Re: Six Sigma Green Belt Training varies from 3 days to 3 weeks? Why such a disparity
1. Deming discusses statistics in Ch3 "Diseases and Obstacles" in "Out of the Crisis". On p132 he says "Analysis of variance, t-test, confidence intervals and other statistical techniques taught in the books, however interesting, are inappropriate because they provide no basis for prediction and because they bury the information contained in the order of production." Imagine a run chart where the time sequence of the data was discarded ... that is in effect what enumerative studies are doing.
I think you might be creating a false dichotomy, that being the idea that "enumerative" tests and control charting are mutually exclusive. I wholeheartedly agree that chronology is indispensable in control charting, but that doesn't mean that you can't do control charting
and use other types of statistical analysis when appropriate.
Shewhart said that if we had a process that was exactly stable and if we knew the details of its underlying distribution, we could work in terms of probability limits. However, in practice, neither of these conditions is ever met. The power of the control chart lies in the fact that it does not depend on the distribution of the data, which we can never know. Most importantly, the control chart is a predictive tool, whereas probability (enumerative) approaches are not.
I think that our only difference here is one of semantics. You can't be "predictive" without knowing something about "probability." You're defining "probability" more narrowly than I was, which is fine, so long as we understand one another.
One of six sigma's fundamental flaws is that it has lost sight of the above, focussed on probability and forgotten the basics of control charts.
I don't disagree with this.
Yes. Processes are not limited in how far out of control they may become. Bill Smith's suggestion that the mean of out of control processes may vary "as much as 1.5 sigma" is quite incorrect. There is no limit to how far things can go wrong. Bill Smith suggested widening spec limits (as well as reducing variation) to avoid defective product. This is not enough. Processes must be in control. Only an in control process is predictable.
I'm wondering now if you misunderstood the question. It was,
Do you actually believe that a process can meet specifications only if the process is in statistical control?
Note that I did not ask if a process that is not in statistical control can
consistently produce product that meets specifications. My point was that you seem to be confusing specification limits and control limits, but since that is a very basic error, I doubt that that was what you meant to do. Processes that are not in statistical control
can produce product within specification limits. You say that they cannot.
There is no such thing as a "confidence level" for future behaviour.
My assumption is that you're referring to an analytically-derived, quantitative confidence level, although I'm not sure about the scare quotes. I think I agree, but we have to make sure that everyone who's likely to read this will understand what we're talking about. We can't lose sight of the fact that process
design is a critical element of process
control, and that it's possible to state that the probability of maladjustment of some process variable
A resulting in nonconforming product is 1 without fear of contradiction.
Studying normal distributions is of no value for beginners. For experts, it should be studied as another form of theoretical distribution. It is of some historical interest as discussed in a very readable fashion in "Normality and the Process Behaviour Chart" by Wheeler, however it is of no relevance to process management. It should also be mentioned that while normal distributions are an interesting outcome of Laplace's central limit theorem, and Shewhart was are of this, he did not use it in his formulation of control charts.
Here I will disagree unequivocally. The theoretical nature of the normal distribution is largely irrelevant to the question. If we want neophytes to gain any sort of useful knowledge of statistical analysis at all, they
must be conversant with normal curve theory. You are certainly correct in pointing out that Shewhart recognized that manufacturing processes don't perform the same way that processes in nature perform, but unless one understands that, there is no basis for moving forward. In other words, in order to understand why there is a difference between natural processes and man-made processes, a fundamental understanding of normal-curve statistics is necessary. My original point (regarding requisite knowledge for green belts) was that if they have a basic understanding of normal-curve theory and probablility theory, they have some basis for proceeding up the dubious belt chain. I did not mean to suggest that basic knowledge should be considered comprehensive knowledge.