DPO

0.175889

0.175889

PPM

175889

175889

ZShift

1.500

1.500

ZBench

2.431

2.431

Report 7: Product Performance

DU

OP

DPMO ZST

In addition to the Product Performance table, Minitab provides two graphical charts for discrete data. The product benchmarks allows one to see visually how theZBench values compare for each characteristic (8A).

To verify our answer:

DPO =

DPMO =

Go to Abridged Process Sigma Conversion Table,

)( )( 0.1758891506

89

OPU

D==

∗

175,8891,000,000DPO =∗

2.4ST

Z =

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48Yield

Four parts are made1. After first inspection: 1 passed, 3 failed

Rework 3 parts

2. After second inspection: 1 passed, 2 failedRework 2 parts

3. After third inspection: 1 passed, 1 scrapped

What is the Yield of this Process?What is the Yield of this Process?

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49Types Of Yield

Classical Yield = YC = 3/4 = 75%Classical yield is the percent of defect-free parts for the whole process divided by the total number of parts inspected. If we say the yield is 3/4 or 75%, we lose valuable data on the true performance of the process. This loss of insight becomes a barrier to process improvement.

First-Time Yield = YFT = 1/4 = 25%First-time yield is the percent of defect-free parts divided by the total number of parts inspected for the first time. If we say the yield is 1/4 or 25%, we are really talking about the First-Time Yield (FTY). This is the best yield estimate to drive improvement. This is also Throughput Yield (YTP): the percent of units that pass through an operation without any defects.

Classical Yield:YC = ¾# parts making it through final inspections = 3Total # Parts = 4

First-Time YieldYFT = ¼# Parts that are acceptable after first inspection = 1Total # Parts = 4

Probability of Single Unit Being Defect-Free (SDF)SDF = P(0) = e-DPU = e-2.25 = .1054 = 10.54%DPU = Defects per unit = 9/4 = 2.25

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When the defects of the subsequent operations are independent, rolled throughput yield (YRT) = .99 x .99 = .9808

50Extending The Concept

A given process has two operations. Each operation has a throughput yield of 99 %. The rolled yield equals:

. . . There is an 98% probability that any given unit of product could pass through both operations defect free.

99% 99% 98%

Op 1 OutputOp 2x =

Without Inspection or Test Without Inspection or Test Without Inspection or Test

Process Centered Process Centered

Rolled Throughput Yield = YRT = 98%Rolled Throughput Yield = YRT = 98%

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You can establish a yield for each step of your process. If you have multiple processes, each time you go through additional steps, you lose yield at the end of the process.

This is called Rolled Throughput Yield. YRT is calculated by multiplying all the yields together.

The more complex the process, the worse the YRT becomes.

We waste a lot of time scooping up the spilled paint.

51Rolled Throughput Yield (YRT)

G. Reimer 12/21/94 - Charlotte NC

Receive parts from Supplier

Following ReceivingInspection and Line Fall-out...

99.53% Yield (YTP)

From Machining Operations97.13% Yield (YTP)

At Test Stands on first attempt

94.52% Yield (YTP)

RightFirst TimeYRT = .9953*.9713 *.9452 = 91.38%

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Let n denote the number of defects going into an inspection operation.

Let E denote the proportion likelihood of detecting a defect.

Inspection catches E*n.

The number escaping to the customer is (1-E)*n.

If you submit parts with a DPUS level, inspection observes (catches) a DPUO level of E*DPUS = Observed DPU.

The customer sees a product with an escaping DPUE = (1-E)*DPUS.

Submitted DPUS = Observed DPUO + Escaping DPUE.

52Quantification Of Defects

Knowing the observed defect level and the test effectiveness, we can estimate submitted defects and escaping defects.For example:

DPUS = DPUO + DPUEDPUO = DPUS x EDPUE = DPUS x (1-E)

InspectionE = 0.8

SubmittedDPU Level(DPUS )

EscapingDPU Level(DPUE )

Observed DPU Level(DPUO )

Example

If we have a process that is submitting 100 defects (DPUS=100) and our inspection process is 80% effective (E=.8) at finding these defects, then we could observe 80 (DPUO) and 20 would escape to the customer (DPUE).

E = 0.8DPUS=100 DPUE=20

DPUO=80

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The only thing that is real is the DPU observed–that is what we caught at inspection. In this example DPUO = .25.

A typical value for E = .9. Your operation will differ slightly; in this example E = .8.

Review the calculations below:DPUS*.8 = DPUO

DPUS = DPUO /.8

DPUE = DPUS- DPUO

53Quantification Of Defects (continued)

Given:Observed Defects = DPU of 0.25 and E = .8Then:Submitted Defects = DPUS = DPUO /E = (0.25/0.8)

= DPUS = 0.31Escaping Defects = DPUE = DPUS - DPUO = (0.31 - 0.25)

= DPUE = 0.06

InspectionE = 0.8

SubmittedDPUS Level= 0.31 (calc)

EscapingDPUE Level= 0.06 (calc)

Observed DPUO Level = 0.25 (given)

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Use the worksheet on the following page to help you work through this exercise.

54Exercise (15 minutes)

Calculating Submitted, Observed andEscaping Defect LevelsGiven:

The requirement is to ship the product with no more than one defect in 500 units shippedThe final test is to be performed using automatic test equipment having an effectiveness of 0.95

Knowing the maximum level of escaping defects, we can estimatethe maximum defect/unit level:

Observed in the final test. (This sets a minimum throughput yield limit.)Submitted to the final test. (This sets a minimum on the combination of defects created in model assembly and from the escaping defect levels from prior tests.)

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55Exercise (continued)

Calculating Submitted, Observed and Escaping Defect Levels

1. Expressed as a decimal, what is the given acceptable maximum escaping defectlevel? ___________

2. What then is the acceptable maximum defect level for:a. Units submitted to final test? ___________b. Defects observed at final test? __________

3. What is the observed throughput yield figure? ______

InspectionE = 0.95

SubmittedDPUS Level

EscapingDPUE Level

Observed DPUO Level

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56Answers To Exercise

Calculating Submitted, Observed, andEscaping Defect Levels

1. DPUE = = 0.0021500

2. Maximum acceptable submitted defects =

2b. Maximum acceptable observed defects =

DPUO = DPUS - DPUE = 0.040 - 0.002 = 0.038 DPUO

3. YTP = 1-.038 = .962 = 96.2%

0.0020.05

DPUE1 -E

defects escaping1 - effectiveness = = 0.040 DPUSDPUS = =

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57Summary–Discrete Data Process Capability

Define defects, units and opportunities with your team. Be surethe definitions make sense and are consistent with similar processes and customer definitions. Defects will be stated as defects per million opportunities. Discrete data is generally considered long-term data.For discrete data, Minitab Six Sigma product report is used to calculate capability from defects and opportunitiesDetermine DPMO (which is long-term), then determine the corresponding Z–value (ST capability)

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58Summary–Z-Shift

Often, you must assume a shift value (default 1.5) to estimate short-term capability Our customers experience the long-term capability of the processTo minimize shift, we need to reduce special cause variation

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5.1 Identify Performance Objectives.




What does it mean to Define Performance Objectives?A performance objective is a statement of your project Y’s performance level that will satisfy the project CTQ(s). It is the projected reduction in defects you plan to achieve for your process or product. Typically, this is stated in terms of defects per million opportunities (DPMO) reduction and a corresponding target Z-value. In Step 4 you determined the current process performance. In Step 5 you will state what the end results of the Six Sigma project will be by statistically defining the goal of the project.In addition, an estimate of financial benefits is due in Analyze.

Why is it important to Define Performance Objectives?It is important to identify your improvement goals in measurable terms in order to define the level of improvement you wish to achieve and provide a focused target toward which you can direct your efforts.

What are the project tasks for completing Analyze 5?5.1 Identify Performance Objectives.

Analyze 5–Define Performance Objectives 1

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2How Do I Define My Performance Objectives?

Use benchmarkingUse other sources

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3Defining Performance Objectives With Benchmarking

If I benchmark, performance standards are based upon:Closing the gap with the competitionExceeded projected competitive performanceSimilar performance in dissimilar businessesGathering best practices from multiple sources to become best in classBecoming as good or better than a substitute product/service

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4Defining Performance Objectives With Other Sources

If I don’t benchmark, performance objectives are based upon:For a process with ZST ≤ 3 Sigma Capability, decrease % defects by 10x and for ZST > 3, decrease % defects by 2xIf your process is in statistical control (Run Chart), the next improved performance objective comes from a capability investment as in facilities, equipment, digitization, etc.Corporate mandateCompliance/legalVOC data

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The remaining pages are for your reference on Benchmarking.

There are different types of Benchmarking. These include:

Competitive BenchmarkingProduct BenchmarkingProcess BenchmarkingBest Practices Benchmarking

5Nature Of Benchmarking–Reference Material

Benchmarking is the process of continually searching for the best methods, practices and processes, and either adopting or adapting their good features and implementing them to become the “best ofthe best”.

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6What It Is And What It Isn’t

Benchmarking Is…

A continuous processA process of investigation that provides valuable informationA process of learning from others; a pragmatic search for ideasA time-consuming, labor-intensive process requiring disciplineA viable tool that provides useful information for improving virtually any business process

Benchmarking Isn’t…

A one-time eventA process of investigation that provides simple answersCopying, imitatingQuick and easy

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7Common Benchmarking Mistakes

1. Internal process(es) is unexamined2. Site visits “feel good,” but don’t elicit data or ideas3. Questions and goals are vague4. The effort is too broad or has too many parameters5. The focus is not on processes6. The team is not committed to the effort7. Homework and/or advanced research isn’t assigned8. The wrong benchmarking partner is selected9. The effort fails to look outside the industry (outside the box)10. No follow-up action is taken

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Feel comfortable with and confident about your homeworkFoster the right atmosphere to maximize resultsConclude in thanking organization and ensure follow-up if necessary

Research the organization and ground yourself in their processesDevelop a detailed questionnaire to obtain desired informationSet up logistics and send preliminary documents to organization

Review team observations and compile report of visitCompile list of best practices and match to improvement needsStructure action items, identify owners and move into Improve phase

Identify Process to Benchmark

Select process and define defect and opportunitiesMeasure current process capability and establish goalUnderstand detailed process that needs improvement

Select Organization to Benchmark

Outline industries/functions which perform your processFormulate list of world class performersContact the organization and network through to key contact

Prepare for the Visit

Visit the Organization

Debrief & Develop an Action Plan

Retain and Communicate

Report out to business management and 6σ leadersPost findings and/or visit report on local server/6σ bulletin boardEnter information on GE Intranet benchmarking project database

Benchmarking Six-Step Process 8

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9Sources Of Information

Library Database Company WatchesInternal Reviews NewspapersInternal Publications AdvertisementsProfessional Associations NewslettersIndustry Publications Original ResearchSpecial Industry Reports Customer FeedbackFunctional Trade Publications Supplier FeedbackSeminars Telephone SurveysIndustry Data Firms Inquiry ServiceIndustry Experts NetworksUniversity Sources Worldwide Web

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10Capital Logistics Case Study

Project Goal(s)Reduction of deliveries that are too early or too late

Benchmarking ProcessIdentified 20 similar 3rd party Logistics providers from Logistician MagazineSelected 3PL (2) that provide supply chain solutions to the petroleum industry (Non-competitors–Capital Logistics strategically avoids supporting petroleum industry because of risks)Polled logistics managers (telephone polls) to determine delivery practices

ResultsIdentified one viable new delivery method…The Dynamic Routing System

– Computer system that selects routes based on individual driver performance for load types and regional deliveries

Invited Petro-hauz to Stamford, CT for product demo with Capital Logistics Engineering and Technology Teams

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11

For the Capital Logistics Case Study– Target is the same = 0 minutes– Best in Class performance is a s = 12 minutes– Theoretical calculation of Sigma based on normal distribution would be

Benchmarking Example

Characteristic

1

Defs

60

Units

25000

Opps

1

TotOpps

25000

DPU

0.002

DPO

0.002400

PPM

2400

ZShift

1.500

ZBench

4.320

Report 7: Product Performance

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12Summary–Analyze 5

A performance objective is determined by using Z–short-term, benchmarking, or defect reduction goals Benchmarking is a process of identifying best practices, measuring our own practices against those best practices, and adapting the appropriate best practices to our own processesRevenue & cost implications are also due for benefit analysis

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6.1 Identify possible causes of variation6.2 Narrow list of potential causes




What does it mean to Identify Variation Sources?In step 6 you develop a list of statistically significant X’s, chosen based on analysis of historical data. This list is then prioritized to identify those X’s that have the most impact on the project Y. The question in this step is “What are the variables that are preventing us from reaching our goal?” You will identify all possible X’s before selecting the Critical (or Vital Few) X’s in the next step.

Why is it important to Identify Variation Sources?The output of a process (Y) is a function of the input sources of variation (X’s). In other words, you can change the output of a process (Y) only by changing the input & process variables (X’s). Therefore, in order to improve products and processes, you must shift your focus from monitoring the outputs of a process (Y’s) to optimizing the inputs to the process and correcting the root causes of defects (X’s). You should use data and process analysis to identify potential X’s, and not make any assumptions.

What are the project tasks for completing Analyze 6?6.1 Identify possible causes of variation6.2 Narrow list of potential causes

Analyze 6–Identify Variation Sources 1

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2Identify The Vital Few

Transfer Function

=

Project Y Relationship that explains Y in terms of X

Process variables

YY ff (X)(X)

Understanding The ƒ Gives Insight Into The Vital Few X’s

Understanding The ƒ Gives Insight Into The Vital Few X’s

The Project Y (or dependent variable) is determined by the values of the process variables X (or independent variables). Once we have a clearer understanding of the relationship between the X and Y (f–transfer function), we will be able to pinpoint the key X’s that drive the variation in Y.

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3Identify The Vital Few

Process Measures(X’s)

Process

InputMeasures

(X’s)Outputs

(Y’s)

X X X X

Definitions:Project Y (Dependent Variable)Product or service produced or delivered by the processProcess X’s (Independent Variable)Those variables that influence the output and are generally controllable by those who operate the processInput X’s (Independent Variable)Materials and information used by the process to create the outputs. Inputs are often outside the control of the process operator.

ProcessProvides context for improvementLinks outputs (Y’s) to inputs (X’s) and process variables (X’s)

In Analyze 6 we will be analyzing upstream variables, or input and process variables (X’s), to determine how they affect output variables (Y’s) and to what extent.

Remember Y=f (X1, X2, ..., Xn)

or in words…. The results we get (the Y’s) are a function of the process and input variables (the X’s). In Analyze, we will study the process and the data in order to gain understanding of how it all fits together.

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4

Analyze 6.1: Identify Possible Causes of Variation

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5Methods To Identify Possible Sources Of Variation

Methods To Identify Vital X’s

Graphical Analysis

Process Map Analysis



ProblemStatement

As we work our way down into the process seeking the vital few causes, we analyze both the data and the process–gaining knowledge of what impacts the output. How do the various X’s impact the Y’s? With this knowledge, we will pursue a solution that will improve the process.

We have already learned about graphical analysis, process map analysis and cause and effect analysis in previous modules. In step 6, we will learn how to apply them in the Analyze phase.

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6Review: Graphical Analysis

Looking For Patterns In Data

Continuous Y Discrete YBoxplot Pareto ChartScatterplotHistogram

We learned about these tools in the Minitab and Graphical Analysis module. These graphical analysis tools are used in the Analyze phase to look for patterns in the project Y data that help to identify potential critical X’s.

Let’s do an activity to briefly review these tools.

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7Review Activity–Which Graphical Analysis Tool Would You Use?

For each scenario described below, which tool would you use to investigate? For each scenario, what pattern would you look for to make your conclusions?

1. (a) A Six Sigma project is being conducted in the field to improve the cycle time for warranty repair returns. The warranty return cycle time was measured for a period of 6 weeks for 4 regions. The Green Belt wants to investigate whether there is any difference in average warranty repair cycle time between each of the regions.

(b) The Green Belt would also like to know if there is any difference in the variance of the cycle time between each of the regions.

2. Checks Are Us is a payroll processing firm. Timecard errors are routinely monitored and recorded. A Black Belt investigating the errors wishes to determine if there are any differences in the number of errors between five of its major customers. The number of errors contained in a sample of 150 employees was recorded for five weeks. How would you proceed with stratifying the data to make this investigation?

3. Tungsten steel erosion shields are fitted to the low pressure blading in steam turbines. The most important feature of a shield is its resistance to wear. Resistance to wear can be measured by abrasion loss, which is thought to be associated with the hardness of steel. How would you investigate the relationship between hardness (the X) and abrasion loss (the Y)?

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To create Boxplots:Stat > Basic Statistics: > Display Descriptive Statisticsvariable: timeclick: by variable: load type or driverclick Graph > Choose Boxplots

To create Scatter Plots:Graph > PlotX: DistanceY: Time

Graphical Analysis–Breakout Activity (15 minutes) 8

Desired Outcome: Identify possible causes of variation in the Capital Logistics case study data. File: Green Belt Case Study.mtw

AllBe prepared to share your resultswith the class

ReportOut

15 mins.AllUse the appropriate graphicalanalysis tool in Minitab toinvestigate

– Differences in delivery cycle timebetween the two different loadtypes (See note below)

– Differences in delivery timebetween drivers

– Relationship between delivery cycle time and distance

MinitabAnalysis

TimingWhoHowWhat

Load types: D/H Drop & Hook–A driver unhooks their full trailer, and then hooks into an empty to take back. Unload–The driver opens the trailer and allows the store to unload its freight, and brings back the trailer.

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9Process Map Analysis

Types Of AnalysisMoments of truth–What does the customer feel?Nature of work–What is of value to the customer?Flow of work–What makes the customer wait?

The purpose of Process Map Analysis is to:View our process and its performance from the customer’s perspectiveIdentify current process problems and opportunitiesCreate a shared sense of urgency for improving the process clearly identify and document value-added/nonvalue-added activities and process flow measures and characteristics.

There are three key components to the Process Map Analysis step:

The first, Moments of Truth, ensures that we are “Completely Satisfying Customer Needs” through a customer-focused process improvement perspective.

The second, Nature of Work, is concerned with value analysis: understanding whether or not the work in your process is valued by the customer or by your internal culture.

The third, Flow of Work, characterizes the work along the dimension of time. The two latter components are focused on the “Profitability” piece of the GE Capital Quality Vision.

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10Moments Of Truth

A Typical Deployment Flow Chart

Customer

IntermediariesOr Front Line

BackroomActivity

Support Or Suppliers

Initial Contact Service/Produce Delivery Follow-Up

Moments of Truth

Moments of Truth

A moment of truth is defined as anytime a customer draws a critical judgment, positive or negative, about the service, based upon a service experience (or lack thereof). Certainly every time we “touch” the customer is a moment of truth, but it isn’t limited to these cases.

From the customer’s view, the process is a set of service encounters. In this case, the customers believe the steps should be simple: apply for the loan and receive the money.

In the best of cases, the customer is unaware of all the hard work, delays, and hand-offs which go into making their loan a reality. It occurs behind the scenes.

“If you’re a service person and you get it wrong at your point in the customer’s chain of experience, you are very likely erasing from the customer’s mind all the memories of the good treatment he or she may have had up until now.

But if you get it right, you have a chance to undo all the wrongs that may have happened before the customer got to you. You really are the moment of truth.”

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11Nature Of Work–Value Analysis

Value-Added Work Nonvalue-Added Work

Value-Enabling Work

Steps That Are Considered Non-Essential To Produce And Deliver The Product Or Service To Meet The Customer’s Needs And Requirements. The Customer Is Not WillingTo Pay For Them.

Steps That Are Considered Non-Essential To Produce And Deliver The Product Or Service To Meet The Customer’s Needs And Requirements. The Customer Is Not WillingTo Pay For Them.

Steps That Are Essential Because They Physically Change The Product/Service, The Customer Is Willing To Pay For Them, And They Are Done Right The First Time.

Steps That Are Essential Because They Physically Change The Product/Service, The Customer Is Willing To Pay For Them, And They Are Done Right The First Time.

Steps That Are Not Essential To The Customer, But That Allow The Value-Adding Tasks To Be Done Better/Faster.

Steps That Are Not Essential To The Customer, But That Allow The Value-Adding Tasks To Be Done Better/Faster.

Your policies address only control issuesThere are more managers than workersPeople get rewarded for managing problems (e.g., Manager of Reissues, Special Expediting)Rework is a common characteristic of most processes

– RE’s are things in your process that are done more than one time (Redo, Recall, Reissue).

– RE’s usually cause you to loop back to an earlier point in your process.

– RE’s consume time, add to the complexity, and use additional resources.

OPTIONAL: Show the video: “Time the dimension of Quality”

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12Types Of Nonvalue–Added Work

Internal FailureInternal Failure DelayDelay

External FailureExternal Failure Preparation/Set-UpPreparation/Set-Up

Control/InspectionControl/Inspection MoveMove

What Does The Customer Value?What Does The Customer Value?

Internal FailureSteps that are related to correcting in-process errors due to failures in current or prior step in the process. Example:

ReworkExternal FailureSteps which relate to fixing errors in the product that the customer has found and has returned to you. Examples:

Customer Follow-upRecallControl/InspectionSteps for internal process review often referred to as “the checker-checking-the checker.” Examples:Approval/reviewInspectionBureaucracy

DelaySteps where work is waiting to be processed at that step.Examples:

BacklogsQueuesStorageBottlenecks

Preparation/Set-UpSteps that prepare work for a subsequent activity in the process.Examples:

Entering into a computerRetrieve policies/pricing

MoveSteps that entail the physical transport or transmit of outputs between activities in a process.Example:

Fax/mail

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13Flow Of Work

Cycle TimeCycle Time

Process TimeProcess Time

Delay TimeDelay Time+

To analyze the flow of work, break the process flow down to its lowest component, and analyze the movement of the component through the process. For example, “become an application” and trace its progress through the process. It is similar to a process flowchart, but with the value-added and nonvalue-added steps clearly identified.

Terms

Cycle TimeThe total time from the point in which a customer requests a good or service until the good or service is delivered to the customer. Cycle time includes process time and delay time.

Process TimeThe total time that a unit of work is having something done to it other than time due to delays or waiting. It includes the time taken for value-added steps, internal failure, external failure, control, inspection, preparation/set-up, and more.

Delay TimeTotal time in which a unit of work is waiting to have something done to it.

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14Flow Of Work–Process Disconnects

GapsRedundanciesImplicit or unclear requirementsInefficient hand-offsConflicting objectivesCommon problem areas

Process disconnects can often be found where there are delays in the process. These are points in the process where work can be disrupted or delayed, or where defects can be created. They include:

Gaps: responsibility for a given step in the process is unclear, or the process seems to go off track.Redundancies: duplication of efforts such as when two people or groups approve a document. Redundancies occur when different groups take action that they are unaware is being done somewhere else in the process.Implicit or unclear requirements: operational definitions do not exist or clear differences exist in perspective or interpretation.

Inefficient hand-offs: no check is in place to assure the process is continuing without delays. For example, Department A sends something to Department B but neither has a way to know if it was properly received.Conflicting objectives: the goals of one group cause problems or errors for another. For example, one group is focused on process speed while another is oriented to error reduction–the result may be that neither group accomplishes its objectives.Common problem areas: occurs when steps are repeated in a variety of places in process. Noting these areas may provide insight into potential solutions.

Your team should encode these “disconnects” and highlight them directly on your process map.

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15Flow Of Work–”Be The Unit”

Unclear requirements

1. Receive application in mail and open

envelope

2. Place application in

mail slot

3. Move application to Entry Dept.

4. Place application in

in-box

5. Retrieve application and

review for completeness

Is application complete?

7. Enter applicationto computer

system

6. Call to obtain necessary information

8. Score application

9. Queue application for credit review

10. Review for completeness

and make decision

Are we extending

loan?

19. Generate turndown letter

12. Generate loan packet

13. Place in out-box

14. Move to mailroom

15. Wait for postage

16. Post package or letter

17. Place in outbound mail

basket

18. Postman picks up

outbound mail

No

Yes

Yes

No

Unclear requirements

Inefficient hand-off

Redundancy

Inefficient hand-off

11. Make loandecision

Cycle time is the total time taken from the point at which the customer requests a good or service until the good or service is delivered to the customer. It is the sum of the process time, move time, inspect time, delay time, and storage time.

Cycle time analysis often provides eye-opening insights. People seldom think of work in this context. When an Improvement Team presents cycle time data, management may become defensive. For example, when one manager at a commercial insurer found out it was taking 100 days, on average, to process the commercial line of a new business, she resisted the analysis. After heated “discussion,” she suggested that the period sampled did not reflect normal conditions. She recommended looking at another period of time to get a “better number.” The team obliged. The next sample averaged 103 days!

Constructing a time line helps identify areas of potential improvement by illustrating the time required for each step in a process.

Remember:Time data may not be available for all steps in a process. Some possible sources include:

Time, schedule, and activity logsFiles, studies, and reports

If data is not available:

Estimate and ten track to determine actual average value

Use minimum of 30 data points to determine an average value when calculating averages, also record the highest and lowest time so consistency is understood.

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16Linking Value Analysis With Process Flow

Summarized Analysis

Process Step

Est. Avg. Time (Mins)

Value-Added

Nonvalue-Added

Internal Failure

External Failure

Control/Inspection

Delay

Prep/Set-Up

Move

Value-Enabling

Total

1 2 3 5 6 7 8 9 10 144 1211 13 15 16 17 18

1 1803 7120 12015 51051201 1202120159015

Total%

Total

3.1%

957

72.1%690

.8%8

100%

48 5.0%

30

100%

180 18.8%

1 .1%

19

9578

% Steps

Linking value analysis with cycle time analysis creates a compelling business case for change.

Displaying this information on process maps emphasizes focus areas for improvement.

Tips/TrapsDon’t get stuck on deciding if a step isvalue-added or nonvalue-added– Allow the team to discuss it.– Consensus with 2/3s majority vote.Push the team to make the process map a true “as is.”– The ratio for an average “as is” map is 20% value-

added, 80% nonvalue-added.– Think of the process map from the point of view of

the product or service.

Conclusion: Example7 steps (-40% of total steps) provide 100% value and take 48 minutes or 7% of total cycle time.11 steps (-61% of steps) are non-value-added, and consume 94.9% of cycle time.

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17Review: Cause & Effect Diagrams

A visual tool used by an improvement team to brainstorm and logically organize possible causes for a specific problem or effect.



Potential High-Level Causes ProblemStatement

We learned about this tool in the Measure phase. In the Analyze phase the Cause and Effect diagram is often used to identify X’s.

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18Cause & Effect Diagrams–The Five Why’s

The “Five Why’s” drill deep into the process to identify potential Root Cause(s)

Ask “why” five times to identify deeper causesUse process data to answer each “why” question

ExampleA project team has verified that the X (complicated form) accounts for the difference in cycle times between small and medium loans. They use the Five Why’s to drill deeper in the process.

1. Why do complicated forms cause delays in the underwriting steps?

Because underwriters receive incomplete applications

2. Why do they receive incomplete applications?Because customers don’t fill out the form accurately or completely

3. Why don’t customers fill out the form accurately or completely?

Because the format is confusing

4. Why is the format confusing?Because the directions are hard to read

5. Why are the directions hard to read?Because the font size is too small

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Desired Outcome: Identify possible causes of variation in the Capital Logistics case study data

Cause And Effect–A Breakout Activity (25 minutes) 19

5 mins.AllChoose a spokesperson to share theresults with the class

Close

AllUse the ask “why” approach to identifydeeper causes as appropriate

FiveWhy’s

15 mins.AllAs a result of the QFD constructed in Measure 1 for the Capital Logistics customer service desk, a project team elects a project Y of cycle time toresolve customer problems

In the Analyze phase of the project, the team uses a cause and effect diagramto brainstorm potential X’s

Construct a cause and effect diagramfor the problem statement “Why is it taking too long to resolve customer problems?”

Base cause and effect diagram on yourgeneral knowledge of customer servicedesks. What might be potential X’s?

Construct Cause And EffectDiagram

5 mins.AllSelect a facilitator, scribe and timekeeperPreparation

TimingWhoHowWhat

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20Prioritization Of X’s–Control/Impact Matrix

In Our Control

Out Of Our Control

CONTROL

IMPACT

High Medium Low

Always Verify With DataAlways Verify With Data

Use your team’s process knowledge and business experience to list possible X’s in a Control/Impact Matrix. Then use process data to verify or disprove placement of the X’s.

Prioritization Steps

1. Using the Control/Impact Matrix shown above, examine each X in light of two questions:

What is the impact of this X on our process?Is this X in our team’s control or out of our team’s control?

2. With your team, place each X in the appropriate box on the matrix.

3. The validated matrix is a guide to addressing the X’s. Begin with the “High Impact/In Our Control” category.

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21Prioritization Of X’s–Control/Impact Matrix (continued)

Too manydefectsComplicatedformToo muchreviewDuplicationof effort

Too long forcustomernumber

ComplexityEvaluationof riskworthiness

Too long toget creditreport

Not enoughstaffNot welltrained

In Our Control

Out Of Our Control

CONTROL

IMPACTHigh Medium Low

ExampleMethodsMachines

People

MaterialsWhy Is There

Difference In The Variation In Cycle

Time Between Small And Medium Loans?

Why Is There Difference In The Variation In Cycle

Time Between Small And Medium Loans?

MotherNature

Measure-ments

The project team completed the Cause & Effect diagram and the prioritization matrix. The X’s that are identified as “in control/high impact” appear to be the top priority. However, the team should discuss the other X’s to make sure they have reached consensus for those priority X’s.

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Desired Outcome: Practice using a Control/Impact Matrix to prioritize X’s

Control/Impact Matrix–Breakout Activity (15 minutes) 22

3 mins.AllChoose a spokesperson to report out on your high impact X’s. Are all of these X’s within the control of theteam?

Close

10 mins.AllUse the Control/Impact Matrix onthe next page to prioritize the X’sidentified by your team

Prioritize Potential X’s

AllReview the potential X’s generated for the customer service desk projectin the cause and effect diagramactivity

Construct Cause And EffectDiagram

2 mins.AllChoose a facilitator, scribe,timekeeper and/or note taker

Preparation

TimingWhoHowWhat

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23Prioritization Of X’s–Control/impact Matrix

In Our Control

Out Of Our Control

CONTROL

IMPACT

High Medium Low

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24

Analyze 6.2 Narrow list of Potential Causes

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25The Idea Of Sampling

Population (Universe): A set of characteristics that defines membership in the complete set.

Why should we take a sample?

Should the sample be random?

Is it possible to have sampling error?

How many samples should be taken?

What are some everyday examples of sampling?

Based on the sample, we make decisions about the population.

Sample: A subset of members that possesses the same characteristics as that of the population.

In most cases under study, it is impossible to measure every element of a population. In particular, we want samples that consist of observations that are independent and random. These samples, called random samples, can be used to make decisions about the population. This involves a certain amount of risk. We can minimize this risk, and, more importantly, understand what the risks are if we use statistical tests.

If you were interested in finding the average height of all of the people in the United States, what advantages would exist in taking a sample?

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26Hypothesis Testing–Introduction

Refers to the use of statistical analysis to determine if observed differences between two or more data samples are due to random chance or to be true differences in the samplesIncrease your confidence that probable X’s are statistically significantUsed when you need to be confident that a statistical differenceexists

An assertion or conjecture about one or more parameters of a population(s).

To determine whether it is true or false, we must examine the entire population, this is impossible!!Instead, use a random sample to provide evidencethat either supports or does not support the hypothesisThe conclusion is then based upon statistical significanceIt is important to remember that this conclusion isan inference about the population determined from the sample data

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27Hypothesis Testing For Equal Means

The histograms below show the height of inhabitants of countriesA and B.Both samples are of size 100, the scale is the same, and the unit of measurement is inches.Question: Is the population of country B, on average, taller than that of country A?

Country A

Country B[inch]60.0 62.0 64.0 66.0 68.0 70.0 72.0 74.0 76.0 78.0 80.0

Issue: how conclusive is the evidence that the sample results indicate a real, more-than-random effect in the underlying population or process?

In the Analyze phase we will try to determine which X’s have an effect on the Y. We can compare two sets of data, with X set at different values, thereby determining if that X has an effect.

Examples: Does a process perform better using machine/material/fixture/tool A or B? Does the purchased material conform to the desired specifications? Is there a difference in performance between vendor A or B? Is there a difference in your process after you make a change? Is the process on target?

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28Concepts Of Hypothesis Testing

1. All processes have variation.

2. Samples from one given process may vary.

3. How can we differentiate between sample–based “chance” variation anda true process difference?

To improve processes, we need to identify factors which impact the mean or standard deviation.

Once we have identified these factors and made adjustments for improvement, we need to validate actual improvements in our processes.

Sometimes we cannot decide graphically or by using calculated statistics (sample mean and standard deviation) if there is a statistically significant difference between processes.

In such cases the decision will be subjective.

We perform a formal statistical hypothesis test to decide objectively whether there is a difference.

This way everyone makes the same decisions.

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29Kinds Of Differences

Continuous data:Differences in averagesDifferences in variationDifferences in distribution “shape” of values

Discrete data:Differences in proportions

There are a variety of different hypothesis tests. Each one tests for a different kind of “difference.”

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30Hypothesis Testing

Guilty vs. Innocent Example

The American justice system can be used to illustrate theconcept of hypothesis testing.

In America, we assume innocence until proven guilty.This corresponds to the null hypothesis.

It requires strong evidence “beyond a reasonable doubt”to convict the defendant. This corresponds to rejecting the nullhypothesis and accepting the alternate hypothesis.

Ho: person is innocentHa: person is guilty

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31Nature Of Hypothesis

Null Hypothesis (Ho):Usually describes a status quoThe one you assume unless otherwise shownThe one you reject or fail to reject based upon evidenceSigns used in Minitab:= or > or <

Alternative Hypothesis (Ha):Usually describes a differenceSigns used in Minitab:

or < or >≠

Note that we are not proving the hypothesis to be true or false. We will reject or fail to reject the null hypothesis based on the evidence from our samples. Failing to reject the null hypothesis implies that the data does not provide sufficient evidence to conclude that a difference exists. On the other hand, rejection of the null hypothesis implies that the sample data provides sufficient evidence to say that a difference exists.

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32Activity–Hypothesis Statements (10 minutes)

Scenario 1: You have collected delivery time of supplier A and supplier B. You wish to test whether or not there is a difference in delivery time from supplier A and B.

Null hypothesis statement :

Alternate hypothesis statement:

Scenario 2: You suspect that there is a difference in cycle time to process purchase orders in site 1 of your company compared to site 2. You are going to perform a hypothesis test to verify your hypothesis.



Scenario 3: You have implemented process improvements to reduce the cycle time to process purchase orders in your company. You have collected cycle time before the process improvements and after the process improvement was implemented. You are going to perform a hypothesis test to verify that the process improvements have resulted in a reduction in cycle time.



Write the null and alternate hypothesis testing statements for each scenario below:

Scenario 1: You have collected delivery time of supplier A and supplier B. You wish to test whether or not there is a difference in delivery time from supplier A and B.



Scenario 2: You suspect that there is a difference in cycle time to processpurchase orders in site 1 of your company compared to site 2. You are going to perform a hypothesis test to verify your hypothesis.



Scenario 3: You have implemented process improvements to reduce the cycle time to process purchase orders in your company. You have collected cycle time before the process improvements and after the processimprovement was implemented. You are going to perform a hypothesis test to verify that the process improvements have resulted in a reduction in cycle time.



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Guilty vs. Innocent ExampleThe only four possible outcomes:1. An innocent person is set free. Correct decision

2. An innocent person is jailed. Type I error = α– The probability of this type of error occurring we represent as

3. A guilty person is set free. Type II error = β– The probability of this type of error occurring we represent as

4. A guilty person is jailed. Correct decision

Why is it important to minimize the chance of making a Type I error in a six-sigma project?

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34Hypothesis Testing–Another View

TruthTruth

Ho Ha

VerdictVerdict

Ho

Ha

Innocent,JailedType Iα

Guilty,Set FreeType II

β

Innocent,Set Free

Guilty,Jailed

Innocent Guilty

Set Free

Jailed

Ho: Person is innocent.Ha: Person is guilty.

This is a visual way of looking at the four possible outcomes of hypothesis testing.

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The P-value is calculated by MinitabThe probability of getting the observed difference or greater when the Ho is true. If p ≥ 0.05, then there is no statistical evidence of a difference existing.Ranges from 0.0 - 1.0The alpha (α) level is usually set at 0.05. Alpha is the probability of making a Type I Error (concluding there is a statistical difference between samples when there really is no difference).

P < α: Reject HoP > α : Accept Ho

The p (probability) value is the statistical measure for the strength of H0, usually reported with a range between 0.0 and 1.0. The higher the p-value, the more evidence we have to support H0, that there is no difference. Think of the null hypothesis as a jury trial: the accused is innocent until proven guilty. In hypothesis testing, the samples are assumed equal until proven not. Since we are usually doing a hypothesis test to prove there is a difference, we are looking for p-values less than 0.05.

By convention if p >.05 accept H0 (no difference). If p ≤.05 reject H0 (difference exists).

Reject HoDifferent

Accept HoNot Different

0.00 0.05 1.00

p-value

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Some basic statistical tests are shown below with the command for running each test in Minitab.

Statistical Tests In Minitab 36

Variance among two or more populations is different. Homogeneity of

VarianceStat > ANOVA >

Homogeneity of Variance

Output (Y) changes as the input (X) changes.

LinearRegression

Stat > Regression >Fitted Line Plot

Output counts from two or more subgroups differ.

Chi-Square Testof Independence

Stat > Tables > Cross Tabulation OR

Chi-Square Test

ScatterPlots

C AB D E

Freq

uenc

y

CategoryM NO

What The Tool Tests Statistical Test Graphical TestMean of population data is different from an established target.

1-Sample t-testStat > Basic Statistics

> 1-Sample t

Mean of population 1 is different from mean of population 2.

2-Sample t-testStat > Basic Statistics

> 2-Sample t

The means of two or more populations is different.

1-Way ANOVAStat > ANOVA > One-Way

Histogram

Histogram

Histogram

Normality TestStat > Basic

Statistics

Data is normally distributed

BoxPlots

Pareto

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37Select A Statistical Test

Hypothesis tests to find relationships between project Y and potential X’s

Simple Linear Regression

2 Sample t-Test(Compare Means of two

samples)

ANOVA (Compare means of multiple samples)

Homgeneity of Variance (Compare variances)

ContinuousContinuous DiscreteDiscrete

Discrete

Continuous

XChi-Square Test

Y

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38Hypothesis Test Summary

Normal DataVariance Tests (Continuous Y)X2 - Compares a sample variance to a known

population variance.F-test- Compares two sample variances.Homogeneity of Variance

Levine’s–Compares two or more sample variances

Mean Tests (Continuous Y)T-test One-sample–Tests if sample mean is equal

to a known mean or target.T-test Two-sample–Tests if two sample means are

equal.ANOVA One-Way–Tests if two or more sample

means are equal.ANOVA Two-Way–Tests if means from samples

classified by two categories are equal.Correlation–Tests linear relationship between

two variables.Regression–Defines the linear relationship

between a dependent and independent variable. (Here, “Normality” applies to the residuals of the regression.)

Non-Normal DataVariance Tests (Continuous Y)Homogeneity of Variance Levine’s–Compares two or more sample variances.Median Tests (Continuous Y)Mood’s Median Test–Another test for two or more medians. More robust to outliers in data.Correlation–Tests linear relationship between two variables.Proportion Tests (Continuous Y)P-Test–Tests if two population proportions are equal.Chi-Square Test–Tests if three or more relative counts are equal.

There are a number of hypothesis tests for both normal and non-normal data. You should consult a Black Belt or Master Black Belt if you are not sure which test to use for you project, or if your project involves non-normal data.

The next page shows a summary of the tests that we will look at in detail during this training. We have already looked at the Normality Test in previous modules.

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39We Always Look At Our data In This Way

1. Check Stability–Run Chart, p-values2. Check Shape–Anderson-Darling Normality Test3. Check Spread–Appropriate Hypothesis Test4. Check Center–Appropriate Hypothesis Test

The remainder of this module will teach you how to choose the correct hypothesis test. Not all material will be covered in class. The instructor will choose the tests to cover, based on time restrictions. Prior to taking the GB certification exam you should review this section and go through the Minitab commands.

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40Choosing The Correct Hypothesis Test

Mood’s MedianHOV

CHI SQUARE (χ2)

Multiple GroupsANOVAHOV

Is the data normal?

Are Y’sContinuous?

Comparing Only 2

Groups?

Can I Match X’s With X’s?

Are We Comparing

To A Standard?

Paired t 1 Sample t

NO

NO

NO

NO NO

YES YES

YES

YES

YES

2 Sample t–TestHOV

Are X’sDiscrete?

YES

RegressionNO

Note: In order to use this chart, we are assuming our X’s are discrete. Otherwise, use Regression.

Moods Median Test

Homogeniety of Variance (Hov) – Levene’s Test

Chi Square

Analysis of Variance (ANOVA)

Paired t-Test

One Sample t-Test

Two Sample t-test

n21o ...MedianMedianMedianH ===Different is Median one least AtHa =

2n

23

22

21 σ...σσσHo ===

Different is σ least AtH 2a =

0H 2o == χ

0H 2a ≠= χ

n21o ...H µµµ ===Different is one least AtHa µ=

0DifferenceHo ==0DifferenceHa ≠=

TargetHa ≠= µTargetHo == µ

21oH µµ ==

21aH µµ ≠=

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1. A six-sigma project is being conducted in the field to improve the cycle time for warranty repair returns. The warranty return cycle time was measured for a period of 6 weeks for 4 regions. The Green Belt suspects that there is a difference in average warranty repair cycle time among each of the regions. How would you test whether there is a statistically significant difference in mean cycle time for the different regions?

2. Tungsten steel erosion shields are fitted to the low pressure blading in steam turbines. The most important feature of a shield is its resistance to wear. Resistance to wear can be measured by abrasion loss, which is thought to be associated with the hardness of steel. How would you test whether there is a statistically significant relationship between resistance to wear and abrasion hardness of steel?

3. Your business purchases sheet stock from two different suppliers. It has found an unacceptably large number of defects being caused by thickness beyond tolerance levels. Data for overall mean thickness data was analyzed and found to be on target. Data was collected that would identify a potential difference in the variation of the thickness of the material by supplier.

4. Checks Are Us is a payroll processing firm. Timecard errors are routinely monitored and recorded. A Black Belt investigating the errors wishes to determine if there are any differences in the number of errors among five of its major customers. The number of errors contained in a sample of 150 employees was recorded for five weeks. How would you test if there is a statistically significant difference in the number of errors among the customers?

For each scenario described below, which hypothesis testing toolwould you use? Assume normal distribution, where appropriate

Which Hypothesis Testing Tool Would You Use? 41

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Data Analysis 42

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43Stability–Minitab Run Chart

Let’s look at an example from our GB ANOVA.mpj.

Step 1: Check the stability of the processing time for SOUTH Territory. Are there any trends in the data?

MINITAB FILE: GB ANOVA.mpj

File Description:

Territory (C1): Sales Territory

Zone (C2): city within the sales territory

Total Time (C3): Processing Time- stacked Territories C4-C8– processing time per territory noted

Use Minitab to check the stability of your processing time data by territory.

The Run chart is used to look at the stability of data in time order or sequentially ordered.

Is the process stable over time for the South Territory?

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Stability–Minitab Run Chart 4444Stability–Minitab Run Chart

1. Double Click.

2. Type in a “1.”

Process is Stable if all p-Values are > 0.05Process is Stable if all p-Values are > 0.05

It is important to note that the data should be in time order for run charts to be valid.

A run is one or more consecutive points in the same direction. A new run begins each time there is a change in direction. Do not count points exactly on the median.

Test for Clusters: Ho: No fewer runs observed than expected. Ha: Fewer runs observed than expected. Clusters result from sampling from one process for a period of time and then from another process with a different center for a period so there are fewer runs than expected by sampling error alone.

Test for Mixtures: Ho: No more runs observed than expected. Ha: More runs observed than expected. Mixtures result from two or more processes with different centers alternately sampled so there are too many runs than expected by sampling error alone.

Test for Trends: Ho: No fewer runs observed than expected. Ha: More runs observed than expected. Trends result from a gradual increase or decrease in the measure so that there are fewer runs than expected by sampling error alone.

Test for Oscillations: Ho: No more runs observed than expected. Ha: More runs observed than expected. Oscillations are similar to mixtures in that they indicate too many runs—more than expectedby sampling error alone.

Since all p-values are less than 0.05, the process is stable for the south territory. You would also need to check each of the other territories for stability.

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45The P-Value Review

Alpha is the probability of making a Type I errorThe p-value is the probability of getting the observed difference or greater when Ho is trueUnless there is an exception based on engineering judgment, we will set an acceptance level of a Type I error at a = 0.05Thus, any p-value less than 0.05 means we reject the null hypothesis

p < α: Reject Hop > α: Accept Ho

p < α: Reject Hop > α: Accept Ho

The alpha is another decision criteria. It will give you the same conclusions as the confidence interval.

In general, comparing p-value to alpha is the decision criteria we use most often in this course.

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Data Analysis 46

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47Shape–Minitab Descriptive Statistics

Step 2: Check the shape of the data. Is the data normally distributed?

MINITAB FILE: GB ANOVA.MPJ

Ho: The data is normally distributedHa: The data is not normally distributed

Ho: The data is normally distributedHa: The data is not normally distributed

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48Descriptive Statistics–Input and Output

1. Double Click

3. Click OK 2. Click on Graphs,

Select Graphical Summary

1. Double Click

3. Click OK 2. Click on Graphs,

Select Graphical Summary

0 10 20 30 40


7 8 9 10 11 12 13 14 15 16


Variable: South

A-Squared:P-Value:



8.6366

9.2120

6.9173

3.0950.000

11.934811.1064123.3511.753182.69797

46

1.0000 4.0000 9.0000

14.250045.0000

15.2330

13.9887

12.0000






Non-normal distribution!

0 10 20 30 40


7 8 9 10 11 12 13 14 15 16


Variable: South

A-Squared:P-Value:



8.6366

9.2120

6.9173

3.0950.000

11.934811.1064123.3511.753182.69797

46

1.0000 4.0000 9.0000

14.250045.0000

15.2330

13.9887

12.0000






Non-normal distribution!

Data is Normal if P-Value is > 0.05 (Accept Ho)Data is Normal if P-Value is > 0.05 (Accept Ho)

If the p-value is > 0.05, then we Accept the Ho and the data is normally distributed. In this case, our p-value is 0.000, therefore, we have a non-normal distribution.

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49Non-Parametric Tests

What if I don’t have normal data?

Perform Non-parametric Tests

Use HOV for spread and

Mood’s Median for Center

Normal data allows a great variety of techniques to be used in analyzing itHowever, responding correctly is critical if the data is not normal (which is not at all uncommon)

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50Non-Parametric Tests

One of the advantages of nonparametric tests is that they assume no knowledge about the underlying distributions. They often use an analysis of the ordered ranks of the data.Nonparametric tests are more powerful for non-normal data than the equivalent t-tests and ANOVA testsThe Mood’s Median and Homogeneity of Variance Test(HOV) are nonparametric tests which are very similar to the One-Way ANOVA test

Many times in commercial projects the data are not normally distributed. Cycle time is one example. Cycle time will often be skewed to the right.Another example is ordinal data. This is data that is not continuous but can be placed in ordered categories such as good, better, and best. This often occurs with survey data.In these cases a test that does not depend on assumptions of normality may be very useful

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51Spread–Test On Variances

Many times we want to know if we have succeeded in reducing the variation of a process, or we might want to know if a change in a variable (X) changes the variation in the output (Y).

Knowing if the variances of two (or more) samples are different is also a prerequisite to the test on means.

Are these Variances Different?

Xb

Xa

Xb

Xa

The hypothesis test for comparing variances is the Homogeneity of Variance Test

The hypothesis test for comparing variances is the Homogeneity of Variance Test

In the Analyze phase we will try to determine which X’s have an effect on the Y. We can compare two sets of data, with X set at different values, thereby determining if that X has an effect.

Examples: Does a process perform better using machine/material/ fixture/tool...A or B? Does the purchased material conform to the desired specifications (m & s)? Is there a difference in performance between vendor A or B? Is there a difference in your process after you make a change? Has a variation source been removed?

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52Spread–Homogeneity Of Variance

Step 3: You want to compare the variability of the Sales Regions. You have established that each process is stable but non-normally distributed. Perform the Homogeneity of Variance Test .


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53Test On Variances, Example–Input

a : at least one is different α = .05H

2West

2Easto σσ:H = IFGσ= σ2 2= Centralσ

2= South

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54Test On Variances, Examples–Output

.05 α =a

2West

2Easto

: at least one is differentH

σσ:H =IFGσ= σ2 2= Centralσ

2= South

5 15 25 35 45 55

95% Confidence Intervals for Sigmas

Bartlett's Test

Test Statistic: 58.348

P-Value : 0.000

Levene's Test

Test Statistic: 10.396

P-Value : 0.000

Factor Levels

Central

East

IFG

South

West

Homogeneity of Variance Test for total time

p < α: Reject Ho

p > α: Accept Ho

We have standardized on

The Levene’s test because

it is more robust to non-

normality of samples.

If you want to compare the performance of two territories, you should test their variances independently of the other territories. This way the extra noise of the other territories will not interfere with the analysis. You may end up with different conclusions running them independently, versus running them with all the other territories.

The confidence intervals that are shown are intervals for the standard deviation, even though we are comparing variances (variance = σ2).

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55Center–Non-Normal Data Test

Mood’s Median TestA Mood’s Median Test is used to test two or more population medians. This test is robust to outliers or errors in data (shows statistical significance).This test will show statistical significance. It will not show practical significance.

Just as with our earlier example, a picture is worth a thousand words. Looking at a graphical depiction of the data can help to verify whether or not findings (even findings with statistical significance) have any practical significance. By way of an analogy, even though you could statistically prove that people are heavier before a haircut than they are afterwards, nobody seeks out a barber shop when they go on a diet. Even though a statistical difference might be able to be proven, the difference is negligible from a practical standpoint. Viewing the data graphically helps to confirm how much practical significance exists in what you’ve found.

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56Center–Mood’s Median Test

Step 4: Check the centers. Are the centers different by region?


Stat > Nonparametrics > Mood’s Median Test– Response = Total Time– Factor = Territory

Answer the following questions:1.Are the medians different?

(interpret the p-value)2.Which medians are different?

(interpret the confidence intervals)

different is oneleast At :HXXXXXH

a

54321o :~~~~~

====

Another type of analysis that may be investigated is whether or not multiple samples of data can be shown to be different from each other by a (statistically) significant amount. The example shown here is questioning whether similar territories are taking different amounts of time to process loan applications as measured in days.

One test which can check for this condition in non-normal data is called a Mood’s Median Test.

It should be noted that, unless it can proven otherwise, the two groups are assumed to have the same median. In other words, the null hypothesis for a Mood’s Median Test is that the medians are equal.

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57Mood’s Median Test

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58Mood’s Median Test

Mood Median Test

Mood median test for total ti

Chi-Square = 108.88 DF = 4 P = 0.000

Individual 95.0% CIs

Territor N<= N> Median Q3-Q1 ---------+---------+---------+-------

Central 97 15 3.0 4.7 (+

East 47 1 10.0 8.8 (+)IFG 2 11 28.0 56.5 ------+---------------------)

South 25 21 9.0 10.3 (-+)

West 22 91 15.0 17.5 (+-)---------+---------+---------+-------

20 40 60

Overall median = 9.0

Recall, when two groups are equal, the confidence intervals overlap.

Ho: All medians are equalHa: At least one median is not equal

Notice that Minitab has converted the continuous data into attribute data. For each level of the X, Minitab supplies a count of how many values fall at or below and above the overall median.

The Mood’s Median test then performs a simple Chi-square test (which we’ll cover later) on this summary table

− If the number above and below are proportional, Chi-square will be low and p will be high, resulting in the conclusion that the medians are equal.

− If the number above and below are not proportional, Chi-square will be high and p will be low, resulting in the conclusion that the medians are not equal

The results from manually performing a Chi-square test using this summary table are the same as the Mood’s Median test

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59Hypothesis Testing Procedure

Team preparation

1. Write the null hypothesis Ho: There is no difference between Population A and B

2. Write the alternate hypothesis

3. Decide on the alpha level

4. Chose hypothesis test

5. Gather evidence and test/conduct analysis

6. Decide to Reject H0, or not reject H0, and draw conclusion

α =.05 (typical for DMAIC projects)

Choose the correct test, given the type of X and Y data.

Collect data, run analysis, get p-value

If p 0.05 conclude, no difference between populationsIf p < 0.05 conclude, the populations are different

Ha: There is a difference between Samples A and B

≥

pop2pop1 µµ =

pop2pop1 µµ ≠

The first step in hypothesis testing is to write a null hypothesis for the population being investigated. State that there is no difference between populations that you are studying. The next step is to write the alternate hypothesis (which is often what your team REALLY thinks is true), which indicates that a difference does exist between the population. The decision regarding a p-value is usually straightforward. By convention, a p-value of .05 is typical because that is sufficient to give us the confidence we need to go forward whether we reject or do not reject the null hypothesis. The team then collects whatever additional data is necessary. The correct hypothesis test can then be chosen and the analysis is conducted. The team now has the necessary information in order to know whether or not to reject or accept the null hypothesis.

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601-Sample Hypothesis

1. Ho : µ = constant = T

Ha : µ ≠ constant = T

HHoo HHaa

TT

2. Ho : σ 2 = constant = T

Ha : σ 2 ≠ constant = T

There are 7 types of hypotheses that we will be covering.

We are standardizing the method by always trying to accept, with a degree of confidence, the alternative hypothesis when evidence supports the decision. We are the prosecuting attorney. Set up the hypotheses according to this standard convention.

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611-Sample t-Test

Minitab File: GB case study.mtwNull Hypothesis: There is no difference in June’s delivery time average with that of a target set by May’s delivery time average of 5 minute’s late.Minitab Command: Stat > Basic Statistics > 1–Sample t–test

Ho : µ = constant = T

Ha : µ ≠ constant = T

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621-Sample t-Test


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63

1. Double click anywhere on the C5 line to select time as a variable

2. Click Test Mean and enter 5.0 as May’s average, the Alternative is that they are not equal

3. Click Graphs to show a pictorial

4. Click on Histogram of data

5. Click OK

1-Sample t-Test

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641-Sample t-Test

Histogram of time

-100 0 100

0

10

20

30

40

50

time

Freq

uenc

y

(with Ho and 95% t-confidence interval for the mean)

[ ]X_

Ho

The session window has our answer. If the p-value is less than .05, we reject the Null Hypothesis and accept its alternate, that there is a statistical difference in averages between this month’s data and May’s data.

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652-Sample Hypothesis

3. Ho :µ1 = µ2

Ha : µ1≠ µ2

4. Ho : µ1 ≤ µ2

Ha : µ1 > µ2

5. Ho : σ12 = σ2

2

Ha : σ12 ≠ σ2

2

µ1 µ2

σ2

σ1

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662-Sample t-Test

Minitab File: GB case study.mtwNull Hypothesis: There is no difference in the average delivery time between the two different load types.Minitab Command: Stat > Basic Statistics > 2–Sample t–Test

Ho :µ1 = µ2

Ha : µ1≠ µ2

Let’s test the hypothesis that there is no difference in the average delivery time between the two different load types.

D/H–Drop & Hook–A driver unhooks their full trailer, and then hooks into an empty trailer to take back.

Unload–The driver opens the trailer and allows the store to unload it’s freight, and brings back the trailer.

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672-Sample t-Test


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682-Sample t-Test

1. Double click anywhere on the C5 line to select time as a variable for samples.

2. Click on C3 to chose LoadType as the variable for subscripts.

3. Click Graphs to show a pictorial.

4. Click on Boxplots of data.

5. Click OK.

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692-Sample t-test

D/H Unload

-100

0

100

LoadType

time

Boxplots of time by LoadType(means are indicated by solid circles)

The session window has our answer. If the p-value is less than .05, we reject the Null Hypothesis and accept its alternate, that there is a statistical difference in our Drop & Hook and Unload averages.

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70Multi Sample Hypothesis

7. Ho : σ12 = σ2

2 = . . . = σn2

Ha : at least one is not equal.

6. Ho : µ1 = µ2 = . . . = µn


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71Analyze Of Variance (ANOVA)

Minitab File: GB case study.mtwNull Hypothesis: There is no difference in the average delivery time between Capital Logistics drivers.Minitab Command: Stat > ANOVA > One-Way

Ho : µ1 = µ2 = . . . = µn


Let’s test the hypothesis that there is no difference in the average delivery time between Capital Logistics drivers, Temporary drivers working for us, and our 3 Third party carriers we use in areas that are not supported by Capital Logistics.

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72Analysis Of Variance (ANOVA)


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1. Double click anywhere on the C5 line to select time as a response variable.

2. Double click C2 for Driver as a factor.

3. Click Graphs to show a pictorial.

4. Click on Boxplots of data.

5. Click OK.

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Cap

. Log

.

DNG

Y In

c.

JJ T

ruck

Tem

p La

bor

Tran

s, In

c.

-100

0

100

Driver

time

Boxplots of time by Driver(means are indicated by solid circles)

1. Note the sample number for each group.

2. These 3 are alike.

3. These 2 are definitely different.

The session window has our answer. If the p-value is less than .05, we reject the Null Hypothesis and accept its alternate, that there is a difference in at least 1 average between the 5 different groups of drivers.

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75Homogeneity Of Variance (HOV)

Minitab File: GB case study.mtwNull Hypothesis: There is no difference in the variation in delivery time between Capital Logistics drivers.Minitab Command: Stat > ANOVA > Homogeneity of Variance

Ho :

Ha : at least one is not equal

2n

22

21 σ ...σσ ===

Let’s test the hypothesis that there is no difference in the variation in delivery times between Capital Logistics drivers, Temporary drivers working for us, and our 3 Third party carriers we use in areas that are not supported by Capital Logistics.

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2. Double click C2 for Driver as a factor.

3. Click OK.

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1. We have standardized our Levene’s Test because it is more robust for non-normal data.

2. Our p-value is less than 0.05.

The graphical output has our answer. If the p-value is less than .05, we reject the Null Hypothesis and accept its alternate, that there is a difference in standard deviation between at least two of the drivers.

Always use the p-value for Levene’s Test.

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79Review: Scatter Plots

y

x

y

x

r = 0r = 0

y

x

r = –1.0

x

y r = +1.0

y

x

y

x

r = –.7r = +.7

R-value

The correlation coefficient r measures the strength of linear relationships.

–1 ≤r ≤1

When a relationship exists, the variables are said to be correlated.

Perfect negative relationship: r = –1.0No linear correlation: r = 0Perfect positive relationship: r = +1.0

If no correlation is apparent, don’t stop. Use histograms, regression, rational sub-grouping, etc. to try to extract some meaning from the data.

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80Simple Linear Regression

We have shown/talked about positive and negative correlation of two data setsRegression analysis is a statistical technique used to build theY = ƒ(x) relationship between two or more variables. The model is often used for prediction.Regression is a hypothesis test. Ha: The “X” is a significant predictor of the response.It may be used to analyze relationships between the “X’s”, or between “Y” and “X”Regression is a powerful tool, but can never replace process knowledge about trends

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Ha: The model is a significant predictor of the response.

b0 = Predicted value of Y when X1 = 0b1 = Slope of line

change in Y per unitchange in X1

Minitab File: GB case study.mtwNull Hypothesis: There is no correlation between our continuous Y metric (time) and a continuous X metric (distance)Minitab Command: Stat > Regression > Fitted Line Plot

Y

X

Y = b0 + b1X1

Let’s test the hypothesis that there is no correlation between our continuous Y metric–time and a continuous X metric–distance.

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2. Double click C6 for Distance as a predictor.

3. We believe there to be a linear relationship.

4. Click OK.

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0 100 200 300 400

-100

0

100

Distance

time

Y = -29.1923 + 0.174971XR-Sq = 10.5 %

Regression Plot

1. There is a very weak positive relationship between distance and timely delivery

2. This value means that 10.5% of the variation in Y - time is explained by this X - distance.

Distance is a significant factor.

Entire model is significant.

The session window has our answer. If the p-value is less than .05, we reject the Null Hypothesis and accept its alternate, that there is a correlation between delivery time and distance, but that it is a very weak one (as seen by Low R-Sq value).

Hypothesis test for the model (p-value given for “Regression”)

Ho: Model = O

Ha: Model ≠ O

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85Chi-Square Test

ContinuousContinuous DiscreteDiscrete

Discrete

Continuous

XChi-Square Test

Y

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86Chi-Square Tests

The Chi-Square TestsUsed for:

1 - Goodness-of-Fit Test: To test if an observed set of data fits a model (an expected set of data)

2 - Test of Independence: To test hypothesis of several proportions (contingency table)

It’s for discrete data, any number of categoriesFor all cases, Ho: no difference in data

Ha: difference exists

χ2

The Chi-Square test provides a way to determine if a given set of data has the hypothesized distribution. For example, if we roll a die 600 times., the number 1 occurs 96 times, 2–88 times, 3–104 times, 4–107 times, 5–112 times, and 6–93 times. In theory, each number should occur 100 times. The Chi-Square test enables us to determine if the observed set of data, the output of 600 rolls of a die, fits an expected model.

The Chi-Square test will also let you know if any factor has an impact on the output. If there is no difference in the data (Ho), this means no factor(s) have an impact on the output. If a difference exists (Ha), one or more factors have an impact on the output.

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87The Nature And Use Of Chi-Square

Suppose we flip a coin N = 100 times and observe 63 heads and 37 tails. Could this ratio of heads to tails occur by chance or should we conclude that the coin is somehow biased ?

χ2 = fo - fe2

feΣj = 1

g

g = number of categoriesfo = observed frequencyfe = expected frequency

(f0-fe)2

fe

3.38

3.38

χ 2 = 6.76

Heads

Tails

Penny

63/50*

37/50*

*=Observed Expected(f0) (fe)

The Goodness-of-Fit test examines the difference between what is expected and what is observed. If this difference is large, you should be suspicious that something is influencing the output (one of the factors). The c 2 value represents a test statistic used for comparison to a critical value.

In this example, you would expect an unbiased coin to have equal occurrences of heads and tails (50/50). We know that we won’t always have this ratio of heads to tails because of random chance.

If there is a large difference between what is expected and what is observed, the chi-square value will be large (see formula). If the observed value is close to the expected value, the chi-square value will be small. How large does chi-square have to be to say the coin is biased?

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88The Goodness Of Fit Test

To determine whether a sample comes from a population with a known distribution, calculate chi-square as shown on the previous page.H0 = good fit (observed distribution is consistent

with random outcomes from the expected model)

Ha = sampled population does not have the expected distribution

If the observed frequencies are close to the expected frequencies, chi-square is small. So a low chi-square leads to rejecting Ha. If chi-square is greater than a critical value, the null hypothesis is rejected.The critical values of chi-square for various confidence levels are given in the table “Chi-Square Distribution.”Each of the expected frequencies must be at least 5 for this test to be valid.

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89Degrees Of Freedom

The chi-square distribution has “degrees of freedom” as a parameter.

For a goodness-of-fit test, the number of degrees of freedom is k-1, where k is the number of possible outcomes.

Thus for the penny example,df = 2 - 1 = 1

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90The Statistical Test

For the penny example: Critical value ( α = 0.05, dof = 1) = 3.841

χ2Calculated > χ2

Table => There is a difference (I’m seeing something unusual).

Since the statistic from the data, 6.76, is greater than the table critical value, the alternative hypothesis is accepted: we are confident that we saw unusual behavior with that penny.

Use the tables on the next two pages to determine the chi-square critical value.

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df .250 .100 .050 .025 .010 .005 .0011 1.323 2.706 3.841 5.024 6.635 7.879 10.8282 2.773 4.605 5.991 7.378 9.210 10.597 13.8163 4.108 6.251 7.815 9.348 11.345 12.838 16.2664 5.385 7.779 9.488 11.143 13.277 14.860 18.4675 6.626 9.236 11.070 12.832 15.086 16.750 20.515

6 7.841 10.645 12.592 14.449 16.812 18.548 22.4587 9.037 12.017 14.067 16.013 18.475 20.278 24.3228 10.219 13.362 15.507 17.535 20.090 21.955 26.1259 11.389 14.684 16.919 19.023 21.666 23.589 27.877

10 12.549 15.987 18.307 20.483 23.209 25.188 29.588

11 13.701 17.275 19.675 21.920 24.725 26.757 31.26412 14.845 18.549 21.026 23.337 26.217 28.300 32.90913 15.984 19.812 22.362 24.736 27.688 29.819 34.52814 17.117 21.064 23.685 26.119 29.141 31.319 36.12315 18.245 22.307 24.996 27.488 30.578 32.801 37.697

16 19.369 23.542 26.296 28.845 32.000 34.267 39.25217 20.489 24.769 27.587 30.191 33.409 35.718 40.79018 21.605 25.989 28.869 31.526 34.805 37.156 43.31219 22.718 27.204 30.144 32.852 36.191 38.582 43.82020 23.828 28.412 31.410 34.170 37.566 39.997 45.315

21 24.935 29.615 32.671 35.479 38.932 41.401 46.79722 26.039 30.813 33.924 36.781 40.289 42.796 48.26823 27.141 32.007 35.172 38.076 41.638 44.181 49.72824 28.241 33.196 36.415 39.364 42.980 45.558 51.17925 29.339 34.382 37.652 40.646 44.314 46.928 52.620

26 30.434 35.563 38.885 41.923 45.642 48.290 54.05227 31.528 36.741 40.113 43.194 46.963 49.645 55.47628 32.620 37.916 41.337 44.461 48.278 50.993 56.89229 33.711 39.087 42.557 45.722 49.588 52.336 58.30230 34.800 40.256 43.773 46.979 50.892 53.672 59.703

40 45.616 51.805 55.758 59.342 63.691 66.766 73.40250 56.334 63.167 67.505 71.420 76.154 79.490 86.66160 66.981 74.397 79.082 83.298 88.379 91.952 99.607

70 77.577 85.527 90.531 95.023 100.425 104.215 112.31780 88.130 96.578 101.879 106.629 112.329 116.321 124.83990 98.650 107.565 113.145 118.136 124.116 128.299 137.208

100 109.141 118.498 124.342 129.561 135.807 140.169 149.449

Alpha

df=(# columns-1) x (# Rows-1)

The Chi-Square Distribution 91

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df .995 .990 .975 .950 .900 .750 .5001 .000039 .000160 .000980 .003930 .015800 .101500 .4550002 0.010 0.020 0.051 0.103 0.211 0.575 1.3863 0.072 0.115 0.216 0.352 0.584 1.213 2.3664 0.207 0.297 0.484 0.711 1.064 1.923 3.3575 0.412 0.554 0.831 1.145 1.610 2.675 4.351

6 0.676 0.872 1.237 1.635 2.204 3.455 5.3487 0.989 1.239 1.690 2.167 2.833 4.255 6.3468 1.344 1.646 2.180 2.733 3.490 5.071 7.3449 1.735 2.088 2.700 3.325 4.168 5.899 8.343

10 2.156 2.558 3.247 3.940 4.865 6.737 9.342

11 2.603 3.053 3.816 4.575 5.578 7.584 10.34112 3.074 3.571 4.404 5.226 6.304 8.438 11.34013 3.565 4.107 5.009 5.892 7.042 9.299 12.34014 4.075 4.660 5.629 6.571 7.790 10.165 13.33915 4.601 5.229 6.262 7.261 8.547 11.036 14.339

16 5.142 5.812 6.908 7.962 9.312 11.912 15.33817 5.697 6.408 7.564 8.672 10.085 12.792 16.33818 6.265 7.015 8.231 9.390 10.865 13.675 17.33819 6.844 7.633 8.907 10.117 11.651 14.562 18.33820 7.434 8.260 9.591 10.851 12.443 15.452 19.337

21 8.034 8.897 10.283 11.591 13.240 16.344 20.33722 8.643 9.542 10.982 12.338 14.041 17.240 21.33723 9.260 10.196 11.688 13.091 14.848 18.137 22.33724 9.886 10.856 12.401 13.848 15.659 19.037 23.33725 10.520 11.524 13.120 14.611 16.473 19.939 24.337

26 11.160 12.198 13.844 15.379 17.292 20.843 25.33627 11.808 12.879 14.573 16.151 18.114 21.749 26.33628 12.461 13.565 15.308 16.928 18.939 22.657 27.33629 13.121 14.256 16.047 17.708 19.768 23.567 28.33630 13.787 14.953 16.791 18.493 20.599 24.478 29.336

40 20.707 22.164 24.433 26.509 29.051 33.660 39.33550 27.991 29.707 32.357 34.764 37.689 42.942 49.33560 35.535 37.485 40.482 43.188 46.459 52.294 59.335

70 43.275 45.442 48.758 51.739 55.329 61.698 69.33480 51.172 53.540 57.153 60.391 64.278 71.145 79.33490 59.196 61.754 65.647 69.126 73.291 80.625 89.334

100 67.328 70.065 74.222 77.929 82.358 90.133 99.334

Alpha

The Chi-Square Distribution 92

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93The Statistical Test (continued)

The 5% risk column in the table already tells us there is a difference. Alternately, a p-value (the probability of being wrong if accepting the alternative hypothesis) can be computed in EXCEL as follows:

= CHIDIST(statistic,dof)= CHIDIST(6.76,1)

Excel will return the p-value, in this case 0.0093. Since the probability of being wrong is less than 0.05, we accept the alternative hypothesis: we are confident that we saw unusual behavior with that penny.

Minitab does not have a Macro to accommodate the Goodness-of-Fit test. It is most convenient to compute the chi-square value in Minitab and then evaluate the corresponding p-value in Excel.

One can obtain the p-value in Minitab, but it takes a little work.

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94Test Of Independence

Suppose a bill has been introduced in the Government to raise the speed limit. A polling organization polls 45 members of Political Party 1 and 55 members of Political Party 2, and finds 30 Party 1 and 35 Party 2 members oppose the proposal. Is there a significant effect of party affiliation on preference for the proposal?

Ho = no difference between parties

Ha = one party likes the proposal significantly more than the other

We organize the data in a “contingency table”

fo = 30

fo = 15

fo = 35

fo = 20

Oppose

Favor

Party 1 Party 2

Total = 65

Total = 35

Total = 45 Total = 55

Use this example to demonstrate the test for independence and contingency tables.

The test for independence asks the question: Does some factor have an effect on the output? For example, does car brand affect injury severity?

To test independence, we put the data in a contingency table. We then test to see if the row and column method for classification are independent.

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95Test Of Independence (continued)

Now calculate the expected distribution, given there is no partypreference. For example, the expected frequency of Party 1 opposing the proposal would be:

fe = Row Total x Column TotalGrand Total

Note that for each cell, this is the total frequency for the row, times the total frequency for the column, divided by the total population (see chart on following page).

= (65/100) x 45 = 29.25

You will be determining your expected frequency on the ratio of number of people who oppose the proposal to the number of people who favor the proposal (regardless of party affiliation). Out of the total 100 (party affiliation unknown) people, 65 oppose the proposal and 35 favor the proposal. Expected ratios: 65/100 oppose; 35/100 favor. When you multiply these ratios by the total in a party, you get the expected frequency.

If the population of Party 2 (or Party1) has a statistically different (p < α) observed frequency than the expected frequency (total or average) accept Ha–one party likes the bill significantly more than the other.

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96Expected Frequency And Degrees Of Freedom

When performing a chi-square test on a contingency table, the number of degrees of freedom equals the number of rows in the table minus one, times the number of columns in the table minus one.

df = (2-1) x (2-1) = 1

fe = frow x fcolN

fe = 29.25

fe = 15.75

fe = 35.75

fe = 19.25

Oppose

Favor

Party 1 Party 2

Total = 65

Total = 35

Total = 45 Total = 55

Expected frequencies are calculated using the methodology from the previous page.

We could use the expected and observed frequencies to calculate the Chi-Square statistic like we have seen before, and then compare it to the critical Chi-Square value from the table using (alpha) and df. But, as usual, we will have Minitab do this for us. See the next pages.

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97Minitab Example

MINITAB FILE: (Create Your Own)

Ho: There is no difference between party affiliation and preference on the proposal.

Ha: There is a difference between party affiliation and preference on the proposal.

For this example, Party 1 = RepublicansParty 2 = Democrats

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98Minitab Input And Results

Minitab calculates the expected frequency (fe)

1. Double click on both columns.

2. Click OK.

Minitab calculates the expected frequencies.

The calculated chi-square is less than the critical value of 3.841, so we accept Ho.

The p-value is greater than .05, so we are within our 95% confidence zone of good fit.

There is no apparent relationship between political party affiliation and preference on the speed limit proposal.

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99Chi-Square Test–Case Study Example

Minitab File: GB case study.mtwHo: There is no difference between Driver types and their on-time

delivery performance.Ha: At least one driver type is better or worse at on-time delivery

performance.

Minitab Command: Stat > Tables > Cross–Tabulation

In our familiar case study example, with our data in rows, we will let Minitab build the contingency table.

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100Chi-Square Test

MINITAB FILE: GB case study.MTW

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101Chi-Square Test

1. Double click on both columns C2 & C7..

2. Check the Chi-Square Analysis and Show Count buttons.

3. Click OK.

Since our discrete data is in columns and not tabled, we will first cross-tabulate and then calculate Chi-Square.

Since our p-value is less than .05, we reject the Ho and accept it’s alternate, Ha.

Compare this p-value with the one done on the ANOVA test for driver type & time. Are they the same?

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102Chi-Square Test–Summary

Goodness of Fit Test– Does our data fit an expected distribution?

Test of Independence– Does some factor have an effect on the output?

– critical value Accept H

statistico

– > critical value Reject Ho

p-value– p < 0.05 Reject Ho

– p 0.05 Accept Ho

χ2

χ2

χ2

≥

≤

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Desired Outcome: Select and perform the appropriate statistical test for a given project situation

Hypothesis Testing–Breakout Activity (20 minutes) 103

AllBe prepared to share your analysis andresults with the class

Close

10 mins.AllPerform the test in Minitab

Write the p-value from the test and yourconclusions on the hypothesis testingworksheet

Perform TestIn Minitab

5 mins.AllFor the scenario(s) assigned to your team, complete the hypothesis testingworksheet to select the appropriatestatistical test

SelectTest

5 mins.AllReview the hypothesis testing scenariosrecruitment cycle time case study thatwas introduced in the Minitab andGraphical Analysis module.

ReviewScenarios

TimingWhoHowWhat

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104Hypothesis Testing Scenarios

The following scenarios relate to the HR recruitment cycle time case. In each case, perform the appropriate statistical test. (Data File: fill_time.mtw)

1. The project team wants to determine if there is a statistical difference in mean cycle time to fill technical positions depending on the type of resource requested.

2. The project team wants to determine if there is a statistical difference in cycle time variation, depending on the type of resource requested.

3. The project team wants to determine if there is statistical difference between the number of cycle time defects for each type of resource.

4. The project team wants to determine if recruitment cycle time increases as the number of years of experience of the person hired increases.

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1. State the H0

2. State the Ha

3. State α level

4. What test should we use?

5. Will you reject or accept H0?

1. H0: ___________________________________________________________________

2. Ha: ___________________________________________________________________

3. α level: ________________________________________________________________

4. Test: _________________________________________________________________

5. Accept or Reject H0? _____________________________________________________

Hypothesis Testing Worksheet 105

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1. State the H0

2. State the Ha

3. State α level

4. What test should we use?

5. Will you reject or accept H0?

1. H0: ___________________________________________________________________

2. Ha: ___________________________________________________________________

3. α level: ________________________________________________________________

4. Test: __________________________________________________________________

5. Accept or Reject H0? _____________________________________________________

Hypothesis Testing Worksheet 106

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1Improve Phase Flowchart

ID M A C

IMPROVEPHASE

OVERVIEW

Improve 7:Screen Potential Causes

Improve 8:Discover Variable Relationships & Propose Solution

Improve 9:Establish Operating Tolerance & Pilot Solutions

I

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2Improve Phase Overview

What is the Improve phase?The Improve phase is when your team:

Selects those product performance characteristics that must be improved to achieve the improvement goal by identifying the major sources of variation in the processDevelops and pilots process improvements

Why is the Improve phase important?This phase is important because it specifically identifies how the process should be improved.

Steps involved in the Improve phase:Improve 7: Screen Potential CausesImprove 8: Discover Variable Relationships & Propose SolutionImprove 9: Establish Operating Tolerances & Pilot Solution

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11



Control


9



10




Improve





5



4Analyze




3






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What does it mean to Screen Potential Causes?Potential Causes are the possible Vital Few (or Critical) X’s discovered during Analyze 6 that have a significant effect on the Project Y. The Potential Causes are identified by the improvement team. During this step, the Vital X’s discovered in Analyze 6 will be statistically verified by obtaining more data, if necessary.

Why is it important to Screen Potential Causes?Potential X’s are important because they help Green Belt teams focus their identification of root causes. Once potential X’s are verified as having a significant effect on the Project Y, then Green Belt teams will use the identified Vital X’s to focus improvement efforts.

What are the project tasks for completing Improve 7?7.1 Verify Vital Few X’s

IMPROVE STEP OVERVIEW

7.1 Verify Vital Few X’s

Improve 7:Screen PotentialCauses


Improve 9:Establish Operating Tolerances & Pilot Solution

Improve 7–Screen Potential Causes 4

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8.1 Generate a transfer function to optimize the changes in vital X’s (if necessary)8.2 Propose solution8.3 Refine solution




What does it mean to Discover Variable Relationships and Propose a Solution?A Final Solution is the improvement strategy that the team develops based upon the root causes verified in the previous step.The final solution will address the Vital X’s while maintaining customer focus.

Why is it important to Discover Variable Relationships and Propose a Solution?A Final Solution will eliminate or reduce the effect of the Vital Few X’s, thus improving the process capability of the Project Y. The Final Solution must not only address the Vital Few X’s, but you must also consider whether the solution satisfies the customer’s CTQ’s. By using the FMEA tool, you can identify possible Failure Modes within the Final Solution, identify what effect the Failure Modes would have on either the customer’s CTQ’s or the new process, and create action plans to eliminate or reduce the likelihood of that Failure Mode occurring.

What are the project tasks for completing Improve 8?8.1 Generate a transfer function to optimize the changes in Vital X’s (if necessary)8.2 Propose solution8.3 Refine solution

Improve 8–Discover Variable Relationships and Propose Solution

5

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What does it mean to establish Operating Tolerances and Pilot Solutions?An Operating Tolerance is established when the X-Y transfer function is known and the required specification for Y is known. The tolerance for X can be set by using the specification for Y in the transfer function.A pilot is a test of all or part of a proposed solution on a small scale in order to better understand its effects and to learn about how to make the full scale implementation more effective.

Why is it important to establish Operating Tolerances & Pilot Solution?Operating tolerances allow you to control the settings of Vital X’s so that you can better predict/control the output of the process – the Y. A pilot allows you to improve a proposed solution to better meet customer CTQ’s, lower the risk of failure of a proposed solution, confirm expected results of a proposed solution, and increase the opportunity for feedback and buy-in for a proposed solution.

What are the project tasks for completing Improve 9?9.1 Establish operating tolerances for Vital X’s9.2 Pilot solution


9.1 Establish operating tolerances for Vital X’s9.2 Pilot solution




Improve 9–Operating Tolerances & Pilot Solution 6

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Root cause analysis



Practical Problem

Statistical Problem


Practical Solution

D M A I C




– Risk analysis

– Control plans




Collect data




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1Design Of Experiment: Learning Objectives

Define the purpose & benefits of conducting a Design of ExperimentDescribe screening DOE and optimization DOE and how they are used in the Improve phaseReview full factorial DOE designDescribe the 5 steps in analyzing DOE data, the key components of each step and the use of Minitab to analyze the data – Plot the raw data– Plot the residual*– Examine the factor effects– Confirm impression with statistical procedures– Summarize conclusions

Describe the use of fractional factorial design and explain the benefits & the trade-off over full factorial design

* We don’t discuss residuals here, but to fully analyze your DOE, seek assistance from your BB/MBB and/or the “Book of Knowledge”

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2Design Of Experiments

With the use of Design of Experiments (DOE), we will be able to:

Verify the “Vital Few” X’s that impact the quality of the Project YIdentify the best combination X–values to optimize process performance and meet customer CTQ’s

DOE is powerful in isolating the Vital Few causes from the many factors affecting a process.

In identifying and testing solutions, a team can apply DOE to compare the results of several possible solutions. The team can develop a more effective final solution by measuring effectiveness of the improvements in action.

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3DOE Terminology

Project YDependent

Independent X(5 M’s and 1 P)

Independent VariablesIndependent Variables––X’sX’sAlso called factorsFactors or variables we select in advanceThe causes

Dependent VariablesDependent Variables––YY

Also called responsesThe quantity (Y) that we measure to determine the impact of the X’sThe effect

Project YProject Y

MMM

M MP

(x) (x) (x)

(x) (x) (x)

Remember that the dependent variable (Y) is measured from the customer’s perspective. DOE allows us to identify the X’s that are the key drivers of variation in the Y.

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4DOE Terminology (continued)

LevelsLevels

The test settings for X

For example: In our Capital Logistics GB Case Study:Y = On-Time Delivery of ShipmentsX1 = Truck SizeLevels = 62 ft. & 66 ft. truck

X2 = Tire TypeLevels = Brand X & Brand Y

Main EffectsMain Effects

Differences between each factor level

For example: Is the On-Time Delivery different for:a) 62 ft. trucks vs. 66 ft. trucks?b) Brand X or Brand Y tires?

InteractionsInteractions

Differences between two or more factor level combinations

For example: Is On-Time Delivery different when:a) 62 ft. truck, Brand X tireb) 62 ft. truck, Brand Y tire

c) 66 ft. truck, Brand X tired) 66 ft. truck, Brand Y tire

Interactions

Tire TypeX Y

Main Effects

Dev

iatio

n fro

m re

quire

d de

liver

y tim

e.Y

62 66

X

Dev

iatio

n fro

m re

quire

d de

liver

y tim

e.Y

X Y

62 ft. truck

66 ft. truck

Tire TypeTruck Size

X

Dev

iatio

n fro

m re

quire

d de

liver

y tim

e.Y

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5Strategy For Choosing The Appropriate Design

The Knowledge LineCurrent State of Process Knowledge

Low High

Type of Design Main Effect Fractional Full Response/Screening Factorials Factorials Surface

Usual # of Factors >5 4-10 1-5 2-3

Purpose:Identify Main effect Some Relationships Optimal factor

critical factors interactions among factor settings- vital few

Estimate Crude direction Some All main effects Curvature infor improvement interactions and interactions response,

empirical modelsStep 7 Screening DOE

Step 8 Optimization DOE

Types of Experimental Design

Screening DOE–experiments which are used to screen out the vital few X variables out of many at a very low cost.

Can study the main effectsCan’t study the interactions

Optimization DOE–Experiments which are used to determine the proper settings for each vital X.


Fractional Factorials–provide a middle ground. They are used to expand on the study of the vital few X variables at a low cost.

Can study main effectsCan study selected (and few in number) interactions

Full Factorials–are used to study the vital few X variables and all possible interactions. They can be quite costly when the number of vital few X’s are large.

Can study main effectsCan study all interactions

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6

Benefits of Design of Experiment (DOE)Can be used to identify “Vital Few” sources of variationDefines the relationship between the inputs & outputsAllows you to measure the influence of the “Vital Few” variables on a response variable– Also allows you to measure the interactions between the “Vital Few” variables

Is more effective & efficient than testing one factor at a timeMinimizes the number of test runs you have to make to draw validconclusions about X & Y linkagesProvides knowledge of best set-up conditions of X’s for improved Y performance

DOE Benefits

Statistical Design Of Experiment Raises Your Batting Average

Statistical Design Of Experiment Raises Your Batting Average

Design of Experiment is an approach for effectively & efficiently exploring the cause and effect relationship between numerous process variables (X’s) and a process performance variable (Y).

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7The Process Of Experimentation

1. Define ProjectIdentify responses

2. Establish Current Situation

3. Perform AnalysisIdentify factorsChoose factor levelsSelect designRandomize runsCollect dataAnalyze dataDraw conclusionsVerify results

4. Determine Solutions5. Record Results6. Standardize7. Determine Future Plans

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1. Define Project (problems)The mileage on my new car is not up to advertised standards. I want to improve my car’s mileage.

2. Establish Current Situation (& state hypothesis)I currently do not get the manufacturer’s advertised gas mileage on my car Some combination of speed, gas octane, and tire pressure will provide me with the optimum gas mileage

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9The Process Of Experimentation (continued)

3. Perform AnalysisDependent Variable–Gas Mileage (Y)Identify Factors (independent variables)– Tire Pressure (X)– Octane (X)– Speed (X)

Choose Factor Levels

Independent Variables(X’s) (Factors) Level - Level +

Tire Pressure (psig) 30 35Octane 87 92Speed (mph) 55 65

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3. Perform Analysis (continued)Select Design

- - -+ - -- + -+ + -- - ++ - +- + ++ + +

Tire Pressure Octane Speed Gas Mileage

– Number of test levels (Number of factors) = 23 = trials

How many trials would be necessary if there were 4 variables each at 2 levels? How many variables would there be before the cost became prohibitive?

What would be a different type of experiment that would not require all possible runs?

The experimental trials tables represent all possible combinations of the 3 factor levels.

Note: The table above shows the “standard order” for a 2-level, 3-factor design.

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3. Perform Analysis (continued)Randomize Runs

What effects (main and interaction) seem to be significant?– Main effect is the effect of one X on the Y– Interaction effects are the combined effects of two or more

X’s on the Y

Tire Pressure Octane Speed Gas Mileage- (30) - (87) - (55) 26+ (35) - (87) - (55) 27- (30) + (92) - (55) 30+ (35) + (92) - (55) 33- (30) - (87) + (65) 18+ (35) - (87) + (65) 21- (30) + (92) + (65) 19+ (35) + (92) + (65) 22

In this experiment, only one run of each experimental trial was conducted. Additional runs would increase the confidence level for the results.

Replication is a repeat of all experimental trials to obtain additional data to increase the degree of belief in the experimental results. Replications are used when:

The interactions are of critical importanceData is tricky to get. Replications will supply an extra data point when data from an experimental trial is lostYou need to increase the degree of confidence in the experimental resultsYou need to reduce the risk when implementing solutions

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3. Perform Analysis (continued)Collect & Analyze Data

What factor has the biggest effect on gas mileage?

Pareto Chart of the Effects(Response is Mileage, Alpha = .05)

0 1 2 3 4 5 6 7 8 9

AB

ABC

AC

BC

A

B

C

A: Pressure

B: Octane

C: Speed

Effect Size

The Pareto Diagram bars show the relative importance of each main effect and interaction in the experiment.

The length of each bar shows relative impact. Bars that cross the dashed line have statistically significant impact on the Y.

The dashed line is called the “reference line”. Any effects that extend past this reference line are statistically significant within our chosen confidence level.

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3. Perform Analysis (continued)Collect & Analyze Data (continued)

What is the best speed to get the best gas mileage?

Octane30 35 87 92 6555

26

24

22

20

Pressure Speed

28

Main Effects Plot (data means for Mileage)

- + + –– +

Mi le

age

The Main Effects Plot show the average value for each of the levels of the three independent variables. Each average is based on 4 data points.

Extra credit: Can you look at the experimental trials table and say why each level has a total of 4 data points?

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3. Perform Analysis (continued)Collect & Analyze Data (Continued)

Each corner of the cube represents an experimental trial from the trial tableFor example, when tire pressure is negative (-), octane is negative (-) and speed is negative (-), the gas mileage is 26 (x,y,z is the convention)Can you tell which combination of tire pressure, octane and speed is the best by looking at the cube?

Cube Plot (data means) for gas mileage

Speed

Tire Pressure

Octane

–

+

– +

–

+

19

30

26

18

27

21

22

33

Pressure, Octane, Speed-, +, -

-, +, + +, +, +

+, +, -

-, -, +

+, -, -

+, -, +

-, -, -

The cube shows the result of the interaction between tire pressure, octane and speed.

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3. Perform Analysis (continued)Draw Conclusions- Speed has an important effect on gas mileage- Tire Pressure doesn’t significantly affect gas mileage- Octane doesn’t significantly affect gas mileage

Verify Results- Run additional trials at optimum settings- Conduct MSA on data results

4. Determine SolutionsDrive at 55 mph to get the best gas mileageSet tire pressure for best tire wear resultsBuy the octane that optimizes cost or engine cleanliness

5. Record Results6. Standardize7. Determine Future Plans

Any ideas on how the results from this experiment could be used for further experimentation?

Replicate the experiment to get a better indication of the effects and to quantify variabilityTest beyond the original limits of the XTest at midpoint for nonlinear Y responsesTry additional potential X’sBlock by season, tire type, fuel type, etc.

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16

Full Factorial DOE

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17Full Factorial DOE

Full Factorial Design of ExperimentIs used to study the Vital Few X variables and all possible interactions Can be quite costly when the number of Vital Few X’s is largeCan study main effectsCan study all interactions

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18Full Factorial Layout: 3 Factors, 2 Levels

For 3 factors, each at 2 levels, there are 23 = 2 x 2 x 2 = 8 combinations of factor settings. (Levels Factors = Combinations)Notice the pattern of factor settings in the standard order.

–+–+–+–+

Factor1

12345678

Std.Order

––++––++

––––++++

Factor2

Factor3

This is a 3–factor, 2–level full factorial layout arranged in “standard order.”

Each row of the full factorial layout represents a set of experimental conditions. There are 8 different experimental conditions in this design layout.

Does this full factorial layout look familiar?

Where did you see this before?

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19Visualizing The Experimental Space

+2 Factors = A SQUARE

Factor 1– +

Factor2

–

Factor 2

Factor 1– +

+

– –

+

Factor 3

3 Factors = A CUBE

Review how the square is constructed. To add a third factor, you need a three–dimensional cube plot.

A cube helps us visualize the experimental space covered by the 3 factors.

Each corner represents 1 set of experimental conditions.

23 = (Two Levels)(Three Factors) = 8 experimental conditions.

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20

Order X1 X2 X3 X4 X5k Factors Xk• •

The number of trials = (2 levels) = 2k .

–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+

123456789

1011121314151617181920212223242526272829303132

––++––++––++––++––++––++––++––++

––––++++––––++++––––++++––––++++

––––––––++++++++––––––––++++++++

––––––––––––––––++++++++++++++++

k = 1

k = 2

k = 3

k = 4

k = 5•••2kk

•

(k factors)s

The Factorial Pattern Of Experimentation

Full factorial layouts can be generated for any number of factors.

This table displays factorial designs arranged in standard order.

Notice the pattern. A handy way to remember is by thinking how the levels alternate in the columns.

For the first column, the levels alternate every 20 = 1 trial.

For the second column, the levels alternate every 21 = 2 trials.

For the Kth, the levels alternate every 2K-1 trials.

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21Replication vs. Repetition

Replication: Multiple execution of all or part of the experimental process with the same factor settings – Build different experimental units– In our car mileage example, replicate different experiments at a different time

Repeat tests: 2 or more observations that have the same levels for all factors– Performed on the same experimental unit

DESIGN LAYOUT EXAMPLE22 design with 2 replications 22 design with 2 repetitions

Std. Order Std. Order1 - - 1 - -2 + - 2 + -3 - + 3 - +4 + + 4 + +

Obs 1y11

y12

y13

y14

Obs 2y21

y22

y23

y24

1 - -2 + -3 - +4 + +

Responseyyyyyyyy

1

2

3

4

5

6

7

8

Avgyyyy

1

2

3

4

Replication has 2 important properties:It allows an experimenter to obtain an estimate of

experimental error. This estimate becomes the basic unit of measurement for determining whether observed differences are statistically significant.It yields more precise estimates of factor effects

RepetitionMay affect the precision of the measured response, but it does not affect the logical structure of the experiment

Why Replication?

To measure experimental variability.

So we can decide whether the difference between responses is due to the change in factor levels (an induced special cause) or to common cause variability. To see more clearly whether or not a factor is important.

Replication provides the opportunity for factors that are unknown or uncontrollable to balance out. Along with randomization, replication acts as a bias–decreasing effect.

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22Randomization: The Experimenter’s Insurance

Definition of Randomization: To assign the order in which the experimental trials will be run using a random mechanism.– It is not the standard order– It is not running in an order that is convenient– Minitab will randomize for us

Why Randomization?– Averages the effect of any lurking variables over all of the factors in the

experiment

What is a Lurking variable?– A variable that has an important effect and yet is not included among the

factors under consideration

How and why should we randomize the order in which we conduct an experiment?

Randomization reduces the introduction of a systematic bias into an experiment.

We call this bias a “lurking variable.”

Lurking Variables:

DefinitionA variable that has an important effect and yet is not included among the factors under consideration because:– Its existence is unknown– Its influence is thought to be negligible– Data on it is unavailable

Safeguard:

Randomize the order of the experimental trials to protect against the effect of lurking variables

Action:

If the lurking variable creates a trend, it can be compensated for in the numerical analysis

Conclusions can then be drawn from the original factors that are not affected by such lurking variables

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23Design Of Experiment

SummaryProvides process performance data under different types of operating parametersEstablishes cause and effect relationships between a process Y and possible X’s:– Verify the Vital Few X’s– Determine X values for optimal performance– Predict future process performance

Can be used in both incremental and exponential process improvement studies

Caution: Prior To Implementing Solutions, Understand The Difference Between Experimental And Actual

Business/Process Conditions

Caution: Prior To Implementing Solutions, Understand The Difference Between Experimental And Actual

Business/Process Conditions

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24

Reference Material–Analyzing DOE Data

The following pages are reference only and will become helpful if you are contemplating the use of a DOE in your project. Sit down with your mentor after you review this section and determine feasibility.

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1. Define ProjectIdentify responses

2. Establish Current Situation3. Perform Analysis

3.1 Identify factors3.2 Choose factor levels3.3 Select design3.4 Randomize runs3.5 Collect data3.6 Analyze data3.7 Draw conclusions3.8 Verify results

4. Determine Solutions5. Record Results6. Standardize7. Determine Future Plans

Focus of this module

For review: The steps in Designing an Experiment.

In this module, we will focus on Step #3–Perform Analysis. We will investigate how you analyze the data collected from the experiment.

You saw in the car gas mileage example how we analyzed the data from that full factorial experiment.

Now we will use the Capital Logistics Case Study on “On-Time Delivery” to see how they used Design of Experiment to identify the vital few X’s.

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26

3.6.1. Plot the raw data.

3.6.2. Plot the residuals*.

3.6.3. Examine factor effects.3.6.4. Confirm impressions with

statistical procedures.

3.6.5. Summarize conclusions.

Steps in Analysis: Full Factorial, Replicated Designs

Minitab will provide this for you.

Analysis: Make inferences

Diagnostics: Is data OK?

3.6 Analyze Data:

This is the “Analyze Data” step, which is one step in the process of experimentation on the previous page.

Steps in analyzing the data:

In steps 1 & 2, we begin by checking for problems with the data before doing the DOE analysis on the data. Minitab will plot the data for you. This will help to:

Find defects, outlier or patterns in the dataGet a feel for the actual dataGet impressions of what the data is going to tell us, to guide our analysis

After using Minitab to check the data, the next step is to plot the residuals.

Residuals are the “leftover” variation in the data after you have accounted for the main cause of variation. Plotting the residuals should show a normal distribution. If the residuals are not normally distributed, it is a sign that there is another variable present that has not been accounted for (a “lurking” variable).

* We don’t discuss residuals here, but to continue to Step 3, seek assistance from someone who knows how.

Once the data has been validated and looks acceptable, you are ready to examine the factor effects.

Let’s look at our Capital Logistics GB Case Study.

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27Background For DOE: Capital Logistics GB Case Study

In Step 6 of the Analyze Phase, the Green Belt and the project team at Capital Logistics determined, based on the results of their Hypothesis Testing, that there were 2 X’s that had an impact on the on-time delivery of shipments to customers. The 2 X’s were:

– Drivers– Distance

The team determined that there wasn’t anything that they could do to change the distance that each truck traveled to make their deliveries–the routes were automated by the system and were determined to be the shortest routes. They decided to focus on Driver as a factor, as this was under their immediate control.The team used the Cause & Effect diagram to brainstorm potential root causes as to why Driver/Trucking company influenced Time. The resulting list included:

– size of the vehicle – type of tire– dispatch method – fuel capacity– type of engine

After reviewing their data further, the team decided to conduct a Design of Experiment. They would use Size of Vehicle and Tire Type as possible Vital X’s in their DOE. Each of these factors has 2 levels:

– Size of Vehicle is either 66 or 62 feet– Tire Type is either X or Y

The DOE was set-up and conducted to determine the Vital X that would have the greatest impact on the timeliness of shipment deliveries to their customers.

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28Examine Factor Effects

The 3rd Step in “Analyze Data”:Y = f (X1, X2, X3, …, Xn)Y (Response) = On-Time Delivery of ShipmentXi (Factors) = Size of Truck, Tire Type

How do the factors affect the response?How do the combinations (interactions) of factors affect the response?– We can write the equation that answers these questions

This is your Y = f(X) Transfer function: On-Time Delivery = Constant +(-) Size of Truck + Tire Type +(-) Size of Truck *Tire Type Interaction Effect.

We can simplify the factor names with abbreviations in our DOE (see next page).

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29Factor Names And Interaction Symbols

It is useful to abbreviate factor names. There are several ways to do this:– Choose the first letter or first two letters of each factor– Assign factors a letter: A, B, C, D, . . .

Denote the interaction between Factor A and Factor B as:– A x B or AB

For two factors (A and B) there is one interaction: ABFor three factors there are– Three two-way interactions: AB, AC, BC– One three-way interaction: ABC

How many interactions are there for four factors (A,B,C,D)?

Interactions for 4 factors:

2-way: AB, AC, AD, BC, BD, CD, (6)

3-way: ABC, ACD, BCD, ABD (4)

4-way: ABCD (1)

Total (11)

Higher level interactions (3-way or more) are hard to plot and explain. They are also not very likely to occur.

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30Examine Factor Effects–In Minitab

Create Factorial Design–in Minitab Data File: GB Case Study.mtw

Type of design = full factorial

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Select Two Replicates

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Name Factors

Stat > DOE > Create Factorial DesignClick on Factors.Enter “Name”.Click “OK” twice.

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Inputting Responses into Minitab

Note: Ensure that when you enter this data into your Minitab Worksheet, you put the times in the correct rows, based on the correct truck & tire combination of (+) and (-).

Note: Ensure that when you enter this data into your Minitab Worksheet, you put the times in the correct rows. Your experiment may have run in a different order and you may have coded your factors differently.

Truck Size Tire Size Time66 X 12666 X 14066 Y 3066 Y 6062 X -5062 X -8062 Y -3062 Y -50

(+)

(-)

(+)

(-)

(+)

(-)

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Analyze Factorial DesignIn Minitab: Stat > DOE > Analyze Factorial Design

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Analyze Factorial Design

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What does the Pareto Chart tell you about the factors & interactions?

Is Truck Size significant?

Is Tire Type significant?

Is the interaction of Truck Size & Tire Type significant?

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37Examine Factor Effect–In Minitab

Analyze Factorial Plots

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Set-up Main Effects

Stat > DOE > Factorial PlotsClick OK.

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Set-up Main Effects

Stat > DOE > Factorial PlotsClick OK twice.

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40Main Effect Plots

In our GB Capital Logistics On-Time Delivery Case Study:

How do Truck Size & Tire Type affect Time?

Truck Size Tire Type

-1 1 -1 1

-30

0

30

60

90

Tim

e

Main Effects Plot (data means) for Time

A useful way to graphically show factor effects is by using Main Effects Plot.

Simply plot the average response for each level (+ or -). The steeper the line, the more significant the effect. The slope of the line determines whether the effect is positive or negative. A positive slope is a positive effect and vice versa.

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41Interaction Effect

Differences between 2 or more factor level combinationsIn our Capital Logistics GB Case Study: On-Time DeliveryIf we are looking at 2 factors: Truck Size

Tire TypeIs On-Time Performance different when:

Truck Size Tire Type62 ft. X62 ft. Y66 ft. X66 ft. Y

Question: Which of the following indicates Interactions betweenfactors?

Res

pons

e Factor A

Factor B

+–

– +

Res

pons

e Factor A

Factor B

+

–

– +

Factor A

Factor B

+–

– +

Res

pons

e

Adapted from Lawson, John and John Erjavac, Basic Experimental Strategiesand Data Analysis. Provo, UT: Brigham Young University, p. 104.

We use the same calculation for Interaction Effects as we did for Main Effects. The only difference is we first need to generate the interaction column. We then use this column for the calculation of the Interaction Effect.

Why are interactions important?

Why is it important to determine the effect of interactions?

If the lines are not parallel, there is interaction between the factors (variables).

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42Interaction Effect

In our GB Capital Logistics On-Time Delivery Case Study:

How do Truck Size & Tire Type interact? How do the interactions affect time?

-11

-1-1 11

-50

0

50

100

Tire Type

Truck Size

Mea

n

Interaction Plot (data means) for Time

Late

On-Time

Early

What does this tell us?

In this case, our goal was On-Time-Delivery. None of the points give us OTD for mean=0. Therefore, we should go with the (-) Tire Type and the (-) Truck Size (X Tire Type and Truck Size of 62.) This will get us closest to a mean of zero.

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43

3.6.1. Plot the raw data.3.6.2. Plot the residuals.

3.6.3. Examine factor effects.

3.6.4. Confirm impressions with statistical procedures.

3.6.5. Summarize conclusions.

Steps In Analysis: Full Factorial, Replicated Designs



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44Confirm Impressions

The 4th Step in “Analyze Data”:By now you have a good idea about the influence of the factors in the experiment. You can confirm these impressions statistically by performing a Hypothesis Test.Ho: Factor has no effect on the resultsHa: Factor has an effect on the results

oH Acceptα: poH Reject α: p

Statistical Analysis Confirms The Results Of The Graphical Analysis

Statistical Analysis Confirms The Results Of The Graphical Analysis

Now we are determining the statistical significance of the effects.

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45Confirm Impressions With Minitab

In our GB Case Study: What does the Minitab Session Window tell you ?

What do the p-values for:Truck SizeTire TypeTruck Size * Tire Type

Indicate?

Does this statistical analysis confirm the graphical analysis?

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46

3.6.1. Plot the raw data.3.6.2. Plot the residuals.3.6.3. Examine factor effects.3.6.4. Confirm impressions with

statistical procedures.3.6.5. Summarize conclusions.

Steps In Analysis: Full Factorial, Replicated Designs



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47Summarize Conclusions

The 5th Step in “Analyze Data”:List all the conclusions you have made during the analysisInterpret the meaning of these results– For example, relate them to known physical properties or an expert’s personal

knowledge of the processMake recommendationsFormulate and write conclusions in simple language

What conclusions would you make from the Capital Logistics DOE study?

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48Summarize Conclusions (continued)

From our Capital Logistics GB Case Study on On-Time Delivery:The Green Belt and the project team reviewed the results of the DOE. They saw that there seemed to be a link between on-time performance and the size of the truck unit, as well as an interaction effect between Tire Type and Size of Truck on on-time performance.

They returned to their Fishbone (Cause & Effect) Diagram with greater granularity, and asked why these factors would influence on-time performance. They validated these reasons through field observations.

The team validated that the larger size trucks took longer at some locations. In addition to the time involved with maneuvering in a cramped environment, on certain routes these trucks had a higher incidence of tire failure (lateral movement caused by tight turns increased the stress on the tires, increasing the number of flat tires).

By using the data & results from the DOE, the team had determined the root causes of the on-time performance problem and were ready to start to brainstorm solutions to address/control these “Vital X’s”.

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49

Reducing the Size of Experiments–Fractional Factorial DOE

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50Reducing The Size Of Factorial Experiments

For a 2–Level

Factorial

with k Factors…..

Number of runs = 2k

Numberof Factors

123456789

10•••

15•••

20

Numberof Runs

2481632641282565121024

•••

32,768•••

1,048,576

Many factors potentially impact the quality of any process/productThe factorial strategy is an efficient approach to experimentation, compared to “one-at-a-time”When factors are investigated at 2 levels, the number of experimental runs is 2k (note: the “k” needs to be raised, because it is 2 to the power of k - “k” is the exponent)This can result in a large number of runs, even with a relatively small number of factors

Limited resources allow you time to run only 4 trials in the allotted time.

Which 4 trials will you choose?

Full factorial is time-consuming and costly as the number of factors increase.

Also consider the number of 2-way and higher order interactions as the number of factors increases.

For 4 factors, let’s look at every possible effect (main & interaction) and the overall average. Evaluating the average is what the extra run is used for.

From a Full Factorial (4 factors):

Number

Overall Average 1

Main Effects: A B C D 4

2-way interactions 6

(AB, AC, AD, BC, BD, CD)


(ABC, ABD, ACD, BCD)


(ABCD)

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51Fractional Factorials

Fractional Factorials*:Provide a middle ground for design of experimentAre used to expand on the study of the Vital Few X variables at a low costCan study main effectsCan study selected (and few in number) interactions

Fractional Factorials Allow You To Reduce The Size Of An Experiment And Select Certain Runs

Fractional Factorials Allow You To Reduce The Size Of An Experiment And Select Certain Runs

*Fractional Factorials are beyond the scope of this course. Consult your BB/MBB or refer to the “Book of Knowledge” for further information.

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52Strategy For Choosing The Appropriate Design

The Knowledge LineCurrent State of Process Knowledge

Low High

Type of Design Main Effect Fractional Full Response/Screening Factorials Factorials Surface

Usual # of Factors >5 4-10 1-5 2-3

Purpose:Identify Main effect Some Relationships Optimal factor

critical factors interactions among factor settings- vital few

Estimate Crude direction Some All main effects Curvature infor improvement interactions and interactions response,

empirical modelsStep 7 Screening DOE

Step 8 Optimization DOE


Screening DOE–experiments which are used to screen out the vital few X variables out of many at a very low cost.

Can study the main effectsCan’t study the interactions

Optimization DOE–Experiments which are used to determine the proper settings for each vital X.


Fractional Factorials–provide a middle ground. They are used to expand on the study of the vital few X variables at a low cost.

Can study main effectsCan study selected (and few in number) interactions

Full Factorials–are used to study the vital few X variables and all possible interactions. They can be quite costly when the number of vital few X’s are large.

Can study main effectsCan study all interactions

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Optimization Design Of Experiment Activity (40 minutes) 53

Desired Outcome: Practice how to set-up a DOE

15 mins.FacilitatorFor the example you selected,identify 3 factors at 2 levels (+/-)each

Using the worksheet on the followingpages, design the experiment upthrough Step 6

Set-up the DOE

15 mins.FacilitatorDiscuss what the experiment mightdemonstrate, were you to execute it

Brainstorm your list of questions forhow to run this experiment

Set-up Optimization DOE

8 mins.AllChoose a spokesperson to reportout on the design of yourexperiment, and the questions youhave about running it

ReportOut

2 mins.TeamChoose a facilitator, scribe, timekeeper, and/or note taker

Determine the timing for eachactivity below

Agree on the example you will usefor the exercise

– Your own project

– How to get a great lawn

– How to make the best chocolatechip cookies

– How to lose weight

Team Preparation

TimingWhoHowWhat

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1. Define the problem

2. State the hypothesis

3. Identify the dependent (Y) and independent (X) variables

Dependent Variable (Y) =

Independent Variables (X’s) =

=

=

4. Determine the test levels for each independent variable (X).

5. Calculate the number of trials to test all combinations of test levels.

# of trials = # of test levels# of independent variables

Independent Variables(X’s) (Factors) Level - Level +

Design Of Experiments–Breakout Activity Worksheet 54

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55Design Of Experiments–Breakout Activity Worksheet (Continued)

6. Construct the experimental trials table

Independent Variable (X)#1



DependentVariable (Y)




DependentVariable (Y)

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56Appendix: Example Of Designed Experiment: GE Card Services

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57DOE Example: Defining The CTQOverallQuality

EX/VG - 57%

CustomerService

EX/VG - 44%

AuthorizationsEX/VG - 60%

Marketing RepEX/VG - 54%

New AccountApproval

EX/VG - 34%

CardProduction

EX/VG - 47%

BillingStatementsEX/VG - 40%

PaymentProcessingEX/VG - 54%

Financial &Marketing InfoEX/VG - 30%

.26 .25 .11 .12 .16 * * .15

0

0.59

0.23

0.2

0.20.40.60.81

0.38

0.28

0.24

0.17

00.20.40.60.81

Impact Performance Impact Performance

#1 Speed #1 Speed#2 Accuracy

Inseparable CTQ’sOne Experience To The Customer

100%0%

Overall

Speed OfApprovalAmount/

Type Of Info

Credit LinesGranted

18%

24%

18%

16%

16%

25%

26%

25%

20% 40% 60% 80%

Excellent Very Good

13%

10%

20%

12%

23%

34%

33%

41%

47%

53%

0% 20% 40% 60% 80% 100%

Overall

TimelinessOf Delivery

Accuracy

InsertCapability

Card Quality

Excellent Very Good

Speed Is The #1 CTQ Of The New Account And Card Experience

Speed Is The #1 CTQ Of The New Account And Card Experience

A project team was working to improve customer satisfaction with the process of approval for and issuing of new credit cards.

One of the key drivers of satisfaction was identified as time to issue cards, i.e., the cycle time between a consumer’s approval for a credit card, and the time he/she received it.

Through segmentation, the team found that applications mailed or faxed in took considerably longer than other applications where the application information was entered electronically at the store.

When examining the process map, it became clear that many faxed and mailed applications needed additional information before they could be processed. This often involved phone or written correspondence with the applicant, which slowed the process considerably.

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58DOE Example: Causes Of Time Consuming Delays

79% of queuing for non-fraud! Why?

Missing and illegible information is a major cause of delays. What can be done to reduce missing and illegible information?Many felt that little could be done to improve the situation for handwritten applications.

Non-Fraud Queue Pareto

0%

10%

20%

30%

40%

50%

Msg Home#/AC

WrngPromo

Cd

Msg/WrngBrnch/Dlr/

Str #

Msg/WrngSS#

Unknown CBRIssues

Msg/WrngZip

Duplicate

Freq

uenc

y %

The team discovered that 79% if the applications which were “in queue”–i.e., on hold before being processed –were in queue for reasons other than potential fraud issues. The team analyzed the reasons for non-fraud queuing and created a Pareto chart.

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59DOE Example: The Designed Experiment

Factor Name Explanation Standard Level New Level

App. Type Terms of the credit agreement printed on the application

Present (Full) Absent (Naked)

Instructions Written instructions on how tocomplete the form included

No Yes

Flags Critical information without which the application can’t be processed is specially noted

No Yes

Boxes Delineated boxes to hold numericinformation, e.g., phone

( )- -

No Yes

Insurance Location on the form for the purchaseof the optional credit card insurance

Not Body* Body*

Page Layout Orientation of the form Portrait Landscape

The only influence that the business has on legibility and completeness is through the application itself. The team then decided to study what they could do to the application to make it easier for their customers to fill out.

The factors shown above were chosen for study.

*Body/Not Body–refers to location of the insurance text on the application form. On a landscape layout, “not body” applications had text to the right of the application. On a portrait layout, “not body” applications had text at the bottom of the application.

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60DOE Example: Experimental Complications

The difficulty in tracking many (in this case, 16) different applications through the processLarge amount of person-to-person variation with respect to legibility and completeness, making it difficult to assess the effect of changes

Test the applications outside the normal processHave each tester fill out two applications

ComplicationsComplications

RemediesRemedies

The applications were paired (eight pairs of applications) and customers were asked to fill out a pair of applications and provide feedback regarding the two application versions. The applications were paired so that customers experienced the factors at both levels.

Eighty customers filled out a pair of applications in return for a $10.00 gift certificate. The order which each paired application was presented to the customer was randomized throughout the test to balance the effect of order on the results. Customers were asked whether they preferred one application version over another and why. Applicants signing for credit insurance were asked whether they understood that they had requested insurance coverage.

The completed applications were sent for imaging, and the imaged applications were reviewed by an associate to record the legibility and completeness of each field on each application. A legibility score was assigned using a 5-point scale; missing information was given a “0” and fields not relevant to the applicant were recorded as not being applicable. Preferred applications were given a score of “1,” not preferred “0,” and no preference was indicated by a “0.5.”

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61DOE Example: Responses

Two Key Responses Were Studied:A combined completeness and legibility score, which was based on the percent of necessary information that was both present and legibleA preference score, which told which of the two applications thecustomer preferred

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62DOE Example: Analysis

* Effect was significant

Main Effects Plot – Means For Legibility And Completeness

Main Effects Plot – Means For Preference

Naked Full No Yes No Yes No Yes Body Bottom LandscapePortrait

0.849

0.843

0.837

0.831

0.825

Legi

bilit

y an

d C

ompl

eten

ess

App. Type Instruct Flags Boxes Insurance Pg. Layout

* * *

0.67

0.59

0.51

0.43

0.35

Pref

eren

ce

Naked Full No Yes No Yes No Yes Body Bottom Landscape Portrait

App. Type Instruct Flags Boxes Insurance Pg. Layout

* * * * *

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63DOE Example: Results

Naked

Yes

Yes

No

Not Body

Landscape

ApplicationType

Instructions

Flags

Boxes

Insurance

PageLayout

Full82.8%

H

No82.9%

H

Not Body85.3%

H

Naked84.8%

H

Yes84.8%

H

Body82.4%

H

Full34%

No57%

H

No59%

Not Body56%

Portrait36%

Naked66%

Yes43%

H

Yes41%

Body44%

Landscape64%

1

FactorEffect On Legibility And Completeness Recommendation

Effect OnPreference

1 The data does not show that instructions improve legibility and completeness, but it is felt that instructions should be provided for clarification purposes. Also, consideration should be given to improving the effectiveness of the instructions provided on the application.

Effect not significant

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1Step 9

Step 8 provided the experimental techniques to establish the relationship between the measurable Y characteristics and the controlling X factors. In step 9, those relationships (transfer functions) wil be used to define the key operating parameters and tolerances to achieve the desired performance of the CTQ’s/ One should be able to set the tolerance of X factors if the X-Y relationship and the specifications of Y are given.

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2Principle Of Tolerancing

Tolerance: the allowable range of variation of X while still meeting the requirements of Y.

Establish tolerance of X based on the requirements of Y, or often the specification limits via the Transfer functionThe tolerance should allow the project to reach the project objectives established in step 5When more than one CTQ is involved, be aware of the trade-offs among CTQ’sBe aware of the variations due to the measurement of X’s and Y’s

USL

T

LSL

X

Y

Y = f (X)

Lower Limitof Tolerance

Upper Limitof Tolerance

Tolerance:the allowablerange of X

USL

T

LSL

X

Y

Y = f (X)



Tolerance:the allowablerange of X

It is complicated to calculate tolerance for ƒ (X) with multiple X’s.Use:

Crystal BallCalculus

It will be covered in detail in the GE-DFSS course

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3Consideration Of Measurement Variations

USL

T

LSL

X

Y

Y = f (X)



New tolerance considering the variation of Y measurement

The measurementvariation of Y

USL

T

LSL

X

Y

Y = f (X)



New tolerance considering the variation of Y measurement


USL

T

LSL

X

Y

Y = f (X)

New tolerance considering the variation of X + Y measurement


The measurementvariation of X Upper Limit

of ToleranceLower Limit

of Tolerance

USL

T

LSL

X

Y

Y = f (X)

New tolerance considering the variation of X + Y measurement


The measurementvariation of X Upper Limit

of ToleranceLower Limit

of Tolerance

Estimate the gage error for Y using the σe from the MSA study in Step 3.

The width of the measurement error distribution is 5.15σe

Establish the gage error for X in Step 10. Use the 5.15σe from the MSA of X.

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4Example: Weight Loss Wellness Program

CTQ requirements:Target to lose 2 lbs/weekAt least need to lose 1 lb/weekNo more than 3 lbs/week due to health concerns

lbs. week

3

2

1

0

1 2 3 hrs./week

WeightLoss

Target

USL

LSL

1.4 2.7

lbs. week

3

2

1

0

1 2 3 hrs./week

WeightLoss

Target

USL

LSL

1.4 2.7

Transfer Function

These goals do not take into consideration any error in the Y or X due to measurement error (MSerror)Since we have performed a Gage R&R on both the Y and X measurement system we know the GRR % Tolerance for Y and XLets use the information to develop the operating limit for our actual X

4

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5Example: Weight Loss Wellness Program (continued)

1 2 hr/week

lbs. week

3

2

1

0

Exercise

WeightLoss

Target

USL

LSL

1.55 2.55


New operating limitson X due to variabilityin the Y and Xmeasurements

1 2 hr/week

lbs. week

3

2

1

0

Exercise

WeightLoss

Target

USL

LSL

1.55 2.55


New operating limitson X due to variabilityin the Y and Xmeasurements

To get a more conservative tolerance for X, taking into account measurement error (MSerror) on Y, we center the width of the 5.15 MSerror distribution on both the USL and LSL for Y.

Q: Why center the measurement error distribution on the spec?

A: The error in measurement system will effect us most at the ends of the tolerance

Q: Why start from within the tolerance?

A: This results in a more conservative tolerance for the X factor operating within. The new operating limits of X will ensure you stay in spec for Y.

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6Example: Weight Loss Wellness Program (continued)

How to Determine the values of the new Y start pointsGiven Y Tolerance = 2; GR&R = R&R % Tolerance =10%

1. Calculate MSerror in Y unitsMSerror = (R&R % Tolerance) ٭ (Tolerance)MSerror ٭ (10%) = (2) = .2

2. Take ½ MSerror٭ (½) (MSerror) = ½ (.2) = .1

3. Calculate new start points for Y axisNew Y USL start point

Y USL- (½ MSerror) = 3 - .1 = 2.9New Y LSL start point

Y LSL + (½ MSerror) = 1 + .1 = 1.1

New operating limits on X due tovariability in the Y measurements

1 2 3 hrs./week

lbs. week

3

2

1

0

Exercise

WeightLoss

Target

USL

LSL

1.5 2.6

The measurement variation of Y

New operating limits on X due tovariability in the Y measurementsNew operating limits on X due tovariability in the Y measurements

1 2 3 hrs./week

lbs. week

3

2

1

0

Exercise

WeightLoss

Target

USL

LSL

1.5 2.6

The measurement variation of YThe measurement variation of Y

Our purpose is to get an operating tolerance on the X but we first should adjust the Y tolerance due to measurement error.

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7Example: Weight Loss Wellness Program (Continued)

Given: X is R&R % Tolerance = 20%New X Tolerance = USL – LSL (from last page)New X Tolerance = 2.6 –1.5 = 1.1Calculate MSerror in X units1. MSerror 22. = (1.1)٭ (20%) =2. Take (½) ٭(MSerror) = (½) 11. = (22.)٭3. New X USL = USLx - (½ (MSerror))

= 2.6 - .11 = 2.49New X LSL = LSLx - (½ (MSerror))

= 1.5 + .11 = 1.61

New operating limits on X due tovariability in the Y measurements

1 2 3 hrs./week

lbs. week

3

2

1

0

Exercise

WeightLoss

Target

USL

LSL

1.5 2.6

The measurement variation of Y

New operating limits on X due tovariability in the Y measurementsNew operating limits on X due tovariability in the Y measurements

1 2 3 hrs./week

lbs. week

3

2

1

0

Exercise

WeightLoss

Target

USL

LSL

1.5 2.6

The measurement variation of YThe measurement variation of Y

Correct X USL and LSL for the MSerror of the MSA system used to measure X using same methods as with Y.This has the effect of further tightening the X ToleranceIf you operate in these new operating limits of X you should be ensured of staying in spec on Y. That means no defects.

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8Summary

Set the process tolerances based on product specifications (exercise time needed to achieve desired weight loss goal).Adjusted our process tolerances to account for product measurement variation The tolerance principle is relatively simple and the application is relatively straightforward when:1) The measurement variation of of Y and X are sufficiently small

to be ignored2) Only one X factor involved

However, when measurement variations of Y and X needs to be considered and multiple X factors are involved, the math techniques could be more complicated. Courses on DFSS Statistical Design Method or DFSS Statistical Tolerance are offered in various GE businesses.

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1Control Phase Flowchart

CD M A I

CONTROLPHASE

OVERVIEW

Control 10:Validate Measurement System

Control 11:Determine Process Capability

Control 12:Implement Process Control System & Project Closure

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2Control Phase Overview

What is the Control phase?The Control phase is when your team:

Ensures that the new process conditions are documented and monitored via statistical process control methodsAfter a “settling–in” period, reassesses the process capabilityCloses the project

Why is the Control phase important?This phase is important because it ensures that process improvements are implemented together with appropriate process controls to ensure that the process changes are sustained into the future. It also is an opportunity for the team to “prove” that the project process performance goal has been met.

Steps involved in the Control phaseControl 10: Validate Measurement SystemControl 11: Determine Process CapabilityControl 12: Implement Process Control System & Project Closure

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11



Control


9



10




Improve





5



4Analyze




3







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CONTROL STEP OVERVIEW

10.1 Validate Measurement System10.2 Determine whether Measurement System is adequate to measure Vital Few X’s




What does it mean to Validate Measurement System?In the Measure phase, you focused on validating the measurement system for the Project Y. In this step, you should now validate the measurement system for the Vital X’s. A Measurement System Analysis (MSA) is the overall process to test your data for its validity. Before actually performing the MSA, you will have to develop a data collection plan for the Vital X’s. You should focus on the Vital X’s at this point because you want to develop Control Plans for each Vital X.

Why is it important to Validate Measurement System?Validating the Measurement System is important because you need to have data that you can trust in order to make decisions with that data. If your data is not telling you the truth, you are likely to make a decision with that data that will add more variation to the process. As part of your Process Control System, you will monitor the Vital X’s to make sure they stay in control. Therefore, you must validate the Measurement system used to collect the Vital X data.

What are the project tasks for completing Control 10?10.1 Validate Measurement System10.2 Determine whether Measurement System is adequate to measure Vital Few X’s

Control 10–Validate Measurement System 4

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11.1 Evaluate Process Capability of the improved process11.2 Confirm statistically that the improvement goal has been met




What does it mean to Determine Process Capability?Process Capability is the measure of process performance relative to the Customer’s CTQ. It is measured again at this point in the process in order to see if there was a process improvement. If a pilot is conducted, the improvement team should measure process capability from the pilot and then, once full implementation takes place (after Step 12), measure process capability again.

Why is it important to Determine Process Capability?Process Capability is important at this stage of the project because you want to be able to compare baseline performance before improvements to the new Process Capability once improvements have been implemented.It is also important to statistically validate the improvement in the process through the use of a Hypothesis Test, such as the 2-Sample t-Test.

What are the project tasks for completing Control 11?11.1 Evaluate Process Capability of the improved process11.2 Confirm statistically that the improvement goal has been met

Control 11–Determine Process Capability 5

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12.1 Implement a Control strategy for each Vital X12.2 Prepare Process Control plan12.3 Implement a solution12.4 Close the project




What does it mean to Implement Process Control System?A Process Control System is a system of activities whose purpose is to maintain process performance at a level that satisfies customers’ needs and drives the ongoing improvement of process performance. A Process Control System consists of three parts: Documentation, a Monitoring Plan and a Response Plan. During this step of the project, you are also ready for project implementation. Once the improvement is implemented and the process improvement is verified, the final step of the project is Project Closure. During Project Closure, you will finalize project documentation, leverage learning to other areas of the business and celebrate project completion with your team.

Why is it important to Implement Process Control?A Process Control System will help maintain the gain that occurred with the process improvement. Without control of an improved process, the process tends to revert to its old performance.

What are the project tasks for completing Control 12?12.1 Implement a Control strategy for each Vital X12.2 Prepare Process Control plan12.3 Implement a solution12.4 Close the project

Control 12–Implement Process Control Systems 6

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Root cause analysis



Practical Problem

Statistical Problem


Practical Solution

D M A I C




– Risk analysis

– Control plans




Collect data




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9Forms Of Intellectual Property

PatentBest Protection against independent development by othersGives right to exclude others from making, using selling, the invention or 20 years from filingCan wait 2-3 years for patent to issueRight granted by the government for new, useful, nonobvious inventions

Trade SecretRights exist only so long as actually kept secretProtects against theft or misappropriation, not independent developmentDoes not require inventiveness in the patent sense

CopyrightProtects original works of authorship fixed in a tangible mediumDoes not protect against independent development

TrademarkDefines source of goods or servicesArbitrary, fanciful marks get stronger protection

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10Intellectual Property Infringement Avoidance Clearance And Assessment

It is critical to assure that improvement or new designs developed in the course of the project do not infringe on the Intellectual Property of others, external to GE. GE has a clear policy on infringement avoidance. “Intellectual Property Infringement Avoidance Process”. The team must conduct the necessary reviews to assure no infringement (consult the IP Business Champion for guidance). In general, if the answer is “yes” to any of the questions below, consult with the IP Business Champion and IP Designee for your business to obtain clearance before proceeding.

1) Is the team aware of any non-GE businesses who use substantially the same process or sell substantially the same process?

2) Will the project result in a product or process that is significantly different than a current GE product or process, and will it be commercially significant?

3) Have or will any services or products been obtained from an outside party I connection with this project, and is the project result commercially significant?

4) Will the product or process be exposed to non-GE parties, and be commercially significant?

5) Will the product or process be exposed to the public, and be commercially significant?If the project obtained clearance from the Infringement Avoidance screen, then consider whether there is Intellectual Property to Capture and Protect, via Patent, Trade Secret, Copyright or Trademark. If the project results in a process or product that is new, non-obvious and useful and will be of significant commercial value. It may be patentable. Consult the IP Business Champion and IP Designee for your business and submit the new process or product for evaluation through the IDEAS website.

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1

Statistical Process Control–Overview

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2Statistical Process Control: Learning Objectives

Describe the two types of Control ChartsDescribe and use Variable and Attribute Control ChartsSelect the appropriate Control Chart for a given process based on data typeDefine the control limits and how they differ from specificationlimitsExplain the decision errors in SPCExplain the rules (Minitab and Western Electric) to determine whether a process is out of control Describe and practice the use of Minitab to generate I&MR,

chart NP and P C, U, R,&X

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First developed by Dr. Walter Shewhart, control charts serve as the best way to determine if a process is “in control.”

By “in control,” we mean that the process is consistent and predictable. When a process is out of control, something about the process has changed. A cause for the change in the process should be sought.

3Statistical Process Control

“The Application of Statistical Techniques for Measuring and Analyzing the Variation in Processes”

Control Charts Are The Primary Tools In SPCControl Charts Are The Primary Tools In SPC

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4Five Main Uses Of Control Charts

To reduce scrap and rework and for improving productivityDefect prevention. In control means less chance of nonconforming units produced.Prevents unnecessary process adjustments by distinguishing between common cause variation and special or assignable cause variationProvides diagnostic information so that an experienced operator can determine the state of the process by looking at patterns within the data. The operator can then make the necessary changes to improve the process performance.Provides information about important process parameters over time

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5Process States

The Four States of a Process

1. ChaosProcess out-of-control, producing non-conforming productEven the level of nonconformance is unstableAssignable causes dominate the outputFixes don’t work for very long

How To Begin To Sort Out The Problems To Be Solved?

How To Begin To Sort Out The Problems To Be Solved?

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6Process States (continued)


2. The Brink of ChaosProcess unstable, some nonconforming product is being producedInstability will continually change product characteristicsProcess output is influenced by assignable causesNo assurance the next piece produced will be conforming

How To Determine Existence Of Assignable Causes?How To Determine Existence Of Assignable Causes?

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3. The Threshold StateProcess inherently stable over time, but producing some nonconforming product (process sigma is less than process sigma goal/standardProportion nonconforming predictableSome non-conformances will be shippedIf process natural spread is greater than the tolerance, common causes must be reduced/removedProcess must be monitored to assure desired effect is achieved

How To Be Certain That The Process Has Improved?How To Be Certain That The Process Has Improved?

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4. The Ideal StateThe process is inherently stable over time (process sigma > process goal/standard)Operating conditions are not changed arbitrarily (follow the process plan)The process average is set and kept at the proper levelThe natural spread of the process is less than the specified tolerance

How To Be Certain That None Of These Conditions Change Or Degrade?

How To Be Certain That None Of These Conditions Change Or Degrade?

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Control charts are used to distinguish between common and special causes of variation and use that understanding to control and improve processes.

Control charts are characterized by two things:

1. The average (mean), or centerline, which represents the middle point about which plotted measures are expected to vary randomly.

2. Control limits, both upper and lower, which represent the performance boundaries you can expect for the process. Although measures vary, one would not expect to see plotted measures outside of these boundaries if the process operated predictably.

*Note: Minitab displays UCL as 3.0SL (Three sigma limits) Minitab displays LCL as–3.0SL

9Variation And Control Charts

0 1 0 2 0

0

1 0

2 0

3 0

4 0Upper Control Limit*

(UCL)

Average

Lower Control Limit*(LCL)

Time Order of Sample

Mea

sure

men

t

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Dividing the control chart into zones can aid in detecting special cause variation. Each of the zones represent standard deviations from the mean. Zone C, for example, is + and - one standard deviation from the average.

10Determining If Your Process Is “Out Of Control”

Upper Control Limit(UCL)

Average

Lower Control Limit(LCL)

Zone A

Zone B

Zone C

Zone C

Zone B

Zone A

Source: Memory Jogger Plus, ©1994 GOAL/QPC

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These are the rules available in Minitab. You can find these rules under the “TESTS” button inside the Control Chart screen. GE has standardized on the above-mentioned rules to identify special cause variation..

You can select the rules you want Minitab to use.One thing to be careful with all these rules is that you may not want to react too quickly. Several factors need to be considered:Are consequences high (i.e. cost, safety, etc) if we do not react to a potentially unstable system using the 8 rules?Can we potentially make a process unstable if we react too quickly to the control chart, when in reality the process is not out of control (i.e., “Do not fix it, if it is not broken”)?

11Minitab Rules

1. One point beyond zone A (Western Electric) 2. Nine points in a row in zone C or beyond (All on one side.) (Western

Electric)3. Six points in a row, all increasing or decreasing4. Fourteen points in a row, alternating up and down5. Two out of three points in a row in zone A or beyond (Western Electric)6. Four out of five points in a row in zone B or beyond (Western Electric)7. Fifteen points in a row in zone C, above or below center8. Eight points in a row beyond zone C, above or below center

-3σ-2σ

+2σ+3σ

-1σ

+1σC C

B

B

A

A

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Control limits are not the same as tolerances.Control limits are what you haveTolerances are what you want

Example:

Customer may define the following for shipment delivery from time of order:

Target= 20 days

USL= 45 days

While the data collected for the control charts demonstrates:

Mean = 40 days

UCL= 46 days

LCL= 39 days

The UCL and LCL are calculated based on the data collected–the UCL and LCL are NOT related at all to spec. limits.

12Control Limits vs. Specification Limits

Control LimitsDefined based on process performance (+/- 3 estimated standard deviations from the mean)Help determine if your process is “in control” (without special cause variation)Plotted on control chartsChange when there is a verified, significant change to your processRepresent the voice of the process

Customer Specification Limits

Defined based on feedback from the customer(s)Help determine if your process is producing defectsPlotted on histograms (not control charts)Change when your customers say they do!Represent the voice of the customer

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13Control Limits vs. Specification Limits (continued)

It is possible to have a stable (in control) process that has unacceptable variationAssume both process A and B are statistically performing “in control”

When a process is in statistical control and has unacceptable variation,work on the reduction of variation due to common causesTo reduce common cause variation, make improvements to the Vital Few X variables

PROCESS A PROCESS B

Process A has acceptable variation when evaluated against customer specification limits

Process B has unacceptablevariation when evaluated against customer specification limits

LowerSpec. Limit

UpperSpec. Limit

LowerSpec. Limit

UpperSpec. Limit

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The measures that you choose to monitor in the control plan are the critical measures for your process. These are the process management measures that the process owner will rely on to track process performance over time.

14Selecting Measures For Control Charts

What Do I Monitor? Process

Process Variables(X’s)

Input Variables

(X’s)

Output (Y’s)

Key input and process measures (X) that track variables identified in your project as key drivers of Project (Y) variables

Key output measures (Y) from the customer’s perspective

X X X X

Measure The Process And Not The PeopleMeasure The Process And Not The People

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Following the 4-step data collection plan will ensure that the data collected on an ongoing basis will accurately reflect the variation in the process. Since this data will be collected over a long period of time, measurement systems analysis to ensure consistency should be a major concern for both the project team as well as the process owner after the hand-off. Make sure that periodic audits of the data collection are an integral part of the overall control plan.

15Selecting Measures For Control Charts (continued)

How Do I Monitor The Control Plan?

Use the 4-step data collection plan in order to develop a process that will protect the integrity of the data.

Ensure Data Ensure Data Consistency Consistency

& Stability& Stability

Develop Develop Operational Operational Definitions Definitions

& Procedures& Procedures

Collect Data Collect Data & Monitor & Monitor

ConsistencyConsistency

Establish Establish Data Data

Collection Collection GoalsGoals

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16Types Of Errors In Control Charts

3σ-level Control Limits– Created by Dr. Walter Shewhart to minimize two types of mistakes– Placed empirically because they minimize the two types of mistakes– Are not probability limits

Two types of Mistakes:– Calling a special cause of variation a common cause of variation (Missing

a chance to identify a change in the process) – Calling a common cause of variation a special cause of variation

(Interfering with a stable process, wasting resources looking for special causes of variation that do not exist)

Control limits vs. Specification limits– Control limits are determined by process data– Specification limits are determined by customer needs

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Variable = continuous dataAttribute = discrete data

17

Uses Measured Values – Cycle Time, Lengths, Diameters, etc.

Generally One Characteristic Per ChartMore Expensive, But More Information

Pass/Fail, Good/Bad, Go/No-Go InformationCan Be Many Characteristics Per ChartLess Expensive, But Less Information

Two Types Of Control Charts

VARIABLE CHART

ATTRIBUTE CHART

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There are many different types of control charts. The chart pictured here is a helpful guide to decide which type of chart to use and when. The primary determinant of which type of control chart to use is the type of data being analyzed.

If the data being analyzed is continuous (variable), you would use either:

The “Individuals & Moving Range” (I-MR): use if Rational Subgrouping is not possible (you want to see each transaction on the control chart)The

If the data being analyzed is discrete (attribute), you would need to determine:

If you have a constant lot (sample) size or if the lot (sample) size is not constantIf you are counting defects, you may have multiple defects per unit. If you are counting defectives, the unit either is or is not defective.

In this module we will study the different types of control charts and when to use each one.

What you want the Control Chart to tell you is:

Is my level of non-conformance consistent?Am I controlling my significant X’s?

details.further for JoggerMemory Refer to* TM

greateror 7 is size subgroup if S)-X( Use5.-3between be willsize subgroupTypically possible. isgSubgroupin Rational if use R)-X( Range&Xbar

18Selecting the Appropriate Control Chart

Variable orAttribute Data?*

Defects or Defective

Constant Lot Size?

uu pp


cc npnp

Rational Subgrouping

Possible?

Individuals &MovingRange


VariableVariable AttributeAttribute

No Yes YesNo

Xbar & Range

Xbar & Range

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Interpreting Control Charts–Activity (20 minutes) 19

Desired Outcome: Practice deciding which control chart is the appropriate choice for given data examples

9 mins.PartnersFor each of the examples listed onthe following page

– Determine the appropriate type ofcontrol chart

– Determine how you would labelthe X and Y axes

Review andFeedback

10 mins.PartnersKeep notes on your responses forreport-out

Close

1 min.AllChoose a partner for the exercisePreparation

TimingWhoHowWhat

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20Selecting Control Charts-Partner Activity (continued)

1. A team from Marketing is tracking response rates (yes, no) on telemarketing calls. Each day, they randomly sample 100 responses from their outgoing calls. The number of positive responses is plotted on the chart.

2. The technical support area is monitoring average response time on help requests. Each hour, 5 calls are sampled.

3. A team is monitoring the number of applications received each day with incomplete fields. All applications are being audited. Each day, 200-250 applications are received.

4. A team is monitoring the cycle time for the underwriters’ loan decisions. The data comes in slowly; that is, one loan is completed daily.

5. A team is tracking the number of fields left blank on an application. Each day, a sample of 100 applications is audited.

6. Another team is doing the same thing as the team in example 5 (counting the number of fields left blank on an application), only they are looking at all the applications that come in daily. Each day, 50-100 applications are turned in.

7. The team is tracking the number of abandoned calls to a customer call center in a shift. Each shift takes from 200-400 calls.

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21

Variable Control Charts–Xbar R-Chart

In class we will show you how to construct in Minitab two continuous Control Charts (Xbar and R Chart and I/MR Chart) and one Discrete Chart (p Chart). The remainder will be reference material. Note: All Control Chart interpretation is identical.

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We will now focus on the Variable Control Chart with Rational Subgrouping: the Xbar & Range Chart.

22Selecting The Appropriate Control Chart



Constant Lot Size?

uu pp


cc npnp


Possible?




No Yes YesNo

Xbar & Range

Xbar & Range

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General Comments on Xbar & Range Charts:

Cluster or periodic measurements of characteristicFrequency depends on speed and stability of process. Subgroup averages are plotted on Xbar chartXbar chart monitors central tendency of a process over timeSubgroup ranges plotted on Range ChartR-Chart monitors the variability of a process over timeProvides data-smoothing effect

In Minitab: Stat > Control Charts > Xbar-R

23A Valid Variable Control Chart Has…

Data in time or production sequence – To show stability, time-to-time variationA measure of central tendency – To portray behavior of process centerA measure of variabilityControl limits – To allow separating common cause from assignable (special) cause

Xbar & Range Charts

Xbar Chart: a plot of the sample means over timeR-Chart: a plot of the range (difference between highest and lowest values) of a sample over time

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24

Variable Control Charts–I & MR Chart

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Constant Lot Size?

uu pp


cc npnp


Possible?




No Yes YesNo

Xbar & Range

Xbar & Range

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General Comments on I & MR Charts:Range value artificially constructed from successive readingsSubgroup size for X is n = 1; for MR is usually 2Some correlation between charts is possibleMore “noise” in chart–tougher to spot true process shiftDisplays the variability between individual observations over time Assumes that past and present data is equally important

In Minitab: Stat > Control Charts > I-MR

26Individuals & Moving Range Charts

Can use in intermittent operationsSimilar to Xbar & R-Charts, Except...– Single Values, Not Subgroups– Range Values must be artificially constructed– Somewhat “Noisier”, since you track each individual

value (transaction,etc.)Individuals Chart: a plot of the individual values over timeMoving Range Chart: a plot of the moving range (for two samples |Xi –( Xi-1)|over time)

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An Individuals chart plots actual data–each transaction.

A Moving Range chart calculates ranges between consecutive data points (absolute value). You lose one data point, since the range is not calculated for the first point.

27Building An Individuals And Moving Range ChartIndividual Data Moving Range

55 N/A

56 ABS(55-56) = 1

59 ABS(56-59) = 3

55 ABS(59-55) = 4

Individuals

4

3

2

1

0

Moving Range

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28Take Aways–Variable Control Charts

Variable control charts can be used with continuous data to tellwhen a process is:– Experiencing only common cause variation and working at its intended

best– When the process is disturbed and needs corrective action

Control charts:– Time ordered plot of data– Reflect the expected range of variation of the data– Identify when a special cause appears to be influencing the data

Xbar & R-Charts are used for plotting means and ranges of subgroups over time I & MR charts are used for plotting individual values and moving ranges over time

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29Take Aways–Variable Control Charts

Control limits are typically calculated as + 3 standard deviations away from the mean of the process Control limits and specification limits are not the same– Control limits are calculated from the sample data; they are internal to the

process– Specification limits are determined by your performance standard; they

are external to the process (generally come from the customer)Know when a process is out of control: Western Electric RulesControl charts are only as good as the actions that you take to keep the process in control

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30Variable Control Charts: Activity (10 minutes)

Practice using Minitab to generate an Xbar and R Chart.Think about the correct Data File: Variable Control Charts.mtwrational subgroup.

The quality team has 25 weeks of historical data, contained in the file listed above. You have been asked to examine their data andbelieve an Xbar and R Chart, or an I/MR Chart would be the appropriate tool to use.

1. Plot the data using an I and MR chart.

2. Plot the data as Xbar/R-charts, forming subgroups by shift, day, and week.

3. For each chart created in 1 and 2 above, answer the following:A. Is the chart for spread stable?B. Is the chart for center stable?

10 minutes


ObjectiveObjective

TimeTime

Stat > Control Charts > Xbar-R.

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Stat > Control Chart > I-MRVariable: Response TimeClick on TESTS: Perform “All 8 Tests”

Minitab Output 31

1000500Subgroup 0

600500400

300200100

0-100

12

11

444

1

511

6 22

1115

1

11

515511 1 11

777

111

44444

11 1

77 7 2X=84.00

3.0SL=205.2

-3.0SL=-37.19

500

400

300

200

100

0

1

2

1112

11

2 2 222

111

11

1

2

1111

1 11 111

2

11111

111

22222222 2R=45.57

3.0SL=148.9

-3.0SL=0.00E+00

I and MR Chart for Response

Indi

vidu

al V

alue

Mov

ing

Ran

ge

Response Time

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Minitab Output (continued) 32

Xbar/R Chart for ResponseTime: Day

SUBGRP.MTW: Xbar/R for Response Time

Stat > Control Charts > Xbar-RSingle Cause: Response TimeSubgroup Size: DayClick on > Tests: “Perform All 8 Tests”

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33

Attribute Control Charts

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If the data being analyzed is discrete (attribute), you would need to determine:

If you have a constant lot (sample) size or if the lot (sample) size is not constant

If you are counting defects you may have multiple defects per unit. If you are counting defectives, the unit either is or is not defective.

In this module, we will study the different types of control charts and when to use each one.

What you want the Control Chart to tell you is:Is my level of non-conformance consistent?Am I controlling my significant X’s?

details.further for JoggerMemory Refer to* TM

34Selecting The Appropriate Control Charts

Attribute DataVariable or

Attribute Data?*


Constant Lot Size?

uu pp


cc npnp


Possible?




No Yes YesNo

Xbar & Range

Xbar & Range

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Other terminology may also be used:

A defect is also known as a nonconformanceA defective is known as a nonconforming

35Important Definitions

A DefectA single characteristic that does not meet requirements

A DefectiveA unit that contains one or more defects

Attribute Charts Can Consider Either Case, Depending On The Chart Type Chosen

Attribute Charts Can Consider Either Case, Depending On The Chart Type Chosen

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To choose the appropriate attribute control chart, use the following factors:

1. Is it defects or defectives that you are investigating in the data you are collecting?

For example:Is it pass/fail for the part or process?Or is it several sub-components or sub-processes passed/failed for the part or process)?

2. Is it a constant lot (sample) size or variable lot (sample) size?

36Classification Of Attribute Chart Types

c u

n p p

ConstantSample Size

VariableSample Size

Defects Can not count non-occurrences

Can count occurrencesDefective

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37

Attribute Control ChartsP-Chart

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P-ChartVariable or

Attribute Data?*


Constant Lot Size?

uu pp


cc npnp


Possible?




No Yes YesNo

Xbar & Range

Xbar & Range

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P–chart shows the Proportion Defective–the proportion that do not conformThe units may have one or more defects

39P-Chart

Chart of proportion defective Variable subgroup/lot size (n)

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Desired Outcome: Practice interpreting P-Chart

5 mins.TeamInterpret P-Chart results andanswer questions

Interpret Control Charts

5 mins.AllChoose a spokesperson to reportout on your responses to thequestions

CloseExercise

5 mins.TeamIn your team, read backgroundinformation on the next page

Preparation

TimingWhoHowWhat

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41Interpreting Control Charts–Activity

The loan department has made a change to the loan application process. They think the change will help weed out the bad loan risks before the applications are actually submitted. If they are right, the approval rate for submitted applications should increase. They want to check to see if this change in the process has had the desired effect.1. Is there evidence that the new process made a difference?2. What is the number of opportunities for defect in this process measure? 3. Is this an input, process, or output variable? Why?

% A

pplic

atio

ns A

ppro

ved

Week (Time Order)

3.0SL = 97.71

-3.0SL = 74.18

= 85.94

0 10 20 3070

80

90

New Process Implemented 93.79

89.86

82.02

78.09

•• •

•

•

•• • •

•

••

•

•

• •

••

•

•

•

••

•

•

••

Note: “SL” is the standard Minitab notation for “Sigma Limits” which are the same as Control Limits.

P-Chart Of Loan Approval Rate

May 1 To November 5

P

To create a p-chart in Minitab:

STAT > CONTROL CHARTS > P

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42Reference Materials–Attribute Control Charts C-Chart

Reference Materials–Attribute Control Charts

C-Chart

Pages 43-60 cover c, np and u charts. All Attribute Charts are interpreted as discussed in the previous pages for p-charts. Review these charts with your mentor for additional exercises.

Proceed to page 61

Stat > Control Charts:

All 4 Attribute Charts: (p,np,c,u) can be generated from this menu.

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Attribute Data?*


Constant Lot Size?

uu pp


cc npnp


Possible?




No Yes YesNo

Xbar & Range

Xbar & Range

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44C-Chart

Chart for countsBased on Poisson distribution– High probability of finding defect of some

type. Large samples are needed if defectprobabilities are low.

– Lower probability of a defect of a giventype

Works best on complex unit of productConstant subgroup/lot size

C bar = DPU = number of defects detected/subgroup

A subgroup may contain one or more “physical” units.

You need C bar up around 5. If it is less than 5, your distribution will be skewed because it will be truncated by 0.

Increase your subgroup size if you need to increase C bar or collapse existing categories into meaningful groups. More specifically, combine two or more categories so that the frequencies are greater than 5.

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Desired Outcome: Practice interpreting C-Chart

5 mins.Facilitator(Sub-group)

Interpret C-Chart by answering thequestions on the page

InterpretControl Charts


CloseExercise

5 mins.AllIn your team, read background information. Review chart on next 2 pages

Preparation

TimingWhoHowWhat

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46Interpreting Control Charts–Activity (continued)

An applications group of a large insurer recently made some changes to the design of their application. The old applications had 10 fields for the customer to fill out; the new application has 5 fields for the customer to fill out. They are now monitoring the incoming applications to ensure the new design has had an impact on completeness. A random sample of 100 applications are reviewed each day and the total number of incomplete fields are plotted.The chart for this data is on the following page.1. Why is the control chart a C-Chart?2. Is the number of errors in a sample stable over the 20–day sample?3. What questions does the chart raise?Extra Credit!! Calculate baseline sigma for the first 20 days of service for the new application.

Day Data Day Data Day Data Day Data

1 5 6 9 11 6 16 7

2 5 7 9 12 6 17 7

3 11 8 8 13 7 18 8

4 5 9 8 14 5 19 12

5 8 10 7 15 6 20 13

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0 10 20

0

5

10

15

Day of Sample

Num

ber o

f Inc

ompl

ete

Fiel

ds

C=7.600

3.0SL=15.87

-3.0SL=0.00E+00

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48

Attribute Control ChartsU-Chart

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Attribute Data?*


Constant Lot Size?

uu pp


cc npnp


Possible?




No Yes YesNo

Xbar & Range

Xbar & Range

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50U-Chart

Chart for defects per unit, with variable lot (subgroup) sizeSame logic as C-Chart, except variable lot (subgroup) size (n)

Compare to C-Chart In Minitab:Stat > Control Charts > I

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U-Chart Activity (20 minutes) 51

Desired Outcome: Practice constructing and interpreting U-Chart

10 mins.TeamIn the U-Chart.mtw, column errorscontains data (in time sequence)of the defects found each day oncustomer orders. A defect isdefined to be inaccurateinformation found on a customerorder. Both the number of defectsand the daily number of orders arerecorded.

Using Minitab, construct a U-Chart of the data

What are your observations?

Construct And Interpret The U-Chart

9 mins.AllChoose a spokesperson to reportout your conclusions

Close

1 min.AllIn your team, prepare to create a U-Chart in Minitab

Preparation

TimingWhoHowWhat

Note: Do not turn the page until you have completed the activity.

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52U-Chart Example Minitab Menu Commands

MINITAB FILE: U_Chart.mtw

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53U-Chart Minitab Input & Output

0 10 20 30

1

2

3

Sample Number

Sam

ple

Cou

nt

U Chart for errors

U=1.764

3.0SL=2.114

-3.0SL=1.415

CONTROL: The process does not look stable–there are indications pf special cause variations.

Why do the control limits vary? Lot (Sample) size varies.

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54

Attribute Control ChartsNP-Chart

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NP-ChartVariable or

Attribute Data?*


Constant Lot Size?

uu pp


cc npnp


Possible?




No Yes YesNo

Xbar & Range

Xbar & Range

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56NP-Chart

NP-chart: number of defectives (non-conforming items) in subgroupSame logic as the P-Chart, except constant subgroup/lot size (n)

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Desired Outcome: Practice interpreting NP-Chart

5 mins.TeamInterpret NP-Chart results andanswer questions

Interpret Control Charts


CloseExercise

5 mins.TeamIn your team, read backgroundinformation on next 2 pages

Preparation

TimingWhoHowWhat

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An applications group of a large insurer recently made some changes to the design of their application. They are now monitoring the incoming applications to ensure the new design has had an impact on completeness. 150 applications are chosen randomly and reviewed each day. The number that are incomplete are plotted each day

The chart for this data is on the following page.1. Why is the chart an NP–chart?2. What questions does the chart raise about the completeness of the insurance

application?3. What is the number of opportunities for defect in this measure?4. What is the difference between the value plotted on a P–and an NP–Chart?

Day Data Day Data Day Data Day Data

1 12 6 14 11 2 16 11

2 22 7 16 12 15 17 17

3 14 8 19 13 8 18 12

4 15 9 11 14 12 19 11

5 12 10 1 15 12 20 21

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Day of Sample

# of

Inco

mpl

ete

Appl

icat

ions

0 10 20

0

5

10

15

20

25

NP=12.85

3.0SL=23.13

-3.0SL=2.567

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60Attribute Chart Subgroup Size

Rule of Thumb:– Select a subgroup size that will provide an average defect/defective of

approximately

To Make UCL & LCL Nearly Symmetrical Around the Mean

– For NP-charts, to select the appropriate sample size such that 95% of the subgroups will have at least one defective, use the relationship

pn 3=

5.0 NP ,U ,C >

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Defects orDefective

ConstantLot Size?

uu pp

Defects orDefective

cc npnp

RationalSubgrouping

Possible?



Xbar &Range

Xbar &Range


No Yes No Yes

61Summary Of Attribute Charts

Useful when variable data not availableUse count/classification data–pass/fail, good/bad Same general rules for interpretation as variable chartsUseful as end-to-end overview; use variable charts for further study of problemsCan use data gathered for other purposesGenerally less expensive to administer, but tell you less

ShortcomingsIncluding too many variables makes interpretation difficultMust fit the parameters you are evaluating to theoretical distribution [Poisson (C, U-Charts), Binomial (P, NP-Charts)]Need to evaluate whether constant/non-constant lot size will help you with root cause analysisSensitivity is dependent on magnitude of defect level

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62Take Aways Attribute Control Charts

Attribute control charts are used to monitor the level of nonconformance of a processSelect the appropriate attribute control chart based upon– Constant vs. variable lot (sample) size– Defects vs. defectives

Defect– A single characteristic that does not meet requirements

Defective– A unit that contains one or more DEFECTS

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63Summary–Control Charts

All control charts have the same form– Time plot of data– Statistical limits placed +/- 3s from center lineChoose the control chart according to:– Data type– Sample sizeInterpret and act on the control chart– Investigate special causes of variation– Assess baseline sigma in order to understand if we are performing to

customer CTQ’s– Shrink common cause variation by making fundamental changes in the

Vital Few X variablesMaintain the control chart– Make notes on the control chart to indicate problems, changes, or

important events

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64

Calculating Control Limits(Optional)

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65Control Limit Calculations

The formulas for calculating control limits are shown on the following pagesThere are different tables for continuous and discrete dataBoth continuous and discrete data control charts have control limits that are placed +/- 3 estimated sigma from the average line

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66Control Limit Calculations–Formulas

Continuous DataControl limits are calculated using control chart factors and the Range-Bar (an estimate of short-term sigma)Control chart factors were invented by Shewart in the 1920’s to avoid long-hand calculationControl chart factors are shown in the table according to the sample size for each subgroupIndividual control charts are considered to have a sample of size 2, the number of data points make up the moving range

Discrete DataControl limits are calculated using a formula that estimates sigma without the necessity to transform the dataThe normal estimate for sigma (under radical) is then multiplied by three

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67Control Limit Calculations–Continuous Data Table

Type Control Chart

Average and Range

Sample Size n

Central Line* Control Limits

Median and Range

(X1 + X2 + … Xk)k

(X1 + X2 + … Xk)k

UCLx = X + A2RLCLx = X - A2R

UCLx = X + E2RmLCLx = X - E2Rm

˜ ˜ ˜

X and Rm

Individuals and Moving Range

1

(R1 + R2 +…Rk-1)k-1Rm =

X =

I(Xi+1 - Xi)IRm =UCLRm = D4RmLCLRm = D3Rm

ΣXin

k = # of subgroups, X = median value within each subgroup

*X =

˜

X and R

< 10, butusually 3 to 5

X =

(R1 + R2 +…Rk)kR = UCLR = D4R

LCLR = D3R˜

˜ ˜

X and s

Average andStandardDeviation

(X1 + X2 + … Xk)kX =

(s1 + s2 +…sk)ks =

UCLx = X + A3sLCLx = X - A3s

UCLs = B4sLCLs = B3s

Usually ≥ 10

˜

X and R

(X1 + X2 +…Xk)kX =

(R1 + R2 +…Rk)kR =

UCLx = X + A2RLCLx = X - A2R

UCLR = D4RLCLR = D3R

< 10, butusually 3 to 5

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68Control Limit Calculations–Table Of Contents

A2 D3 D4 A3 B3 B4 c4*

2 1.880 0 3.267 2.659 0 3.267 .7979

3 1.023 0 2.574 1.954 0 2.568 .8862

4 0.729 0 2.282 1.628 0 2.266 .9213

5 0.577 0 2.114 1.427 0 2.089 .9400

6 0.483 0 2.004 1.287 0.030 1.970 .9515

7 0.419 0.076 1.924 1.182 0.118 1.882 .9594

8 0.373 0.136 1.864 1.099 0.185 1.815 .9650

9 0.337 0.184 1.816 1.032 0.239 1.761 .9693

10 0.308 0.223 1.777 0.975 0.284 1.716 .9727

A2 D3 D4 E2 D3 D4 d2*

2 – 0 3.267 2.659 0 3.267 1.128

3 1.187 0 2.574 1.772 0 2.574 1.693

4 – 0 2.282 1.457 0 2.282 2.059

5 0.691 0 2.114 1.290 0 2.114 2.326

6 – 0 2.004 1.184 0 2.004 2.534

7 0.509 0.076 1.924 1.109 0.076 1.924 2.704

8 – 0.136 1.864 1.054 0.136 1.864 2.847

9 0.412 0.184 1.816 1.010 0.184 1.816 2.970

10 – 0.223 1.777 0.975 0.223 1.777 3.078

X and R ChartSampleSize

n

X and s Chart

X and R ChartSampleSize

n ˜

˜ X and Rm Chart

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69Control Limit Calculations–Discrete Data Table

np = # defectivesc = # of defectsn = sample size within

each subgroupk = # of subgroups

* This formula creates changing controllimits. To avoid this, use average sample sizes n for those samples that are within±20% of the average sample size. Calculate individual limits for the samples exceeding ± 20%.

If the Lower Control Limit (LCL) is a negative number, set the LCL to zero.

Type Control Chart

Fraction Defective

Number Defective

Number of Defects

Number of Defects Per

Unit

Sample Size

Variable,usually ≥ 50

Constant, usually ≥ 50

Constant

Variable

Control Limits

*UCLp = p + 3

*LCLp = p - 3

UCLnp = np + 3

LCLnp = np - 3

UCLc = c + 3

LCLc = c - 3

*UCLu = u + 3

*LCLu = u - 3

p-Chart

np-Chart

c-Chart

u-Chart

Central Line

For each subgroup:p = np/n

For all subgroups:p = ∑np/ ∑n

For each subgroup: np = # defectivesFor all subgroups:

np = ∑np/k

For each subgroup:c = # defects

For all subgroups:c = ∑c/k

For each subgroup:u = c/n

For all subgroups: u = ∑c/ ∑n

p(1 - p)n

p(1 - p)n

np(1 - p)

np(1 - p)

c

c

un

un

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DMAIC Book of Knowledge Green Belt

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