by Donald J. Wheeler

What Are Shewhart's Charts?

One day my friend David Chambers found a graph summarizing the " daily percentage of defective pairs" on the office wall of the president of a shoe company. Intrigued, David asked the president why he had this graph on the wall. The president condescendingly replied that he had the chart on the wall so he could tell how the plant was doing. David immediately responded with, "Tell me how you're doing." He paused, looked at the chart on the wall, and then said, "Well, some days are better than others!"

Even though the president displayed his data in a suitable graphic format, and even though he felt that these data were important enough to require their posting each day, he did not have a formal way to analyze these values and interpret them.

Data must be filtered in some manner to make them intelligible. This filtration may be based upon a person's experience plus presuppositions and assumptions, or it may be more formalized and less subjective, but there will always be some method of analysis. Of course, inadequate experience, flawed assumptions or inappropriate presuppositions can result in incorrect interpretations. However, in the absence of a formal and standardized approach to interpreting data, most managers use the seat-of-the-pants approach.

Walter Shewhart developed a simple and effective way to define the voice of the process- he called it a control chart. A control chart begins with a time-series graph. A central line is added as a visual reference for detecting shifts or trends, and control limits (computed from the data) are placed equidistant on either side of the central line. Thus, a control chart is simply a time series with three horizontal lines added. The key to the effectiveness of the control chart is the way in which these limits are computed from the data.

The control chart shown below consists of a sequence of single values. In other situations, the control chart may be based upon a time series of average values, ranges or some other function of the raw data. While there are several different types of control charts, they are all interpreted in the same way, and they all reveal different aspects of the voice of the process.

Control charts also characterize the behavior of the time series. Occasionally you will encounter a time series that is well-behaved; such time series are predictable, consistent and stable over time. More commonly, time series are not well-behaved; they are unpredictable, inconsistent and change over time. The lines on a control chart provide reference points for use in deciding which type of behavior is displayed by any given time series.

Shewhart wrote that a process "will be said to be in control when, through the use of past experience, we can predict, at least within limits, how the process will behave in the future." Thus, the essence of statistical control is predictability, and the opposite is also true. A process that does not display a reasonable degree of statistical control is unpredictable.

This distinction between predictability and unpredictability is important because prediction is the essence of doing business. Predictability is a great asset for any process because it makes the manager's job that much easier. When the process is unpredictable, the time series will be unpredictable, and this unpredictability will repeatedly undermine all of our best efforts.

Shewhart's terminology of "controlled variation" and "uncontrolled variation" must be understood in the context of predictable and unpredictable, rather than in the sense of being able to exert control. The user does not get to "set the limits." We should talk about " predictable processes" and "unpredictable processes."

The control chart shows a time series that remains within the computed limits, with no obvious trend nor any long sequences of points above or below the central line. Thus, this process appears to be predictable. Unless the process is changed in some fundamental way, the plant will continue to produce anywhere from 7-percent defectives to 30-percent defectives, with a daily average of about 19-percent defective.

Predictable performance is not necessarily the same as desirable performance. Notice how the control chart has helped interpret the data. First, the chart is used to characterize the behavior of the data- are they predictable or not? Second, the control chart allows the manager to predict what to expect in the future- the voice of the process!

Finally, notice the difference between the shoe company president's interpretation of these data and the interpretation based on the control chart. Some days only appeared to be better than others! In truth, both the "good" days and the "bad" days came from the same process. Looking for differences between the "good" days and the "bad" days will simply be a waste of time.

About the author . . .

Donald J. Wheeler is an internationally known consulting statistician and the author of Understanding Variation: The Key to Managing Chaos {\i and} Understanding Statistical Process Control, Second Edition. 1996 SPC Press Inc. Telephone (423) 584-5005.

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