FW: Shewhart's Maximum Control

["Mowery, R. Neal (RNM) " <RNM@y12.doe.gov>]

When Dan Swart asked the question about modelling, I didn't realize he had
asked through the DEN, and I responded directly to him instead of to the
DEN.  I'm attaching the note I wrote responding to his question in case
anyone is interested.


*********************************************
Neal Mowery 
Statistician - Lockheed Martin Energy Systems
Oak Ridge, Tennessee
moweryrn @ y12.doe.gov     Voice (865) 574-0796
*********************************************

> ----------
> From: 	Mowery, R. Neal (RNM) 
> Sent: 	Monday, March 27, 2000 11:49 AM
> To: 	'danswart@aol.com'
> Subject: 	RE: Shewhart's Maximum Control
> 
> Hi Dan!  Good to hear from you.
> 
> Your "common sense" picture of modelling is probably correct.  Basically
> it is to try to develop a mathematical surrogate for purposes of planning
> or prediction.  Cycle time in particular is a good example, because of the
> serial nature of processes.
> 
> In a simple assembly, I may machine two parts, weld them together, and
> plate them.  Machining may take 4 hours nominally, welding (including
> setup) two hours, and plating six hours.  This adds to 12 hours.  
> 
> But if I assume for planning purposes (like to ship, or to support later
> production) that each one will take 12 hours, I will be late about half
> the time.   I could look at the 95th percentile for each, but that might
> give me a lead time far longer than what I really need, because the
> likelihood of being near or above the 90th percentile three times is very
> very small.  And you of course appreciate more than I the importance of
> minimizing work in progress inventory for economic reasons.  This means
> (among other things) not over-estimating cycletime.
> 
> If I have a good model of the time distributions from each of the three
> subproceses, I can combine (or if necessary simulate) the distribution of
> the larger process from start to finish in a way that is more accurate
> than simply adding.  That will allow me to establish schedules that I
> expect to be able to meet a high percentage of the time without creating
> an excessively conservative lead time.
> 
> Why is matching the distribution important?  Modelling the *distribution*
> allows us to make assumptions about the data we haven't seen yet.  When we
> take 20 data points and talk about a mean and std dev and upper 95%
> limits, etc, it is the fact that we have assumed normality (or some other
> distribution) that allows us to do that.  We have, in essence, decided
> that the model of a normal distribution is a good approximation for the
> reality that we see.  Sometimes we don't use a lot of data to do this
> however.  :)
> 
> I think of much of statistics as modeling... mapping reality into "math
> space" so I can talk about it, add it, change it, make inferences about
> it.  Then mapping the results back to "reality" where the results really
> matter.  Deciding what that math-space representation of the process will
> look like is all I mean by modelling.  
> 
> I hope that answers it.  If not, holler back at me.
> 
> Neal
> 
> 
> *********************************************
> Neal Mowery 
> Statistician - Lockheed Martin Energy Systems
> Oak Ridge, Tennessee
> moweryrn @ y12.doe.gov     Voice (865) 574-0796
> *********************************************
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