RE: Use of Control Charts

[Rip Stauffer <rstauffer@bluefirepartners.com>]

I recommend you get two books:  "Normality and the Process Behavior Chart
and "Advanced Topics in Statistical Process Control," both by Don Wheeler,
both available from SPC Press, Inc. Also read Davis Balestracci's "Data
Insanity" paper in the DEN.

This is a very controversial topic; most of the treatment of it has been
based on a mathematical, "theorem-proof" paradigm, using inductive logic
more appropriate to enumerative studies. Wheeler is one of the few treating
it from a retroductive viewpoint, which is appropriate to analytic studies.
He has done considerable research to demonstrate the practical limits of
various Shewhart charts.

In a post several months ago, Mike Tviete pointed out that the theory of
Variation, as discussed by Deming, is different from statistical theory.
Knowledge of mathematical statistical theory is important in designing and
assessing the results of studies, but knowledge of the process is just as
important, especially in analytic studies. Why are the data "non-normal?" If
you could answer that question, it might help decide what chart to use. By
the way, all data are "non-normal"...some distributions just look reasonably
close to "normal." As Wheeler points out, 
"--A mathematical probability model, such as a normal distribution, is a
limiting characteristic of an infinite sequence. It is a characteristic of
any finite portion of that sequence. 
--Histograms always have a maximum and a minimum. Probability models often
have infinite tails.
--Observations are always recorded to some finite number of digits, and
hence are ultimately discrete. Probability models often assume the
measurements to be discrete.
...Probability models allow us to treat the problem of uncertainty
mathematically. Without this treatment of uncertainty we [would be]
overwhelmed by empirical data....However, there comes a point where we need
to distinguish between theory and practice. Theory can suggest an approach
that may work. But the final justification for any technique comes from
empirical evidence that it does work in practice."

If by non-normal you mean asymmetrical, there are discussions in both the
above references that treat this problem. The first book treats it
logically, the second mathematically. Both make pretty convincing cases that
the XmR chart can be used effectively in a lot of situations. For your
process, it might work as well...I couldn't tell without knowing something
about the process and seeing the data. It might not, though, and in that
case you might need to look for some other tool that will provide the
insight you need. I have used XmR charts successfully with some fairly
skewed data sets. I have also tried transforming the data and then putting
them into a chart, but the transformation confused the signals.

Hope this hasn't muddied the waters too much...I'm sure Tom Ryan will jump
in with a counterpoint :--)

Best regards to all,

Rip

Rip Stauffer, Senior Consultant
BlueFire Partners
1300 Fifth St. Towers, 150 So. Fifth St.
Minneapolis, MN 55402
612-344-1027
rstauffer@bluefirepartners.com
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