About the "modern" gurus I've just encountered one of them once more
http://www.elitetrader.com/vb/showthread.php?s=&threadid=30502&perpage=6&pagenumber=2
At least their manual is not trustable as for statistical process control (spc): shewart - the statistician who invented this method - has never said what they pretend he had said : sure they didn't read him but just report from "modern" gurus who have completely forgotten the original epistemology !
From their manual what is said is not true :
"X-bar Charts For Non-Normal Data. The control limits for standard X-bar charts are constructed based on the assumption that the sample means are approximately normally distributed. Thus, the underlying individual observations do not have to be normally distributed, since, as the sample size increases, the distribution of the means will become approximately normal (i.e., see discussion of the central limit theorem in the Elementary Concepts; however, note that for R, S¸ and S**2 charts, it is assumed that the individual observations are normally distributed). Shewhart (1931) in his original work experimented with various non-normal distributions for individual observations, and evaluated the resulting distributions of means for samples of size four. He concluded that, indeed, the standard normal distribution-based control limits for the means are appropriate, as long as the underlying distribution of observations are approximately normal. (See also Hoyer and Ellis, 1996, for an introduction and discussion of the distributional assumptions for quality control charting.)
However, as Ryan (1989) points out, when the distribution of observations is highly skewed and the sample sizes are small, then the resulting standard control limits may produce a large number of false alarms (increased alpha error rate), as well as a larger number of false negative ("process-is-in-control") readings (increased beta-error rate). You can compute control limits (as well as process capability indices) for X-bar charts based on so-called Johnson curves(Johnson, 1949), which allow to approximate the skewness and kurtosis for a large range of non-normal distributions (see also Fitting Distributions by Moments, in Process Analysis). These non- normal X-bar charts are useful when the distribution of means across the samples is clearly skewed, or otherwise non-normal. "
What Shewart said is in fact THE OPPOSITE : NON NORMAL LAW CANNOT GIVE TRUSTABLE RESULTS or to quote him exactly (I translate from french version book translated itself from english
)
"Theorically it is possible to find a solution to make prediction for any kind of [statistical] universe with the statistical theory of distribution. But ... when the distribution is known but abnormal, the mean, the standard deviation and the size of the sample cannot make prediction, in particular prediction of Student type interval and tolerance interval with the same degree of validity than when the distribution is normal."
This is just an illustration of what I said about "modern" gurus:
http://www.elitetrader.com/vb/showthread.php?s=&postid=462164&highlight=Shewart#post462164
"'It is rather the "modern" gurus that have totally forgotten the foundation and forget to transmit essentials' "
