©2004 Prentice-Hall S. Thomas Foster, Jr. Boise State University PowerPoint prepared by prepared by...

©2004 Prentice-Hall©2004 Prentice-Hall

S. Thomas Foster, Jr.S. Thomas Foster, Jr.Boise State UniversityBoise State University

PowerPointPowerPoint prepared byprepared byDave MageeDave Magee

University of KentuckyUniversity of KentuckyLexington Community CollegeLexington Community College

Chapter 12Chapter 12

Statistically-Based QualityStatistically-Based Quality

Improvement for VariablesImprovement for Variables

2Slide 12-2© 2004 Prentice-Hall© 2004 Prentice-HallManaging Quality: An Integrative Approach; 2nd EditionManaging Quality: An Integrative Approach; 2nd Edition

Chapter OverviewChapter Overview

• Statistical Fundamentals• Process Control Charts• Some Control Chart Concepts for Variables• Process Capability for Variables• Other Statistical Techniques in Quality

Management


Statistical FundamentalsStatistical FundamentalsSlide 1 of 11Slide 1 of 11

• Statistical Thinking– A decision-making skill demonstrated by the ability to

draw to conclusions based on data.

– Based on three concepts• All work occurs in a system of interconnected processes.

• All processes have variation (the amount of which tends to be underestimated).

• Understanding and reducing variation are important keys to success.

– Guides people to make decisions based on data, which needs to be done in business.



• Why Do Statistics Sometimes Fail in the Workplace?– Many times statistical tools do not create the desired

result, because many firms fail to implement quality control in a substantive way.

• They prefer form over substance.



• Reasons for Failure of Statistical Tools– Lack of knowledge about the tools; therefore, tools are

misapplied.

– General disdain for all things mathematical creates a natural barrier to the use of statistics.

– Cultural barriers in a company make the use of statistics for continual improvement difficult.

– Statistical specialists have trouble communicating with managerial generalists.

– Statistics generally are poorly taught, emphasizing mathematical development rather than application.



• Reasons for Failure of Statistical Tools (continued)– People have a poor understanding of the scientific

method.

– Organizations lack patience in collecting data. All decisions have to be made “yesterday.”

– Statistics are viewed as something to buttress an already-held opinion rather than a method for informing and improving decision making.

– People fear using statistics because they fear they may violate critical statistical assumptions.



• Reasons for Failure of Statistical Tools (continued)– Most people don’t understand random variation

resulting in too much process tampering.

– Statistical tools are often reactive and focus on effects rather than causes.

– People make mistakes with statistics, because of Type I error (producer’s risk) and Type II error (consumer’s risk). These erroneous decisions can result in high costs or lost future sales.



• Understanding Process Variation– All processes exhibit variation.

– Some variation can be controlled and some cannot.

– Two types of process variation• Random

• Nonrandom

– Statistical tools presented here are useful for determining whether variation is random.



• Random variation – Random variation is centered around a mean and

occurs with a consistent amount of dispersion.

– This type of variation cannot be controlled. Hence, we refer to it as “uncontrolled variation.”

– The statistical tools discussed in this chapter are not designed to detect random variation.

• Nonrandom variation – Nonrandom or “special cause” variation results from

some event.

– The event may be a shift in a process mean or some unexpected occurrence.



Random Variation Figure 12.1



Nonrandom Variation Figure 12.2



• Process Stability– Means that the variation we observe in the process is

random variation (common cause) and not nonrandom variation (special or assignable causes).

– To determine process stability we use process charts.

– Process charts are graphs designed to signal process workers when nonrandom variation is occurring in a process.

• Sampling Methods– Process control requires that data be gathered.

– Samples are cheaper, take less time and are less intrusive than 100% inspection.



• Sampling Methods– Random samples

• Randomization is useful because it ensures independence among observations. To randomize means to sample in such a way that every piece of product has an equal chance of being selected for inspection.

– Systematic samples• Systematic samples have some of the benefits of random

samples without the difficulty of randomizing.

– Sampling by Rational Subgroup• A rational subgroup is a group of data that is logically

homogenous; variation within the data can provide a yardstick for computing limits on the standard variation between subgroups.


Process Control ChartsProcess Control ChartsSlide 1 of 20Slide 1 of 20

• Statistical Process Control Charts– Tools for monitoring process variation.

– The figure on the following slide shows a process control chart. It has an upper limit, a center line, and a lower limit.

• Variables and Attributes– To select the proper process chart, we must

differentiate between variables and attributes.• A variable is a continuous measurement such as weight,

height, or volume.

• An attribute is the result of a binomial process that results in an either-or-situation.



Control Chart Figure 12.3



Variables and Attributes

Variables Attributes

X (process population average) P (proportion defective)

X-bar (mean or average) np (number defective)

R (range) C (number conforming)

MR (moving range) U (number nonconforming)

S (standard deviation)



Central Requirements for Properly Using Process Charts

1. You must understand the generic process for implementing process charts.

You must know how to interpret process charts.

You need to know when different process charts are used.

You need to know how to compute limits for the different types of process charts.

4.

3.

2.



• A Generalized Procedure for Developing Process Charts– Identify critical operations in the process where

inspection might be needed. These are operations in which, if the operation is performed improperly, the product will be negatively affected.

– Identify critical product characteristics. These are the aspects of the product that will result in either good or poor function of the product.

– Determine whether the critical product characteristic is a variable or an attribute.



• A Generalized Procedure for Developing Process Charts (continued)– Select the appropriate process control chart from

among the many types of control charts. This decision process and types of charts available are discussed later.

– Establish the control limits and use the chart to continually monitor and improve.

– Update the limits when changes have been made to the process.



• Understanding Control Charts– A process chart is nothing more than an application of

hypothesis testing where the null hypothesis is that the product meets requirements.

• An X-bar chart is a variables chart that monitors average measurement.

– Control charts draw a sampling distribution rather than a population distribution.

– Control charts make use of the central limit theorem, which states that when we plot sample means, the sampling distribution approximates a normal distribution.



• X-bar and R Charts– The X-bar chart is a process chart used to monitor the

average of the characteristics being measured.

– To set up an X-bar chart • Select samples from the process for the characteristic being

measured.

• Then form the samples into rational subgroups.

• Next, find the average value of each sample by dividing the sums of the measurements by the sample size and plot the value on the process control X-bar chart.



• X-bar and R Charts (continued)– The R chart is used to monitor the dispersion of the

process. It is used in conjunction with the X-bar chart when the process characteristic is a variable.

– To develop an R chart• Collect samples from the process and organize them into

subgroups, usually of three to six items.

• Next, compute the range, R, by taking the difference of the high value in the subgroup minus the low value.

• Then plot the R values on the R chart.



X-bar and R Charts Figure 12.6



• Interpreting Control Charts– Before introducing other types of process charts, we

discuss the interpretation of the charts. – The figures in the next several slides show different

signals for concern that are sent by a control chart, as in the second and third boxes.

– When a point is found to be outside of the control limits, we call this an “out of control” situation.

– When a process is out of control, the variation is probably no longer random.



Control Chart Evidence for Investigation Figure 12.10



• Implications of a Process Out of Control– If a process loses control and becomes nonrandom, the

process should be stopped immediately. – In many modern process industries where just-in-time

is used, this will result in the stoppage of several work stations.

– The team of workers who are to address the problem should use a structured problem solving process.



• X and Moving Range (MR) Charts for Population Data– At times, it may not be possible to draw samples. This

may occur because a process is so slow that only one or two units per day are produced.

– X chart. A chart used to monitor the mean of a process for population values.

– MR chart. A chart for plotting variables when samples are not possible.

– If data are not normally distributed, other charts are available.



• g and h Charts – A g chart is used when

data are geometrically distributed

– h charts are useful when data is hypergeometrically distributed.

– If a histogram of data appears like either of these distributions, you may want to use either an h or a g chart instead of an X chart. Figure 12.13



• Median Charts – Many be used when it is too time consuming or

inconvenient to compute subgroup averages or when there is concern about the accuracy of computed means.

– Small sample sample sizes are generally used like the x-bar chart.

– Equations for computing the control limits are: = Mean of medians = sum of the

medians/number of mediansx

x 2LCL = x - A R x 2UCL = x + A R



• x-bar and s Charts– When dispersion of the process is of particular concern the

s (standard deviation) chart is used in place of the R chart.

– Different formulas are used to compute the limits for the x-bar chart.

s 4

s 3

x 3

x 3

UCL = B s

LCL = B s

UCL = x + A s

LCL = x - A s



• Other Control Charts – Moving Average Chart. The moving average chart is

an interesting chart that is used for monitoring variables and measurement on a continuous scale.

– The chart uses past information to predict what the next process outcome will be. Using this chart, we can adjust a process in anticipation of its going out of control.

– Cusum Chart. The cumulative sum, or cusum, chart is used to identify slight but sustained shifts in a universe where there is no independence between observations.



Summary of Variable Chart Formulas

Chart LCL CL UCL

2 2

3 4

3 3

2 2

3

x x - A R x x + A R

R D R R D R

x (with s) x - A s x x x + A s

-E MR + E MR

s B s

X X X X

4

2 2

s B s

Median x - A R x x + A R


Some Control Charts Concepts for Some Control Charts Concepts for VariablesVariables

Slide 1 of 4Slide 1 of 4

• Choosing the Correct Variables Control Chart– Obviously, it is key to choose the correct control chart.

Figure 12.18 in the textbook shows a decision tree for the basic control charts. This flow chart helps to show when certain charts should be selected for use.

• Corrective Action. – When a process is out of control, corrective action is

needed.

– Corrective action steps are similar to continuous improvement processes.


Some Control Charts Concepts for Some Control Charts Concepts for Variables Variables


• Corrective Action (continued) – Correction action steps :

• Carefully identify the problem.

• Form the correct team to evaluate and solve the problem.

• Use structured brainstorming along with fishbone diagrams or affinity diagrams to identify causes of the problem.

• Brainstorm to identify potential solutions to problems.

• Eliminate the cause.

• Restart the process.

• Document the problem, root causes, and solutions.

• Communicate the results of the process to all personnel so that this process becomes reinforced and ingrained in the organization.




• How Do We Use Control Charts to Continuously Improve?– One of the goals of the control chart user is to reduce

variation.

– Over time, as processes are improved, control limits are recomputed to show improvements in stability.

– As upper and lower control limits get closer and closer together, the process improving.

– Two key concepts:• The focus of control charts should be on continuous

improvement.

• Control chart limits should be updated only when there is a change to the process. Otherwise any changes are unexpected.




• Tampering With the Process– One of the cardinal rules of process charts is that you

should never tamper with the process.

– You might wonder, why don’t we make adjustments to the process any time the process deviates from the target?

• The reason is that random effects are just that—random. This means that these effects cannot be controlled.

– If we make adjustments to a random process, we actually inject nonrandom activity into the process.


Process CapabilityProcess CapabilitySlide 1 of 11Slide 1 of 11

• Process Stability and Capability– Once a process is stable, the next emphasis is to ensure

that the process is capable.

– Process capability refers to the ability of a process to produce a product that meets specifications.

– Six-sigma program such as those pioneered by Motorola Corporation result in highly capable processes.



Six-Sigma Quality Figure 12.20



• Process Versus Sampling Distribution– To understand process capability we must first

understand the differences between population and sampling distributions.

• Population distributions are distributions with all the items or observations of interest to a decision maker.

• A population is defined as a collection of all the items or observations of interest to a decision maker.

• A sample is subset of the population. Sampling distributions are distributions that reflect the distributions of sample means.



• Capability Studies – Now that we have defined process capability, we can

discuss how to determine whether a process is capable. That is, we want to know if individual products meet specifications.

– There are two purposes for performing process capability studies:

1. To determine whether a process consistently results in products that meet specifications

2. To determine whether a process is in need of monitoring through the use of permanent process charts.



• Capability Studies (continued) – Process capability studies help process managers

understand whether the range over which natural variation of a process occurs is the result of the system of common (or random) causes.



• Capability Studies (continued) – Five steps in performing process capability studies:

1. Select a critical operation. These may be bottlenecks, costly steps of the process, or places in the process where problems have occurred in the past.

2. Take k samples of size n, where x is an individual observation.

– Where 19 < k < 26

– If x is an attribute n > 50, (as in the case of a binomial)

– Or if x is a measurement 1 < n < 11

(Note: Small sample sizes can lead to erroneous conclusions.)




3. Use a trial control chart to see whether the process is stable.

4. Compare process natural tolerance limits with specification limits. Note that natural tolerance limits are three standard deviation limits for the population distribution. This can be compared with the specification limits.




5. Compute capability indexes: To compute capability indexes, you compute an upper capability index (Cpu), a lower capability index (Cpl), and a capability index (Cpk). The formulas are:

ˆCpu = USL - μ / 3

ˆCpl = μ -LSL / 3

Cpk = min Cpu, Cpl

where USL = Upper specification limit

LSL = Lower specification limit

μ = Computed population process mean

2ˆ = Estimated process standard deviation = = R d



• Capability Studies (continued) – Although different firms use different benchmarks, the

generally accepted benchmarks for process capability are 1.25, 1.33, and 2.0.

– We will say that processes that achieve capability indexes (Cpk) of:

• 1.25 are capable

• 1.33 are highly capable

• 2.0 are world-class capable (six sigma)



• Ppk – Population capability index

– Used when data is not arranged in subgroups, but is only available as population data.

– Formulas:

2i

Ppk = min Ppu, Ppl

Ppu = USL - μ 3

Ppl = μ - LSL 3

= x - x n 1



• The Difference Between Capability and Stability– Once again, a process is capable if individual products

consistently meet specifications.

– A process is stable if only common variation is present in the process.

– It is possible to have a process that is stable but not capable. This would happen where random variation was very high.

– It is probably not so common that an incapable process would be stable.


SummarySummary

• Statistical Fundamentals• Process Control Charts• Some Control Chart Concepts for Variables• Process Capability for Variables• Other Statistical Techniques in Quality

Management

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