One Technique, Many Uses | Quality Digest

One hundred years ago this month, Walter Shewhart wrote a memo that contained the first process behavior chart. In recognition of this centennial, this column reviews four different applications of the techniques that grew out of that memo.

The first principle for interpreting data is that no data have any meaning apart from their context. Context tells us what type of analysis is appropriate, and how to interpret the results of our analysis. The following will illustrate this principle.

Observational studies

The immediate and most common use of Shewhart’s technique is with observational studies. Here, either an Average and Range chart or an XmR chart is used for the real-time, sequential analysis of a continuing stream of operational data. A baseline period is used to compute limits that define what a predictable process is likely to produce, and then these limits are used with additional data as they become available. Every time we add a point to our chart, we perform an act of analysis; the chart asks, “Has a change occurred?”

Every time we add a point to our chart, we perform an act of analysis—the chart asks, “Has a change occurred?”

When an Average and Range chart or an XmR chart is used in this way, it can be called a process behavior chart. Its objective is to characterize the process behavior as being either predictable or unpredictable.

Whenever a point falls outside these limits, either in the baseline period or following the baseline, it’s interpreted as a signal that the process has changed. Moreover, this change is likely to be large enough to be of economic consequence. This will make it worthwhile to investigate such signals. When we discover the assignable cause of the process change and make it part of the controlled process inputs, we not only gain a new variable to use in controlling the process aim, but we also reduce the process variation about that aim point.

So, with process behavior charts, signals on the charts indicate problems with the production process that need to be fixed. As such, they are opportunities for improvement.

Consistency charts

With rational subgrouping and rational sampling, we can adapt Shewhart’s technique to many different situations. One of these adaptations is a consistency chart. As the name implies, a consistency chart tracks the consistency of a measurement process using periodic measurements of the same thing.

Usually these periodic measurements of the same thing are placed on an XmR chart. Here, the X chart will track the consistency of the measurement system over time, while average moving range will provide an estimate of the probable error of a measurement.

A signal on either part of the XmR chart will indicate a problem with the measurement process that needs to be fixed.

Experimental studies

In an experimental study, process inputs are varied in a systematic way in order to create changes in the process outcomes. By using a structured experiment, the idea is to detect, verify, and estimate various cause-and-effect relationships. Each set of process inputs is said to define a “treatment,” and several process outcomes are obtained for each treatment. The question is whether the treatments result in different average outcomes. Thus, the objective in an experimental study is to create signals.

The objective in an experimental study is to create signals.

Although Shewhart’s techniques were created for the sequential analysis of continuing streams of data, we could use the baseline portion of an Average and Range chart for the one-time analysis of the finite amount of data coming from an experimental study. (In fact this was the impetus behind Ellis Ott’s creation of the Analysis of Means technique in 1967.)

The k treatments would define the subgroups, and the n observed outcomes for each treatment would be the values within these subgroups. The differences between the treatments would be seen on the running record of averages, while the subgroup ranges would capture the variation in the outcomes for each treatment.

As in all modern analysis techniques, the Average and Range chart uses the within-subgroup variation to filter out background noise. The limits on the Average chart represent this background noise, and detectable signals exist when points fall outside the limits. So, in an experimental study, signals on the Average chart are desirable. This is what we hoped to find. A lack of signals on the Average chart would mean that any relationships present were too small to show up above the background noise.

However, signals on the Range chart would suggest a lack of homogeneity among the outcomes for a given treatment. This could indicate that important input variables were not included in the experiment.

So, in experimental studies, signals on the Average chart are desirable, but signals on the Range chart are problematic.

Evaluating the measurement process

While a consistency chart will help us operate and maintain a measurement process over time, we will occasionally want to know more about the structure of our measurements. To this end, we can use an experiment to evaluate the measurement process. Typically, these experiments feature repeated measurements of selected parts or batches using different operators and/or different instruments.

For example, we might have two gauges for measuring a particular dimension, as well as three operators that use these gauges, and four parts selected from the product stream to use in our experiment. After labeling these parts to avoid confusion, we could have each operator measure each part using each gauge. This would result in 24 values.

Now, we repeat the above to get a second set of 24 values. Arranging these 48 values into 24 subgroups of size 2, where each subgroup consists of the test and retest values for a specific part, operator, and gauge combination, we have the data for an EMP study. We place these data on the baseline portion of an Average and Range chart.

The within-subgroup variation will consist of the test-retest error, which is the irreducible measurement error for the measurement process. Since the limits all depend upon the average range, the limits on both the Average and the Range chart show the obscuring effects of measurement error. 

With this data structure and subgrouping, the part-to-part variation will show up between the subgroups. Because we want to be able to detect product variation in spite of measurement error, we also want to find averages outside the limits. Detectable differences between the parts are desirable.

Although the operators will always have slightly different averages, we need not be concerned as long as these differences are obscured by measurement error. However, detectable differences between operator averages, or between the average ranges for operators, will define a nuisance component that will degrade your measurement process.

Likewise, the gauges will always have slightly different averages. But again, we need not be concerned as long as these differences are obscured by measurement error. However, detectable differences between gauge averages, or between the average ranges for gauges, will define a nuisance component that will degrade your measurement process.

Finally, if a range falls above the limit on the range chart, the test and retest values are inconsistent, and some problem exists.

So here, some signals on the average chart are desirable, and others are problematic, while all signals on the range chart are problematic.

Summary

There’s much more to the use of Shewhart’s charts than is covered here. The preceding was only intended to illustrate how the context affects both the type of analysis and the interpretation of results.

Shewhart’s charts are the interface between your mind and your process.

 

Shewhart’s charts are the interface between your mind and your process. Rational sampling has to do with where, when, and how your data are obtained. Rational subgrouping has to do with how to organize your data so that the interesting questions can be answered. This involves both an understanding of how the techniques work and an appreciation of the purpose for collecting the data in the first place.

The purpose of analysis is insight that leads to action. But your software can’t practice rational sampling or rational subgrouping, simply because your software will never know the context. Let the software draw your charts if you must, but don’t delegate the organization of the data or the interpretation of the charts to the software.