Re: Tom Ryan's reply to the SPC theory point

[John <jsdwd@ksc.th.com>]

Moderator's Note:  John Dowd's note that follows would seem to put this
discussion in perspective - that of a mathematical or an economic view.
The positions "each side" take would seem to be looking at control charting
as tool based only on hard rules of statistical theory -or- looking at
control charting as a 'best of options' approach, based on the economics
involved.  As I understand it, both Shewhart and Deming taught the latter,
economic view.

Is this debate less an issue of right and wrong and more an issue of which
perspective we chose??

>  Tom Ryan wrote: 
> Simplicity is fine as long as the results are reasonable, but we cannot
> assume that almost everything is normally distributed, or to act as if
> non-normality doesn't matter.  We don't teach statistics that way, and
> statistical methods should not be used in such a manner.

The sustitution of an X chart with limits set by the Moving Range (MR) for
the c Chart is yet another page in an ongoing debate about the relationship
between distribution theory and control charting.  As many people have
cited, Shewhart is clear about it.  But, others have seen this as a kind of
weakness in Shewhart's theory.

Wheeler and Ryan have done a good job setting out the debating points, but I
wonder if we shouldn't think about a prior question as to aim.

One phrase in Tom Ryan's recent post made me pause and that is (as above), "
We don't teach statistics that way,.....".  What struck me is that he
approaches the problem as a statistical/mathematical one and not as an
economic one.  Perhaps that's where the continuing parallel dialogue gets
separated.  

Shewhart differentiated between a 'PhysicalState of Statistical Control' and
a 'Mathematical State of  Statistical Control'.  He also continually in his
publications refers to a distinction between 'the practical man' and the
'theoretiian' and points out that they have differing aims and that the
consequences of their mistakes and conditions of their practice are quite
different..

In a letter he wrote to Deming dated Jan. 25, 1939, Shewhart discusses the
'bridge' between the physical state and the mathematical state and says,
"..the limits (are) not mathematical  but instead (are)  an empirically
chosen rule of operating" and that the 'bridge' between this 'practical' or
'physical' state of control is a 'long, long one in the sense that we must
have more than a thousand drawings before we can get over to the
mathematical statistician's universe or distribution function...."

Thus, he posited a progression as follows:   a physical state of control,
the operation of statistical control, the physical state of statistical
control, operation involving use of statistical limit, and, finally, the
mathematical state of statistical control.

Ryan addresses, I believe,  the latter.  In the world of the  'practical
man', there is typically not the opportunity to draw the thousand-plus
samples needed (in Shewhart's estimation) to cross that bridge.  That is an
economic reality.  With computer simulation there is no problem.  But, a
manufacturing process does not produce 'random normal deviates'.

There has been among some statisticians wishing to 'improve' on Shewhart, a
clear implication that he was unaware of the problem herein discussed.  He
was (as Wheeler points out) very aware of the relationship between
distribution theory and statistical  control charting.

So perhaps we should differentiate between teaching control charts in the
mathematical sense and teaching them in the economic sense.  I'd suspect
most people who we (all) would like to see use the charts, the economics are
more important than the mathematics.  Thus, the many appeals to
'practicality' or 'simplicity' as contrasted with appeals to 'correctness'
and 'theoretical rigor' are perhaps products of a false dichotomy.  It
depends on one's aim.

I do take issue with Ryan's statement that, "...statistical methods should
not be used in such a manner."  (the completion of the above quoted
sentence).  This seems rather over-reaching.   An alternative position might
be that statistical methods can and ought to be used whenever there is some
benefit to mankind that can accrue.   Thus taking advantage of the robust
nature of the control chart makes sense.  Let's keep our eye on the doughnut
and not on the hole.

John Dowd
jsdwd@ksc.th.com