Dr. Donald Wheeler and Dr. Henry Neave wrote an interesting article on the use of control charts (also known as process behavior charts) in Quality Digest recently: Shewhart and the Probability Approach
Shewhart’s use of three-sigma limits, as opposed to any other multiple of sigma, did not stem from any specific mathematical computation. Rather, Shewhart found that the use of three-sigma limits “seems to be an acceptable economic value,” and that the choice of three sigma was justified by “empirical evidence that it works.” This pragmatic approach is markedly different from the strictly mathematical approach commonly taught by those who have not understood what Shewhart was doing.
This is an important point, drawing the upper and lower control limits 3-sigma from the mean is based on practical experience with managing processes. 3 is not a statistically derived measure it is a practical measure based on what works effectively. Using 3 results in the best choice of when to use special cause problem solving methods (what is special about this result) versus common cause problem solving (how can we improve the overall system to improve results.
They also remind us that the process behavior chart (control chart) does not require normally distributed data. And this is a good thing because real processes are not normally distributed – they have impacts to the process that create results that are not normally distributed. It is true many textbooks and other books will say the data needs to be normally distributed, this is due to less useful statistical methods (as they discuss in the paper) that in addition to being less useful are disconnected from how real processes behave.
The crucial difference between Shewhart’s work and the probability approach is that his work was developed in the context, and with the purpose, of process improvement as opposed to process monitoring.
This difference is far more important than you might at first appreciate. It gets right to the heart of the divide between the main approaches to the whole quality issue. On the one hand, we have approaches that regard quality merely in terms of conformance to requirements, meeting specifications, and zero defects. On the other hand, we have Deming’s demand for continual improvement—a never-ending fight to reduce variation. The probability approach can only cope with the former. Shewhart’s own work was inspired by the need for the latter.
Related: Knowledge of Variation – How to create a control chart for seasonal or trending data by Lynda Finn – Enumerative and Analytic Studies – Special Cause Signal Isn’t Proof A Special Cause Exists