Re: SPC Theory Question

[Kromkowski@aol.com]

I'd like to build on what Jean Marie indicates in relation to what I noted:

First, I want to stress that where variable data is not generated by a time series, I am
advocating the quick and dirty use of an IndX/Mr only where the data is randomnly ordered.

Second, as to the issue of many possible random orderings, each of which, will give you a slightly
different UCL and LCL.  Because computers are very dumb and will do ridiculous tasks if you tell
one to do it and don't care about leaving your computer on all night,  I have investigated this phenomena, by
running all possible control charts of random orderings of data sets and then doing control charts on the 
resulting possible UCLs and LCLs!!  There is nothing I found that disputed my intuitive sense that a 
randomly ordered IndX/Mr chart is a pretty robust and simple tool and better in some ways than a S-chart, 
with of course, the obvious but small risk of being wrong from time to time.  Of course, maybe it was all 
flawed because I used 2.66 instead of 2.658!  :o)   

Third, as to the relationship between sigma and the moving range approximation:  

    A. when JMG says that there is only one sigma -- well, this is true but it is never really knowable unless
you are certain that the sample is in fact your complete population and because we are for the most part 
doing analytic studies rather enumertaive studies, our intent is almost always to say something about the future
and hence our population which includes the future is certainly unknown. (We are also seldom sure about the 
past!)

    B.  I like to think of the difference between the measures of dispersion; Sigma, on one hand -- calculated the 
so-called right way namely the square root of the varience and on the other hand the M range calculation 
in IndX/Mr chart as follows:  The former says something about the dispersion as a relation of the data to the "myth" 
(unless sample is the population) of the "mean".  The later says something about the dispersion in relation to how 
the known data differ from each other.  I submit that limitations of measurement and probability, make these often
basically indistinquishable, but the later seems to have included within it a notion of the connectedness between 
things and hence, intuitively only, seems to account for the messiness and interconnectedness of things.

As Vonnegut remarks in "Slapstick":  Hi. Ho.

JDK:
>>I'd go so far as to say (although, I suppose Wheeler and Gogue might
>>disagree) that even when the data is not time ordered, the IndX-MovR
>>chart can be used so long as the data is ordered randomly...
JMG:
>JDK raised an important point: what is the relation between the std
>deviation (sigma) and the mean moving range (mRbar) of a given series of
>data ?
>First, let's assume that the distribution is homogeneous (unimodal).
>Normality is not required.
>When the data is ordered randomly, like data resulting from the Shewhart's
>experiment (drawing chips out of a bowl), they are proportional:
>sigma=0.886*mRbar. Everybody can test the rule, provided the series of data
>is large enough.
>It must be noticed that there is a lot of possible random orders, and that
>each one may result in a particular mRbar. On the other hand there is only
>one value of sigma. You must understand that the above relation is a law of
>probability, not an algebric equation.
>When the data is not ordered randomly, or when the data is autocorrelated
>(especially in the case of tampering), the above relation is no more valid.

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