Re: Probability Estimate

From: Keith A. Lewis (lewis_at_OMEGA.MITRE.ORG)
Date: 12/30/04 

Date: Thu, 30 Dec 2004 19:37:05 +0000 (UTC)

"Philip Holman" <namlohip@comcast.net> writes in article <BoKdnc2het3FoEncRVn-qQ@comcast.com> dated Thu, 30 Dec 2004 09:39:35 -0800:
>I have an assembly of engineering parts which can result in a nominal
>clearance gap of .140 between the surface they are mounted to and the
>feature of interest. The eight part stack up has the following set of
>tolerances:
>Part Tolerance +/-
>1 .010
>2 .010
>3 .020
>4 .075
>5 .010
>6 .010
>7 .010
>8 .075
>
>Total +/- .220
>
>I'm interested in a rough estimate of the probably of the gap being .060
>or less. From a normal distribution curve/table this looks to be .073 if
>I assume +/- .220 is zero probability. Is this a reasonable estimate?

I could be mistaken on this, but the notion I have of tolerance has nothing
to do with a normal (bell curve) distribution. It's just a spec, and if a
manufactured part falls outside the spec it's rejected. So for each
part I would assume a uniform distribution within the tolerance.

I think you do get a normal curve if you add together a large number of
equal uniform distributions, but in this case the two parts with the .075
tolerance are going to dominate.

A Monte Carlo simulation assuming uniform distribution of part sizes within
tolerance produced 115886 out of 1000000 assemblies which were < -.80 from
nominal.

--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.