Re: Use of Control Charts

[Kromkowski@aol.com]

In reply to:
>  Hello All
>  
>  I wonder if you could help me. There is some debate as to the use of the
>  X-mR chart on non-normal data within this organization at the moment. As a
>  pragmatic practitioner I have expressed my views, and referred one of our
>  statistics experts to the Wheeler article on the use of X-mR control charts
>  on non-normal data. He has some problems with this, and the extent of my
>  knowledge of the theory has been surpassed!

If I understand your post, it falls into three main questions:

1.  Why 3, instead of 2 or 4 sd?

I posted a variation on the red bead experiment of 35 pulls, in which a known 
special cause was introduced, by pulling one paddle from a different bucket 
which had a different distribution of red beads.

I then calculated the control limits using .1 increments from, I think, 2.0 
to 4.0.  Then the question was, what value 2 through 4, was the best at 
reducing BOTH types of errors (false negative and false positive for a 
special cause (which we knew in advance).  I thought I also did an indX-mR on 
the same data.  I this generated example, 3 was the better than 2.9 or less 
and better than 3.1 or more. Of course this was just one test.  The post is 
somewhere in the DEN archive, I believe that I concluded (if I didn't then, I 
do now) that 

a.  surely, this kind of test could be run many times to give a good answer 
for what number is optimal even for non-normal distributions and since none 
different that has been forthcoming then we should stick with 3,
b.  even if it turned out that 2.9 was better than 3 over long haul, 3 might 
still be most economical because using 3 reduces potential for arithmetic 
errors and is easier to teach.
c.  Deming wrote in OOTC that a different number could be used, so long as 
you were willing to pay the price for either type I or type II errors 
(remember even 3 will make some mistakes as a guide).  For example, where 
life is at stake maybe 3 is not sufficient.  This is why even when we use 
control charts
we are exercising judgment.

2.  Range as estimator for sd?
3.  The X-mR vs collecting more data and using an X-bar.

Taken together.  I recall seeing in a text that for up to n=10, range may 
actually be a better method than least squares.  You could do a simulation if 
you were curious.  The choice is part of why we say management is about 
judgment and why management gets the big bucks.  There is no cook book for 
this.  And this is also why knowledge of the underlying process is important 
when you get to these nuanced decisions.  There may be an underlying 
chemistry or physics to process that will shed light on these judgment issues.

It is unclear whether there is existing data to do an IndX-mR.  I tend to 
start with existing available data.  If that data does not have rationale sub 
groups then you have your guidance.  On the other hand, knowledge of the 
underlying process and evaluation of the cost of a different inspection 
method is part of the equation.  If there is no significant (a judgment see 
also OOTC) extra cost to a greater sampling sufficient to do an X-bar as 
opposed to an indX-mR, then the Austrian expression  "Mir is wurst" (it's 
sausage to me), may be apropos, as long as there is a theory proposed for the 
action.

John David Kromkowski
Attorney at Law
6600 York Road - Suite 108
Baltimore, Maryland   21212-2028

Kromkowski@aol.comTelephone:  (410) 377-6248Facsimile:  (410) 372-0624
===========================================================================