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The Shewhart control chart is relatively insensitive to non-normal distributions, and the worst foreseeable consequences of a wrong decision involve searching for an assignable or special cause when none is present. The economic consequences depend on the time wasted, and whether unnecessary adjustments (tampering) are made to the process. In addition, the central limit theorem increases the normality of the averages (X-bar) of samples regardless of the distribution from which they come.
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The traditional Shewhart chart may therefore be “good enough” for shop floor use even for non-normal data, but identification of the underlying distribution is mandatory for both probabilistic design applications and process performance index calculations.
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Comments
Where's your evidence?
You claim "the Shewhart control chart is relatively insensitive to non-normal distributions". Dr Wheeler has given volumes of evidence to show that Shewhart Charts work effectively with over 1000 different non normal distributions. You give nothing to support your claim. Where is your evidence?
"Shewhart chart may therefore be “good enough”" ... based on what? Another motherhood statement with nothing to support it. Wheeler has demonstrated that Sheward Charts work in almost every situation.
Poissons and Gammas
Bill, I am curious where you got the idea that gamma distributions are "continuous scale analogues" of the Poisssons.
The kurtosis for a Poisson distribution is 3 + Skewness Squared.
The kurtosis for a Gamma distribution is 3 + 1.5 Skewness Squared.
Thus, the only time a gamma has the same shape as a Poisson, and is therefore analoguous to a Poisson, is when they are both approximately normal.
The two families of distributions are completely different from each other.
Always have been. Always will be.
It is the beta distributions provide continuous scale analogues for the Poissons, not the gammas.
I guess you are right, it does help to know your distributions.
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