Story update 7/08/2011: We corrected an error in Figure 2, and in the section preceded by "Expressed symbolically for a stable process...".
Two topics that have generated significant interest and frequent comments are, “Is normality required for control charts?” and “You need to estimate the tail probabilities for nonnormal processes for SPC to work.” Let’s examine these and see what we find.
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Question: Are process normality or distribution tail probabilities critically important for a control chart to guide the practitioner’s decision making on whether to search for assignable causes?
In my opinion, people who argue that normality or process distribution tail probabilities are critically important haven’t actually read Walter A. Shewhart, or they don’t understand him. On the other side of the controversy, people who support Shewhart’s position haven’t done a good job explaining his reasoning, either. In fact, W. Edwards Deming didn’t help matters when he would make Zen-like comments that are true but did not offer much insight into Shewhart’s reasoning.
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Comments
Synergize cost of quality and false alarm risk
My position is that it IS important to know the tail areas; a Shewhart chart's false alarm risk can easily be ten times what is expected (0.135% at each tail) for a gamma distribution's upper tail if not even worse. It costs time to have production workers chase false alarms and, if the boy cries "wolf" too many times, it may undermine their confidence in SPC. I stand by my recommendation that the practitioner identify the underlying distribution and set control limits with known false alarm risks. HOWEVER, this article brings up the idea of synergizing SPC with the costs of quality as discussed in this article. I recommended that the false alarm risk be set at 0.135% at each end but that is only because it is the way Shewhart did it for the normal distribution. Does the false alarm risk HAVE to be 0.135%? Maybe not. A more scientific approach, and it seems that others have looked into this, involves economic design of control charts. For example, http://www.jstor.org/pss/1269598 Another article talks about economic design of control charts using the Taguchi loss function. However, no economic design model will deliver optimum results unless the underlying statistical model is correct. "The Sound of One Tail Flapping" has definitely stimulated my interest in seeing whether a synergy between process economics and use of the correct underlying distribution can be carried even further to overturn existing paradigms about SPC (e.g. the concept of the 0.135% false alarm rate).
Always interesting
William, please keep in mind that the "concept" of the 0.135% false alarm rate is NOT from Dr. Shewhart. Dr. Shewhart invokes Tchebychev.
Obviously the theoretical debate continues. I agree that the deciding factor is - which application of SPC is the lowest total cost:
1. Shewhart / Tchebychev / Deming using 3 sigma limits as a heuristic
2. Distribution Fitting and using probability limits
Keep in mind in the total cost includes the cost of training of management to use the technique. Does the cost of doing and explaining method 2 outweigh the losses of either missed trends or false trends due to use of method 1?
- Steve Prevette, user of method 1.
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