Training Materials Samples Important information about these Samples
This document contains random samples of Open Source Six Sigmas copyrighted intellectual property. They are intended to be used exclusively for your own personal evaluation of the training materials content. You are strictly prohibited from using these samples for any other reason. The sample modules provided include partial sections of modules from within the Open Source Six Sigma training materials content. Since we offer two versions of the training materials content - one featuring Minitab and one featuring SigmaXL, modules from both versions are included in this sample. When evaluating these samples notice the on-slide content is accompanied by additional explanation per slide, where applicable, in the notes section. Define Phase Six Sigma Fundamentals
Now we will continue in the Define Phase with the Six Sigma Fundamentals. The output of the Define Phase is a well developed and articulated project. It has been correctly stated that 50% of the success of a project is dependent on how well the effort has been defined. Theres that Y = f(X) thinking again. Six Sigma Fundamentals
Voice of the Customer Cost of Poor Quality Process Maps Process Metrics Six Sigma Fundamentals Selecting Projects Elements of Waste Understanding Six Sigma Wrap Up & Action Items The fundamentals of this phase are Process Maps, Voice of the Customer, Cost of Poor Quality and Process Metrics. Why have a process focus?
What is a Process? Why have a process focus? So we can understand how and why work gets done To characterize customer & supplier relationships To manage for maximum customer satisfaction while utilizing minimum resources To see the process from start to finish as it is currently being performed Defects: Blame the process, not the people process (proses) n. A repetitive and systematic series of steps or activities where inputs are modified to achieve a value-added output What is a Process?Many people do or conduct a process everyday but do they really think of it as a process?Our definition of a process is a repetitive and systematic series of steps or activities where inputs are modified and/or combined to achieve a value-added output. Usually a successful process needs to be well defined and developed. Examples of Processes Injection molding Decanting solutions Filling vial/bottles Crushing ore Refining oil Turning screws Building custom homes Paving roads Changing a tire Recruiting staff Processing invoices Conducting research Opening accounts Reconciling accounts Filling out a timesheet Distributing mail Backing up files Issuing purchase orders We go through processes every day.Below are some examples of those processes.Can you think of other processes within your daily environment? These are examples of processes and series of processes.Is your process on the list? The purpose of a Process Map is to:
Process Maps The purpose of a Process Map is to: Identify the complexity of the process Communicate the focus of problem solving Process Maps are living documents and must be changed as the process is changed: They represent what is currently happening not what you think is happening They should be created by the people who are closest to the process Process Map Step A Start Inspect Finish Step B Step C Step D Process Mapping, also called flowcharting, is a technique to visualize the tasks, activities and steps necessary to produce a product or a service. The preferred method for describing a process is to identify it with a generic name, show the workflow with a Process Map and describe its purpose with an operational description. Remember a process is a blending of inputs to produce some desired output. The intent of each task, activity and step is to add value, as perceived by the customer, to the product or service we are producing. You cannot discover if this is the case until you have adequately mapped the process. There are many reasons for creating a Process Map: - It helps all process members understand their part in the process and how their process fits into the bigger picture. - It describes how activities are performed and how the work effort flows, it is a visual way of standing above the process and watching how work is done. In fact, Process Maps can be easily uploaded into model and simulation software allowing you to simulate the process and visually see how it works. - It can be used as an aid in training new people. - It will show you where you can take measurements that will help you to run the process better. - It will help you understand where problems occur and what some of the causes may be. - It leverages other analytical tools by providing a source of data and inputs into these tools. - It identifies many important characteristics you will need as you strive to make improvements. The individual processes are linked together to see the total effort and flow for meeting business and customer needs. In order to improve or to correctly manage a process, you must be able to describe it in a way that can be easily understood. Process Mapping is the most important and powerful tool you will use to improve the effectiveness and efficiency of a process. Standard symbols for Process Mapping:
Process Map Symbols Standard symbols for Process Mapping: (available in Microsoft Office, Visio, iGrafx , SigmaFlow and other products) A RECTANGLE indicates an activity. Statements within the rectangle should begin with a verb A DIAMOND signifies a decision point. Only two paths emerge from a decision point: No and Yes An ELLIPSE shows the start and end of the process A PARALLELOGRAM shows that there are data An ARROW shows the connection and direction of flow 1 A CIRCLE WITH A LETTER ORNUMBER INSIDE symbolizesthe continuation of aflowchart to another page There may be several interpretations of some of the Process Mapping symbols; however, just about everyone uses these primary symbols to document processes. As you become more practiced you will find additional symbols useful, i.e. reports, data storage etc. For now we will start with just these symbols. High Level Process Map One of the deliverables from the Define Phase is a high level Process Map which at a minimum must include: Start and stop points All process steps All decision points Directional flow Value categories as defined here: Value Added: Physically transforms the thing going through the process Must be done right the first time Meaningful from the customers perspective (is the customer willing to pay for it?) Value Enabling: Satisfies requirements of non-paying external stakeholders (government regulations) Non-Value Added: Everything else At a minimum a high level Process Map must include; start and stop points, all process steps, all decision points and directional flow. Also be sure to include Value Categories such as Value Added (Customer Focus) and Value Enabling (External Stakeholder focus). Process Map for a Call Center -
Process Map Example Process Map for a Call Center - START LOGON TO PC & APPLICATIONS SCHEDULED PHONE TIME? LOGON TO PHONE CALL or WALK-IN? PHONE DATA CAPTURE BEGINS DETERMINE WHO IS INQUIRING ACCESS CASE TOOL CASE TOOL RECORD? Y N A Z CALL WALK-IN DETERMINE NATURE OF CALL & CONFIRM UNDERSTANDING C B D PHONE TIME REVIEW CASE TOOL HISTORY & TAKE NOTES PUT ON HOLD, REFER TO REFERENCES IMMEDIATE RESPONSE AVAILABLE? TRANSFER APPROPRIATE? ANSWER? QUERY INTERNAL HRSC SME(S) OFF HOLD AND ARRANGE CALL BACK PHONE DATA ENDS PROVIDE PHONE& NOTE DATA ENDS ADD TO RESEARCH LIST LOGOFF PHONE, CHECK MAIL, ,VOICE MAIL E EXAMINE NEXT NOTE OR RESEARCH ITEM ENTER APPROPRIATE SSAN (#,9s,0s) IF EMP DATA NOT POPULATED, ENTER OLD CASE UPDATE ENTRIES INCL OPEN DATE/TIME CREATE A CASE INCL CASE TYPE DATE/TIME, & NEEDED BY AUTO ROUTE CLOSED CLOSE CASE W/ DATE/TIME TAKE ACTION or DO RESEARCH F GO TO F or E DEPENDING ON NEXT Here is an example of a detailed Process Map. This is a Process Map of Call Center activities. Cross Functional Process Map
When multiple departments or functional groups are involved in a complex process it is often useful to use Cross Functional Process Maps. Draw in either vertical or horizontal Swim Lanes and label the functional groups then draw the Process Map General Accounting Bank Financial Vendor Department Start Request transfer Attach ACH form to Invoice Produce an Fill out ACH enrollment form Receive payment End info in FRS? Input info into web interface Match against bank batch and daily cash batch Accepts transactions, transfer money and provide batch total Review and Process transfer in FRS 3.0 Journey Entry 21.0 Reconciliation Maintain database to balance ACH transfers ACH Automated Clearing House. No Yes Sending Wire Transfers There are other types of Process Maps such as this Cross Functional Process Map. These are best used in transactional processes or where the process involves several departments. The lines drawn horizontally across the map represent different departments in the company and are usually referred to as Swim Lanes. By mapping in this manner one can see how the various departments are interdependent in this process. Create a high level Process Map, use enough detail to make it useful.
Process Map Exercise Exercise objective:Using your favorite Process Mapping tool create a Process Map of your project or functional area. Create a high level Process Map, use enough detail to make it useful. It is helpful to use rectangular post-its for process steps and square ones turned to a diamond for decision points. Color code the value added (green) and non-value added (red) steps. Be prepared to discuss this with your mentor. Read Exercise Objective and conduct the exercise. Measure Phase Process Discovery
Now we will continue in the Measure Phase with Process Discovery. Measurement System Analysis
Process Discovery Detailed Process Mapping Cause and Effect Diagrams FMEA Wrap Up & Action Items Process Capability Measurement System Analysis Six Sigma Statistics Welcome to Measure Process Discovery The purpose of this module is highlighted above.We will review tools to help facilitate Process Discovery. This will be a lengthy step as it requires a full characterization of your selected process. There are four key deliverables from the Measure Phase: (1) A robust description of the process and its workflow (2) A quantitative assessment of how well the process is actually working (3) An assessment of any measurement systems used to gather data for making decisions or to describe the performance of the process (4) A short list of the potential causes of our problem, these are the Xs that are most likely related to the problem. On the next lesson page we will help you develop a visual and mental model that will give you leverage in finding the causes to any problem. Overview of Brainstorming Techniques
We utilize Brainstorming techniques to populate a Cause and Effect Diagram seeking ALL possible causes for our issue of concern. Problem or Condition The Y The Xs (Causes) l Categories Material Measurement Environment People Machine Method The Problem Cause and Effect Diagram You will need to use brainstorming techniques to identify all possible problems and their causes. Brainstorming techniques work because the knowledge and ideas of two or more persons is always greater than that of any one individual. Brainstorming will generate a large number of ideas or possibilities in a relatively short time. Brainstorming tools are meant for teams, but can be used at the individual level also. Brainstorming will be a primary input for other improvement and analytical tools that you will use. You will learn two excellent brainstorming techniques, Cause and Effect Diagram and affinity diagrams. Cause and Effect Diagram are also called Fishbone Diagrams because of their appearance and sometimes called Ishikawa diagrams after their inventor. In a brainstorming session, ideas are expressed by the individuals in the session and written down without debate or challenge. The general steps of a brainstorming sessions are: Agree on the category or condition to be considered. Encourage each team member to contribute. Discourage debates or criticism, the intent is to generate ideas and not to qualify them, that will come later. Contribute in rotation (take turns), or free flow, ensure every member has an equal opportunity. Listen to and respect the ideas of others. Record all ideas generated about the subject. Continue until no more ideas are offered. Edit the list for clarity and duplicates. Cause and Effect Diagram
Products Measurement People Method Materials Equipment Environment Transactional Policy Procedure Place Categories for the legs of the diagram can use templates for products or transactional symptoms. Or you can select the categories by process step or what you deem appropriate for the situation. Problem or Condition The Y The Xs (Causes) l Categories Material Machine The Problem Cause and Effect Diagram A Cause and Effect Diagram is a composition of lines and words representing a meaningful relationship between an effect, or condition, and its causes. To focus the effort and facilitate thought, the legs of the diagram are given categorical headings. Two common templates for the headings are for product related and transactional related efforts. Transactional is meant for processes where there is no traditional or physical product; rather it is more like an administrative process. Transactional processes are characterized as processes dealing with forms, ideas, people, decisions and services. You would most likely use the product template for determining the cause of burnt pizza and use the transactional template if you were trying to reduce order defects from the order taking process. A third approach is to identify all categories as you best perceive them. When constructing a Cause and Effect Diagram, keep drilling down, always asking why, until you find the Root Causes of the problem. Start with one category and stay with it until you have exhausted all possible inputs and then move to the next category. The next step is to rank each potential cause by its likelihood of being the Root Cause. Rank it by the most likely as a 1, second most likely as a 2 and so on. This make take some time, you may even have to create sub-sections like 2a, 2b, 2c, etc. Then come back to reorder the sub-section in to the larger ranking. This is your first attempt at really finding the Y=f(X); remember the funnel? The top Xs have the potential to be the critical Xs, those Xs which exert the most influence on the output Y. Finally you will need to determine if each cause is a control or a noise factor.This as you know is a requirement for the characterization of the process. Next we will explain the meaning and methods of using some of the common categories. Cause and Effect Diagram
The Measurement category groups Root Causes related to the measurement and measuring of a process activity or output: Examples of questions to ask: Is there a metric issue? Is there a valid measurementsystem? Is the data goodenough? Is data readily available? Measurement Y The People category groups Root Causes related to people, staffing and Organizational structure: Examples of questions to ask: Are people trained, do they have the right skills? Is there person to person variation? Are people over-worked, under-worked? Y Please read the slide. Cause and Effect Diagram
The Materials category groups Root Causes related to parts, supplies, forms or information needed to execute a process: Examples of questions to ask: Are bills of material current? Are parts or supplies obsolete? Are there defects in the materials? How is this performed? Are procedures correct? What might be unusual? The Method category groups Root Causes related to how the work is done, the way the process is actually conducted: Y Method Materials Please read the slide. Cause and Effect Diagram
Display Slide: Equipment The Equipment category groups Root Causes related to tools used in the process: Examples of questions to ask: Have machines been serviced recently,what is the uptime? Have tools been properly maintained? Is there variation? The Environment (a.k.a. Mother Nature) category groups Root Causes related to our work environment, market conditions and regulatory issues. Is the workplace safe andcomfortable? Are outside regulations impacting thebusiness? Does the company culture aid theprocess? Y Equipment Environment Please read the slide. WHICH Xs CAUSE DEFECTS?
Classifying the Xs The Cause & Effect Diagram is a tool to generate opinions about possible causes for defects. For each of the Xs identified in the diagram classify them as follows: Controllable:C (Knowledge) Procedural:P (People, Systems) Noise:N (External or Uncontrollable) Think of procedural as a subset of controllable.Unfortunately many procedures within a company are not well controlled and can cause the defect level to increase.The classification methodology is used to separate the Xs so they can be used in the X-Y Matrix and the FMEA taught later in this module. The Cause and Effect Diagram is an organized way to approach brainstorming.This approach allows us to further organize ourselves by classifying the Xs into controllable, procedural or noise types. WHICH Xs CAUSE DEFECTS? Chemical Purity Example
Measurement Incoming QC (P) Measurement Method (P) Capability (C) Manpower Skill Level (P) Adherence to procedure (P) Work order variability (N) Materials Raw Materials (C) Multiple Vendors (C) Specifications (C) Startup inspection (P) Handling (P) Purification Method (P) Methods Room Humidity (N) RM Supply in Market (N) Shipping Methods (C) Mother Nature Nozzle type (C) Data collection/feedback (P) Equipment Column Capability (C) Temp controller (C) Chemical Purity Insufficient staff (C) Training on method (P) This example of the Cause and Effect Diagram addresses a chemical purity issue.Notice how the input variables for each branch are classified as Controllable, Procedural or Noise. Analyze Phase Inferential Statistics (SigmaXL Version)
Now we will continue in the Analyze Phase with Inferential Statistics. Inferential Statistics
Nature of Sampling Central Limit Theorem Inferential Statistics Hypothesis Testing NND P1 Hypothesis Testing ND P1 Intro to Hypothesis Testing X Sifting Welcome to Analyze Hypothesis Testing ND P2 Wrap Up & Action Items Hypothesis Testing NND P2 The fundamentals of this phase are Inferential Statistics, Nature of Sampling and Central Limit Theorem. Putting the pieces of the puzzle together.
Nature of Inference inference (n.) The act or process of deriving logical conclusions from premises known or assumed to be true. The act of reasoning from factual knowledge or evidence. 1 1. Dictionary.com Inferential Statistics To draw inferences about the process or population being studied by modeling patterns of data in a way that accounts for randomness and uncertainty in the observations. 2 2. Wikipedia.com Putting the pieces of the puzzle together. inferenceis The act or process of deriving logical conclusions from premises known or assumed to be true. The act of reasoning from factual knowledge or evidence. Inferential Statistics is used to draw inferences about the process or population being studied by modeling patterns of data in a way that accounts for randomness and uncertainty in the observations. One objective of Six Sigma is to move from only describing the nature of the data or Descriptive Statistics to the ability infer meaning from data as to what will happen in the future or Inferential Statistics. 5 Step Approach to Inferential Statistics
So many questions.? 1. What do you want to know? 2. What tool will give you that information? 5. How confident are you with your data summaries? 4. How will you collect the data? 3. What kind of data does that tool require? As with most things you have learned associated with Six Sigma there are defined steps to be taken. 4. Lack of measurement validity
Types of Error 1.Error in sampling Error due to differences among samples drawn at random from the population (luck of the draw). This is the only source of error that statistics can accommodate. 2.Bias in sampling Error due to lack of independence among random samples or due to systematic sampling procedures (height of horse jockeys only). 3.Error in measurement Error in the measurement of the samples (MSA/GR&R). 4.Lack of measurement validity Error in the measurement does not actually measure what it is intended to measure (placing a probe in the wrong slot measuring temperature with a thermometer that is just next to a furnace). Types of error contribute to uncertainty when trying to infer with data. There are four types of error that are explained above. Population, Sample, Observation
EVERY data point that has ever been or ever will be generated from a given characteristic. Sample A portion (or subset) of the population, either at one time or over time. Observation An individual measurement. X Lets just review a few definitions: A population is EVERY data point that has ever been or ever will be generated from a given characteristic. A sample is a portion (or subset) of the population, either at one time or over time.An observation is an individual measurement. Significance is all about differences
Practical difference and significance is: The amount of difference, change or improvement that will be of practical, economic or technical value to you. The amount of improvement required to pay for the cost of making the improvement. Statistical difference and significance is: The magnitude of difference or change required to distinguish between a true difference, change or improvement and one that could have occurred by chance. Twins: Sure there are differences but do they matter? In general larger differences (or deltas) are considered to be more significant.As you see here we can experience both a practical difference and a statistical difference. Six Sigma decisions will ultimately have a return on resource investment (RORI) element associated with them. So the key question of interest for our decisions is is the benefit of making a change worth the cost and risk of making it? Mean Shift and Variation Reduction
The Mission Variation Reduction LSL USL Mean Shift Mean Shift and Variation Reduction LSL USL Shift & Reduce Your mission, which you have chosen to accept, is to reduce cycle time, reduce the error rate, reduce costs, reduce investment, improve service level, improve throughput, reduce lead time, increase productivity change the output metric of some process, etc. In statistical terms this translates to the need to move the process Mean and/or reduce the process Standard Deviation. You will be making decisions about how to adjust key process input variables based on sample data, not population data - this means you are taking some risks. How will you know your key process output variable really changed and is not just an unlikely sample?The Central Limit Theorem helps us understand the risk we are taking and is the basis for using sampling to estimate population parameters. Remember the law of conservation of mass that, matter can never be created nor destroyed. So the areas under the curves of each of these distributions should always remain the same (relatively = 1) and so when the variation is reduced the peak height will proportionately increase as the sample size (or matter) remains constant. A Distribution of Sample Means
Imagine you have some population. The individual values of this population form some distribution. Take a sample of some of the individual values to calculate the sample Mean. Keep taking samples and calculating sample Means. Plot a new distribution of these sample Means. The Central Limit Theorem says as the sample size becomes large this new distribution (the sample Mean distribution) will form a Normal Distribution no matter what the shape of the population distribution of individuals. Please read the slide. Sampling DistributionsThe Foundation of Statistics
3 5 2 12 10 1 6 14 11 9 Population Sample 1 Sample 2 Sample 3 Samples from the population, each with five observations: In this example we have taken three samples out of the population each with five observations in it. We computed a Mean for each sample. Note the Means are not the same! Why not? What would happen if we kept taking more samples? Every statistic derives from a sampling distribution.For instance if you were to keep taking samples from the population over and over a distribution could be formed for calculating Means, Medians, Mode, Standard Deviations, etc.As you will see the above sample distributions each have a different statistic.The goal here is to successfully make inferences regarding the statistical data. Constructing Sampling Distributions
Roll em! To demonstrate how sampling distributions work we will use some random data for die rolls. Create a sample of 1,000 individual rolls of a die that we will store in a variable named Population. From the population we will draw five random samples. Sampling Distributions
SigmaXL allows us to take a random sample of the population.The data is stored in a newly created sheet.Use Recall Last SigmaXL Dialog with copy and paste to create multiple columns. Select the Die Example worksheet. This sheet has been created using a sample size of 5, 10 and 30 from the Population column. Improve Phase Advanced Process Modeling Multiple Linear Regression (Minitab Version)
Now we will continue with the Improve Phase Advanced Process Modeling MLR. Advanced Modeling & Regression
Review Corr./Regression Non-Linear Regression Transforming Process Data Multiple Regression Full Factorial Experiments Experimental Methods Designing Experiments Advanced Process Modeling: MLR Process Modeling: Regression Welcome to Improve Fractional Factorial Experiments Wrap Up & Action Items Within this module we are going to learn about Multiple Linear Regression. Correlation and Linear Regression Review
Correlation and Linear Regression are used: With historical process data.It is NOT a form of experimentation. To determine if two variables are related in a linear fashion. To understand the strength of the relationship. To understand what happens to the value of Y when the value of X is increased by one unit. To establish a Prediction Equation enabling us to predict Y for any level of X. Correlation explores association. Correlation and regression donot imply a causal relationship. Designed experiments allow for true cause and effect relationships to be identified. Correlations: StirRate, Impurity Pearson correlation of StirRate and Impurity = 0.959 P-value = 0.000 Recall the Simple Linear Regression and Correlation covered in the previous module.The essential tools presented here define the relationship between two variables.An independent or input factor and typically an output response.Causation is NOT always proven; however the tools do present a guaranteed relationship. Use the worksheet named RB STATS CORRELATION.MTW Correlation Review Correlation is used to measure the linear relationship between two Continuous Variables (bi-variate data). Pearson Correlation Coefficient, r, will always fall between 1 and +1. A Correlation of 1 indicates a strong negative relationship, one factor increases the other decreases. A Correlation of +1 indicates a strong positive relationship, one factor increases so does the other. P-value > 0.05,Ho:No relationship P-value < 0.05,Ha:Is relationship -1.0 +1.0 Decision Points Strong Correlation No Correlation r The Pearson Correlation Coefficient, represented here as r, shows the strength of a relationship in Correlation. An r of zero indicates no correlation. The P-value proves the statistical confidence of our conclusion representing the possibility a relationship exists. Simultaneously, the Pearson Correlation Coefficient shows the strength of the relationship.For example, P-value standardized at .05, then 95% confidence in a relationship is exceeded by the two factors tested. Linear Regression Review
Linear Regression is used to model the relationship between a Continuous response variable (Y) and one or more Continuous independent variables (X).The independent predictor variables are most often Continuous but can be ordinal. Example of ordinal -Shift 1, 2, 3, etc. P-value > 0.05,Ho:Regression Equation is not significant P-value < 0.05,Ha:Regression Equation is significant The change in Impurity for every one unit change in StirRate (Slope of the Line) Presented here StirRate is directly related to Impurity of the process; the relationship between the two is one unit StirRate causes Impurity increase. StirRate locked at 30 and Impurity calculated by 30 times , subtracting gives us a 13.3 Impurity.Granted, we have an error in our model, the red points do not lie exactly on the blue line.The dependent response variable is Impurity and the StirRate is the independent predictor as both variables in this example are perpetual. Regression Analysis Review
Correlation tells us the strength of a linear relationship not the numerical relationship. The last step to proper analysis of Continuous Data is to determine the Regression Equation. The Regression Equation can mathematically predict Y for any given X. The Regression Equation from MINITABTM is the best fit for the plotted data. Prediction Equations: Y = a + bx(Linear or 1st order model) Y = a + bx + cx2(Quadratic or 2nd order model) Y = a + bx + cx2 + dx3(Cubic or 3rd order model) Y = a (bx)(Exponential) Numerical relationship is left out when speaking of Correlation.Correlation shows potency of linear relationship, mathematical relationship is shown by and through the Prediction Equation of Regression.As shown these Correlations or Regressions are not proven casual relationships. We are attempting to PROVE statistical commonality.Exponential, quadratic, simple linear relationships or even predictable outputs (Y) concern REGRESSION equations.More complex relationships are approaching. Simple versus Multiple Regression Review
Simple Regression One X, One Y Analyze in MINITABTM using Stat>Regression>Fitted Line Plot or Stat>Regression>Regression Multiple Regression Two or More Xs, One Y Analyze in MINITABTM Using Stat>Regression>Best Subsets Simple Regressions have one X and are referenced as the regressors or predictors. Multiple Xs give reason to the output or response variable, this is Multiple Regression analysis. In both cases the R-sq value estimates the amount of variation explained by the model. Regression Step Review
The basic steps to follow in Regression are as follows: Create Scatter Plot (Graph>Scatterplot) Determine Correlation (Stat>Basic Statistics>Correlation P-value less than 0.05) Run Fitted Line Plot choosing linear option (Stat>Regression>Fitted Line Plot) Run Regression (Stat>Regression>Regression) (Unusual Observations?) Evaluate R2, adjusted R2 and P-values Run Non-linear Regression if necessary (Stat>Regression>Fitted Line Plot) Analyze residuals to validate assumptions.(Stat>Regression>Fitted Line Plot>Graphs) Normally distributed Equal variance Independence Confirm one or two points do not overly influence model. One step at a time. How to run a Regression is defined here.Create a Scatter Plot, and understanding the variation between the Xs and Ys, activate a Correlation analysis allowing a potential linear relationship indication.The third step is to find existing linear mathematical relationships using a Prediction Equation then, fourth, to find the potency or strength of the linear relationship if one exists. Linear Regression accompanied by the variation of the input gives a variety of output results. Then completion of the fifth step yields the percentage a given output has. It also includes the answer to strength of statistical confidence within our linear regression. To conclude a Linear Regression exists a 95% statistical confidence or above has to be obtained.If unsatisfied conclusions are drawn, as a point of contingency, step six becomes essential.In step six we contemplate the potential Non-linear Regression. However this is only necessary if we cannot find a Regression Equation (statistical and practical) variation of output by way of scoping the input or by analyzing the model error for correctness.Step seven, depicted in subsequent slides, validates residuals for a proper model. Simple Regression Example
This data set is from the mining industry. It is an evaluation of ore concentrators. Graph > Scatterplot Recalling tools learned in the Analyze Phase presented here is a Simple Regression example examining a piece of equipment pertaining to a mining company. This diagram plots output to input following the Regression steps. Notice how the equipment is agitated by output of PGM concentrate.Opening the MINITABTM file named Concentrator.MTW will show how output is always applied to the Y axis (dependent) as input is always applied to the X axis (independent). Correlation Example Identifying the existing Linear Regression is the second step.Having the Pearson Correlation Coefficient at .847 and a P-value less than .05 we see with a very strong statistical confidence a Linear Regression.If no Correlation existed the coefficient would be closer to zero, remember? Regression Line Example
Stat > Regression > Fitted Line Plot Now finding the Prediction Equation of the linear relationship involves two factors; output response and input variable.Grams per ton of the PGM concentrate is output and the RPM of the agitator is input.Knowing a positive slope exists, by a greater than zero Correlation Coefficient, indicates the agitators RPM increases in correlation with the PGM concentrate.The slope of Linear Regression equals Did you recall the Pearson Correlation Coefficient exceeded zero? Linear Regression Example
Notice the unusual observation may indicate a Non-linear analysis may explain more of the variation in the data. The P-value < 0.05 therefore the Regression is significant. Shown here is a Linear Regression of 70% process variation. Considering step five, a 12 data point MINITABTM alert for a large residual comes to fruition.R squared, R squared adjusted and a unusual listing of observation pertain to our full Regression analysis.With these concerns refer to MINITABTM window (if necessary) and a Non-linear Regression might be in consideration. Regression Line Example
Stat>Regression>Fitted Line Plot Notice how the new line is a more appropriate demonstration of our data since the curvature better fits the plotted points.This is the essence of choosing a Non-linear Regression and choosing quadratic Regression.This model option can be used by simply clicking the word Quadratic in the MINITABTM window. Linear and Non-Linear Regression Example
Linear Model Non- Linear Model More variation is explained using the Non-linear model since the R-Squared is higher and the S statistic is lower which is the estimated Standard Deviation of the error in the model. We have here both Regression models.In terms of R squared being higher in percentage rate on the Non-linear model as opposed to that of the Linear we see more process variation. In addition S presents the estimated Standard Deviation of errors, Non-linear model has a lower decimal. Lets now consider the model error. You need not be perplexed, model error has many variables.Output dependency on the impact of other input variables and measurement system errors of output and inputs can be causes. MINITABTM Session Window displays these very Regression analyses so feel free to use that functionality. Residual Analysis Example
The recommendation here would be to use standardized residuals and Four in one option for plotting.In the upper left window Graph NEEDS to be clicked yielding appropriate modeling and analyzing the residuals to conclude the seventh step. Control Phase Statistical Process Control
We will now continue in the Control Phase with Statistical Process Control or SPC. Statistical Process Control
Six Sigma Control Plans Defect Controls Lean Controls Advanced Capability Advanced Experiments Welcome to Control Statistical Process Control (SPC) Wrap Up & Action Items Methodology Elements and Purpose Special Cause Tests Examples Statistical techniques can be used to monitor and manage process performance. Process performance, as we have learned, is determined by the behavior of the inputs acting upon it in the form of Y = f(X). As a result it must be well understood we can monitor only the performance of a process output. Many people have applied Statistical Process Control (SPC) to only the process outputs. Because they were using SPC their expectations were high regarding a new potential level of performance and control over their processes. However, because they only applied SPC to the outputs they were soon disappointed. When you apply SPC techniques to outputs it is appropriately called Statistical Process Monitoring or SPM. You of course know you can only control an output by controlling the inputs exerting an influence on the output. This is not to say applying SPC techniques to an output is bad, there are valid reasons for doing this. Six Sigma has helped us all to better understand where to apply such control techniques. In addition to controlling inputs and monitoring outputs control charts are used to determine the baseline performance of a process, evaluate measurement systems, compare multiple processes, compare processes before and after a change, etc. Control Charts can be used in many situations that relate to process characterization, analysis and performance. To better understand the role of SPC techniques in Six Sigma we will first investigate some of the factors that influence processes then review how simple probability makes SPC work and finally look at various approaches to monitoring and controlling a process. SPC Overview: Collecting Data
Population: An entire group of objects that have been made or will be made containing a characteristic of interest Sample: A sample is a subset of the population of interest The group of objects actually measured in a statistical study Samples are used to estimate the true population parameters Population Sample Control Charts are usually derived from samples taken from the population. Sampling must be collected in such a way it does not bias or distort the interpretation of the population. The process must be allowed to operate normally when taking a sample. If there is any special treatment or bias given to the process over the period the data is collected the Control Chart interpretation could be invalid. The frequency of sampling depends on the volume of activity and the ability to detect trends and patterns in the data. At the onset you should error on the side of taking extra samples then if the process demonstrates its ability to stay in control you can reduce the sampling rate. Using rational subgroups is a common way to assure you collect representative data. A rational subgroup is a sample of a process characteristic in which all the items in the sample were produced under very similar conditions over in a relatively short time period. Rational subgroups are usually small in size, typically consisting of 3 to 5 units to make up the sample. It is important that rational subgroups consist of units produced as closely as possible to each other especially if you want to detect patterns, shifts and drifts. If a machine is drilling 30 holes a minute and you wanted to collect a sample of hole sizes a good rational subgroup would consist of 4 consecutively drilled holes. The selection of rational subgroups enables you to accurately distinguish Special Cause variation from Common Cause variation. Make sure your samples are not biased in any way; meaning they are randomly selected. For example, do not plot only the first shifts data if you are running multiple shifts. Do not look at only one vendors material if you want to know how the overall process is really running.Finally do not concentrate on a specific time to collect your samples; like just before the lunch break. If your process consists of multiple machines, operators or other process activities producing streams of the same output characteristic you want to control it would be best to use separate Control Charts for each of the output streams. If the process is stable and in control the sample observations will be randomly distributed around the average. Observations will not show any trends or shifts and will not have any significant Outliers from the random distribution around the average. This type of behavior is to be expected from a normally operating process and that is why it is called Common Cause variation. Unless you are intentionally trying to optimize the performance of a process to reduce variation or change the average, as in a typical Six Sigma project, you should not make any adjustments or alterations to the process if is it demonstrating only Common Cause variation. That can be a big time saver since it prevents wild goose chases. If Special Cause variation occurs you must investigate what created it and find a way to prevent it from happening again. Some form of action is always required to make a correction and to prevent future occurrences. You may have noticed there has been no mention of the specification limits for the characteristic being controlled. Specification limits are not evaluated when using a Control Chart. A process in control does not necessarily mean it is capable of meeting the requirements. It only states it is stable, consistent and predictable. The ability to meet requirements is called Process Capability, as previously discussed. SPC Overview: I-MR Chart
An I-MR Chart combines a Control Chart of the average moving range with the Individuals Chart. You can use Individuals Charts to track the process level and to detect the presence of Special Causes when the sample size is one batch. Seeing these charts together allows you to track both the process level and process variation at the same time providing greater sensitivity to help detect the presence of Special Causes. Using the Orders worksheet, column Avg. Orders Per Month. Individual Values (I) and Moving Range (MR) Charts are used when each measurement represents one batch. The subgroup size is equal to one when I-MR charts are used. These charts are very simple to prepare and use. The graphic shows the Individuals Chart where the individual measurement values are plotted with the Center Line being the average of the individual measurements. The Moving Range Chart shows the range between two subsequent measurements. There are certain situations when opportunities to collect data are limited or when grouping the data into subgroups simply does not make practical sense. Perhaps the most obvious of these cases is when each individual measurement is already a rational subgroup. This might happen when each measurement represents one batch, when the measurements are widely spaced in time or when only one measurement is available in evaluating the process. Such situations include destructive testing, inventory turns, monthly revenue figures and chemical tests of a characteristic in a large container of material. All these situations indicate a subgroup size of one. Because this chart is dealing with individual measurements it is not as sensitive as the X-Bar Chart in detecting process changes. SPC Overview: Xbar-R Chart
If each of your observations consists of a subgroup of data rather than just individual measurements an Xbar-R Chart providers greater sensitivity. Failure to form rational subgroups correctly will make your Xbar-R Charts dangerously wrong. Use the Catapult X-Bar & R worksheet An Xbar-R is used primarily to monitor the stability of the average value. The Xbar Chart plots the average values of each of a number of small sampled subgroups. The averages of the process subgroups are collected in sequential, or chronological, order from the process. The Xbar Chart, together with the Rbar Chart shown, is a sensitive method to identify assignable causes of product and process variation and gives great insight into short-term variations. These charts are most effective when they are used as a matched pair. Each chart individually shows only a portion of the information concerning the process characteristic. The upper chart shows how the process average (central tendency) changes. The lower chart shows how the variation of the process has changed. It is important to track both the process average and the variation separately because different corrective or improvement actions are usually required to effect a change in each of these two parameters. The Rbar Chart must be in control in order to interpret the averages chart because the Control Limits are calculated considering both process variation and Center. When the Rbar Chart shows not in control, the Control Limits on theaverages chart will be inaccurate and may falsely indicate an out of control condition. In this case, the lack of control will be due to unstable variation rather than actual changes in the averages. Xbar and Rbar Charts are often more sensitive than I-MR but are frequently done incorrectly. The most common error is failure to perform rational sub-grouping correctly. A rational subgroup is simply a group of items made under conditions that are as nearly identical as possible. Five consecutive items made on the same machine with the same setup, the same raw materials and the same operator are a rational subgroup. Five items made at the same time on different machines are not a rational subgroup. Failure to form rational subgroups correctly will make your Xbar-Rbar Charts dangerously wrong. C Charts and U Charts are for tracking defects.
SPC Overview: U Chart C Charts and U Charts are for tracking defects. A U Chart can do everything a C Chart can so we will just learn how to do a U Chart. This chart counts flaws or errors (defects).One search area can have more than one flaw or error. Search area (unit) can be practically anything we wish to define. We can look for typographical errors per page, the number of paint blemishes on a truck door or the number of bricks a mason drops in a workday. You supply the number of defects on each unit inspected. Use the worksheet C and U Charts, column numexperr. The U Chart plots defects per unit data collected from subgroups of equal or unequal sizes. The U in U Charts stands for defects per Unit. U Charts plot the proportion of defects that are occurring. The U Chart and the C Chart are very similar. They both are looking at defects but the U Chart does not need a constant sample size as does the C Chart. The Control Limits on the U Chart vary with the sample size and therefore they are not uniform; similar to the P Chart which we will describe next. Counting defects on forms is a common use for the U Chart. For example, defects on insurance claim forms are a problem for hospitals. Every claim form has to be checked and corrected before going to the insurance company. When completing a claim form a particular hospital must fill in 13 fields to indicate the patients name, social security number, DRG codes and other pertinent data. A blank or incorrect field is a defect. A hospital measured their invoicing performance by calculating the number of defects per unit for each days processing of claims forms. The graph demonstrates their performance on a U Chart. The general procedure for U Charts is as follows: 1.Determine purpose of the chart 2.Select data collection point 3.Establish basis for sub-grouping 4.Establish sampling interval and determine sample size 5.Set up forms for recording and charting data and write specific instructions on use of the chart 6.Collect and record data. 7.Count the number of nonconformities for each of the subgroups 8.Input into Excel or other statistical software. 9.Interpret chart together with other pertinent sources of information on the process and take corrective action if necessary NP Charts and P Charts are for tracking defectives.
SPC Overview: P Chart NP Charts and P Charts are for tracking defectives. A P Chart can do everything an NP Chart can so we will just learn how to do a P Chart! Used for tracking defectives the item is either good or bad, pass or fail, accept or reject. Center Line is the proportion of rejects and is also your Process Capability. Input to the P Chart is a series of integers number bad, number rejected.In addition you must supply the sample size. Use the P Chart worksheet, column Late Reports, subgroup size: 100. The P Chart plots the proportion of nonconforming units collected from subgroups of equal or unequal size (percent defective). The proportion of defective units observed is obtained by dividing the number of defective units observed in the sample by the number of units sampled. P Charts name comes from plotting the Proportion of defectives. When using samples of different sizes the upper and lower control limits will not remain the same - they will look uneven as exhibited in the graphic. These varying Control Chart limits are effectively managed by Control Charting software. A common application of a P Chart is when the data is in the form of a percentage and the sample size for the percentage has the chance to be different from one sample to the next. An example would be the number of patients arriving late each day for their dental appointments. Another example is the number of forms processed daily requiring rework due to defects. In both of these examples the quantity would vary from day to day. The general procedure for P Charts is as follows: 1.Determine purpose of the chart 2.Select data collection point 3.Establish basis for sub-grouping 4.Establish sampling interval and determine sample size 5.Set up forms for recording and charting data and write specific instructions on use of the chart 6.Collect and record data. It is recommended that at least 20 samples be used to calculate the Control Limits 7.Compute P, the proportion nonconforming for each of the subgroups 8.Load data into Excel or other statistical software. 9.Interpret chart together with other pertinent sources of information on the process and take corrective action if necessary SPC Overview: Control Methods/Effectiveness
Type 1 Corrective Action = Countermeasure:improvement made to the process which will eliminate the error condition from occurring.The defect will never be created.This is also referred to as a long-term corrective action in the form of Mistake Proofing or design changes. Type 2 Corrective Action = Flag:improvement made to the process which will detect when the error condition has occurred.This flag will shut down the equipment so the defect will not move forward. SPC on Xs or Ys with fully trained operators and staff who respect the rules.Once a chart signals a problem everyone understands the rules of SPC and agrees to shut down for Special Cause identification. (Cpk > certain level). Type 3 Corrective Action = Inspection:implementation of a short-term containment which is likely to detect the defect caused by the error condition.Containments are typically audits or 100% inspection. SPC on Xs or Ys with fully trained operators.The operators have been trained and understand the rules of SPC, but management will not empower them to stop for investigation. S.O.P. is implemented to attempt to detect the defects.This action is not sustainable short-term or long-term. SPC on Xs or Ys without proper usage = WALL PAPER. Worst Best The most effective form of control is called a type 1 corrective action. This is a control applied to the process which will eliminate the error condition from occurring.The defect can never happen. This is the prevention application of the Poka-Yoke method. The second most effective control is called a type 2 corrective action. This a control applied to the process which will detect when an error condition has occurred and will stop the process or shut down the equipment so that the defect will not move forward. This is the detection application of the Poka-Yoke method. The third most effective form of control is to use SPC on the Xs with appropriate monitoring on the Ys. To be effective employees must be fully trained, they must respect the rules and management must empower the employees to take action.Once a chart signals a problem everyone understands the rules of SPC and agrees to take emergency action for Special Cause identification and elimination. The fourth most effective correction action is the implementation of a short-term containment which is likely to detect the defect caused by the error condition.Containments are typically audits or 100% inspection. Finally you can prepare and implement an S.O.P. (standard operating procedure) to attempt to manage the process activities and to detect process defects.This action is not sustainable, either short-term or long-term. Do not do SPC for the sake of just saying that you do SPC. It will quickly deteriorate to a waste of time and a very valuable process tool will be rejected from future use by anyone who was associated with the improper use of SPC. Using the correct level of control for an improvement to a process will increase the acceptance of changes/solutions you may wish to make and it will sustain your improvement for the long-term. Purpose of Statistical Process Control
Not this special cause!! Every process has Causes of Variation known as: Common Cause:Natural variability Special Cause: Unnatural variability Assignable:Reason for detected Variability Pattern Change:Presence of trend or unusual pattern SPC is a basic tool to monitor variation in a process. SPC is used to detect Special Cause variation telling us the process is out of control but does NOT tell us why. SPC gives a glimpse of ongoing process capability AND is a visual management tool. SPC has its uses because every process has variation known as both Special Cause and Common Cause variation.Special Cause variation is unnatural variability because of assignable causes or pattern changes.SPC is a powerful tool to monitor the variation of a process.This powerful tool is often an aspect used in Visual Factories.If a supervisor or operator or staff is able to quickly monitor how its process is operating by looking at the key inputs or outputs of the process this would exemplify a Visual Factory. SPC is used to detect Special Causes in order to have those operating the process find and remove the Special Cause.When a Special Cause has been detected the process is considered to be out of control. SPC gives an ongoing look at the process capability.It is not a capability measurement but it is a visual indication of the continued Process Capability of your process. Elements of Control Charts
Process Center (usually the Mean) Special Cause Variation Detected Control Limits Graphical and visual plot of changes in the data over time. This is necessary for visual management of your process. Control Charts were designed as a methodology for indicating change inperformance, either variation or Mean/Median. Charts have a Central Line and Control Limits to detect Special Cause variation. Use the Orders worksheet, column Avg. Orders Per Month 2. Control Charts were first developed by Dr. Shewhart in the early 20th century in the U.S.Control Charts are a graphical and visual plot of a process and charts over time like a Time Series Chart.From a visual management aspect a Time Plot is more powerful than knowledge of the latest measurement.These charts are meant to indicate change in a process.All SPC charts have a Central Line and Control Limits to aid in Special Cause variation. Notice again we never discussed showing or considering specifications.We are advising you to never have specification limits on a Control Chart because of the confusion often generated.Remember we want to control and maintain the process improvements made during the project.These Control Charts and their limits are the Voice of the Process. These charts give us a running view of the output of our process relative to established limits. Understanding the Power of SPC
Control Charts indicate when a process is out of control or exhibiting Special Cause variation but NOT why! SPC Charts incorporate upper and lower Control Limits. The limits are typically +/- 3 from the Center Line. These limits represent 99.73% of natural variability for Normal Distributions. SPC Charts allow workers and supervision to maintain improved process performance from Lean Six Sigma projects. Use of SPC Charts can be applied to all processes. Services, manufacturing and retail are just a few industries with SPC applications. Caution must be taken with use of SPC for Non-normal processes. Control Limits describe the process variability and are unrelated to customer specifications.(Voice of the Process instead of Voice of the Customer) An undesirable situation is having Control Limits wider than customer specification limits.This will exist for poorly performing processes with a Cp less than 1.0 Many SPC Charts exist and selection must be appropriate for effectiveness. Please read the slide. The Control Chart Cookbook
General Steps for Constructing Control Charts ~ 1.Select characteristic (Critical X or CTQ) to be charted. 2.Determine the purpose of the chart. 3.Select data-collection points. 4.Establish the basis for sub-grouping (only for Ys). 5.Select the type of Control Chart. 6.Determine the measurement method/criteria. 7.Establish the sampling interval/frequency. 8.Determine the sample size. 9.Establish the basis of calculating the Control Limits. 10.Set up the forms or software for charting data. 11.Set up the forms or software for collecting data. 12.Prepare written instructions for all phases. 13.Conduct the necessary training. Stirred or Shaken? Please read the slide. Training Materials Sample End