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Common and Special Causes of Variation

The following is an excerpt from Chapter 4 of The Quality Engineering Handbook by Thomas Pyzdek, © Quality Publishing. It may be ordered from the Quality Publishing Order Form.

Shewhart (1931, 1980) defined control as follows:

A phenomenon will be said to be controlled when, through the use of past experience, we can predict, at least within limits, how the phenomenon may be expected to vary in the future. Here it is understood that prediction within limits means that we can state, at least approximately, the probability that the observed phenomenon will fall within the given limits.

The critical point in this definition is that control is not defined as the complete absence of variation. Control is simply a state where all variation is predictable variation. A controlled process isn't necessarily a sign of good management, nor is an out-of-control process necessarily producing non-conforming product.

In all forms of prediction there is an element of chance. For our purposes, we will call any unknown random cause of variation a chance cause or a common cause, the terms are synonymous and will be used as such. If the influence of any particular chance cause is very small, and if the number of chance causes of variation are very large and relatively constant, we have a situation where the variation is predictable within limits. You can see from the definition above, that a system such as this qualifies as a controlled system. Where Dr. Shewhart used the term chance cause, Dr. W. Edwards Deming coined the term common cause to describe the same phenomenon. Both terms are encountered in practice.

Needless to say, not all phenomena arise from constant systems of common causes. At times, the variation is caused by a source of variation that is not part of the constant system. These sources of variation were called assignable causes by Shewhart, special causes of variation by Dr. Deming. Experience indicates that special causes of variation can usually be found without undue difficulty, leading to a process that is less variable.

Statistical tools are needed to help us effectively identify the effects of special causes of variation. This leads us to another definition:

Statistical process control–the use of valid analytical statistical methods to
identify the existence of special causes of variation in a process.

The basic rule of statistical process control is:

Variation from common-cause systems should be left to chance, but special causes of variation should be identified and eliminated.

This is Shewhart’s original rule. However, the rule should not be misinterpreted as meaning that variation from common causes should be ignored. Rather, common-cause variation is explored "off-line." That is, we look for long-term process improvements to address common-cause variation.

Figure IV.5 illustrates the need for statistical methods to determine the category of variation.

Figure IV.5. Should these variations be left to chance?

(Figure II.19 repeated.)

From Economic Control of Quality of Manufactured Product, p. 13. Copyright © 1931, 1980 by ASQC Quality Press. Used by permission of the publisher.

The answer to the question "should these variations be left to chance?" can only be obtained through the use of statistical methods. Figure IV.6 illustrates the basic concept.

Figure IV.6. Types of variation.

In short, variation between the two "control limits" designated by the dashed lines will be deemed as variation from the common-cause system. Any variability beyond these fixed limits will be assumed to have come from special causes of variation. We will call any system exhibiting only common-cause variation, "statistically controlled." It must be noted that the control limits are not simply pulled out of the air, they are calculated from actual process data using valid statistical methods. Figure IV.5 is shown below as Figure IV.7, only with the control limits drawn on it, notice that process (a) is exhibiting variations from special causes, while process (b) is not. This implies that the type of action needed to reduce the variability in each case are of a different nature. Without statistical guidance there could be endless debate over whether special or common causes were to blame for variability.

Figure IV.7. Charts from Figure IV.5 with control limits shown.

From Economic Control of Quality of Manufactured Product, p. 13. Copyright © 1931, 1980 by ASQC Quality Press. Used by permission of the publisher.