Re: SPC Theory question

[Jim Clauson <jim@jclauson.com>]

Don's forwarded reply.

First a clarification - I got 2 back channel e-mails asking about Don
and his "blue book"  I was referring to _Understanding Statistical
Process Control_ by Don Wheeler at SPC Press ( http://spcpress.com ) 
Next to Deming's books, this is probably the most referenced book on the
DEN. 

Following is Don Wheeler's response to the question I posed:

Hello Jim,

I have updated the lists you quoted from Understanding Statistical
Process Control.  In Building Continual Improvement the lists are more
compact.

In order for a count to be characterized by the binomial probability
model it has to be (1) a count of the number of items out of n items
that possess some attribute, and (2) the probability, p, that an
individual item possesses the attribute remains constant for each of the
n items in a single sample.

In order for a count to be characterized by the Poisson probability
model it has to be (1) a count of events and (2) these events must occur
independently of each other in such a way that the likelihood of an
event is proportional to the size of the area of opportunity.

The reason for these requirements is that the formulas for the np-chart
and the p-chart, the c-chart and the u-chart all use a theoretical
relationship between the mean and the standard deviation as the basis
for computing the limits.  If the theory is correct, then the formulas
are appropriate.  However, if the theory is incorrect, then the formulas
are inappropriate.  In my experience, very few practitioners are
sophisticated enough to correctly judge when the binomial or Poisson
conditions are satisfied.

Many years ago David Chambers opened my eyes with a simple statement
that  all of the attribute charts are charts for individual values.
They are all special cases of the XmR chart.  However, unlike the XmR
chart, they do not directly (empirically) measure the variation present
in the data, but instead, they assume that a theoretical relationship
exists between the central line and the three-sigma distance.  It is
this theoretical relationship that we are checking with the binomial and
Poisson conditions.  Regardless of whether the counts can be said to
follow the binomial model or the Poisson model, or any other model, the
XmR chart will empirically determine the appropriate limits for the
count data.

So if you want to simplify attribute charts for your students, just use
the XmR chart.

Don

--
Donald J. Wheeler, Ph.D.
Statistical Process Controls, Inc.
5908 Toole Drive, Suite C  •  Knoxville, TN 37919  •  USA
phone  865-584-5005  •  fax 865-588-9440




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