## spctoolkit

by Donald J. Wheeler

### Foundations of Shewhart's Charts

Any program designed to increase organizational
efficiency that does not use SPC is doomed to fail.

Last month, I described four myths relating to Shewhart's charts. This month I will discuss four foundations of the charts.
Foundation One: Shewhart's charts always use three-sigma limits. Regardless of the type of chart you're using, the limits depend on the same principle. The data will be used to determine the amount of variation that is likely to be background noise, and the limits will be placed three estimated standard deviations on either side of the central line.

Three-sigma limits are action limits-they dictate when action can be taken on a process. They are not probability limits. While they have a basis in probability theory, three-sigma limits were chosen because they provided reasonable action limits. They strike an economical balance between the two possible errors you can make in interpreting data from a continuing process. Three-sigma limits neither result in too many false alarms nor do they miss too many signals. In addition, they are unaffected by data nonnormality, even when the subgroup size is one.

Foundation Two: Computing three-sigma control limits requires the use of an average dispersion statistic. By computing several dispersion statistics, using either an average or a median dispersion statistic, computation stability increases. This use of the subgroup variation will provide measures of dispersion that are much less sensitive to a lack of control than most other approaches.

The choice of dispersion statistic is unimportant-ranges, standard deviations or root mean square deviations may be used. If the proper approach is used, different statistics will yield similar results. If the wrong approach is used, different statistics will yield similar incorrect results.

Foundation Three: The conceptual foundation of Shewhart's control charts is the notion of rational sampling and rational subgrouping. How the data are collected, how they are arranged into subgroups and how these subgroups are charted must be based on the context of the data, the sources of data variation, the questions to be answered by the charts and how the knowledge gained will be used.

Failure to consider these factors when placing data on a control chart can result in nonsensical control charts. The effective use of Shewhart's charts requires an understanding of rational sampling and rational subgrouping.

Foundation Four: Control charts are effective only to the extent that the organization can use the knowledge. Knowledge gathering is in vain without an organization that can disseminate and use this knowledge. As long as there are internal obstacles that prevent an organization from utilizing SPC charts, nothing will happen.

This is why so many of W. Edwards Deming's 14 points bear directly upon this one foundation and why SPC alone isn't enough. On the other hand, any program designed to increase organizational effectiveness and efficiency that does not use SPC is doomed to fail.

This fourth foundation of Shewhart's charts is only implicit in Shewhart's work-there was always the assumption that organizations behave in a rational manner. However, Deming came to see that this wasn't the case. Simply giving people effective methods for collecting, organizing and analyzing data wasn't enough. In the absence of such methods, businesses had come to be run by the emotional interpretation of the visible figures-a universal "My mind is made up, don't bother me with the facts" syndrome.

While Deming's 14 points do not constitute the whole of his philosophy, they are a profound starting point. They are not a set of techniques, a list of instructions nor a checklist. They are a vision of just what can be involved in using SPC. And they ultimately lead to radically different and improved ways of organizing businesses and working with people. However, a deep understanding is required before these 14 points can be used to accomplish the total transformation. The need is not to adopt the 14 points individually or collectively, but rather to create a new environment conducive to their principles.

For further reading about Deming's 14 Points, I recommend The Deming Dimension by Dr. Henry Neave (SPC Press).