From: Stan Hilliard hilli004@tc.umn.edu
Date: 01 Dec 1998
Time: 01:56:12
Remote Name: 160.94.26.6
Hello Rick, I examined the DOT website.
YOU SAID: > Does anyone have any background material on Mil Spec 414?
I can't find my copy of mil-std-414, so I used ANSI/ASQC standard Z1.9-1980. Z1.9 is supposed to replace 414, and is based on the same philosophy. I verified that the mdot table 106-1 is derived from Table B-5 on page 45 of that standard.
YOU SAID:> I believe this unfairly tips the balance of risk in favor of the producer.
Rick, I agree that Mil-Std-414 considers only the producers point of the operating characteristic curve-- not the consumer's point. The definitions of AQL in 414 and Z1.9 imply wrongly that the consumer is protected by AQL.
Your example illustrates the problem I have with one-point sampling plans. See the comments about AQL in the glossary under [sampling practices] [study area] [glossary of terms] of this web.
The main issue with one-point sampling plans is that for a given sample average, smaller sample size (at constant AQL) increases the probability of acceptance for all quality levels worse than AQL. And very small sample sizes increase the probabilities of accepting lower quality very much.
If this is rational, then consider the extreme case: why not reduce the sample size to n=zero. The oc-curve becomes a horizontal line at 100% on the y-axis. You don't even need to use statistics to calculate it - every lot passes - 100% probability. Actually, this plan meets the one-point requirement that at lot that is 95% within specification will pass (and so will a lot that is 0.0%!.).
Thus, when tables are derived from one-point sampling plans - like table 106-2 for PF - you can get strange results like this: A quality level of P=75% earns a pay factor of PF=1.02 if the sample size were n=3, A quality level of P=75% earns a pay factor of PF=0.84 if the sample size were greater than n=200.
I would recommend considering how a modern two-point sampling plan approach would work, as in [sampling practices] [study area] on this sampling plan website. The software TP414 (TP is an acronym for Two-Point) can generate the oc-curves -- see the software area. TP414 uses the alternative K-method of calculation because it is simpler.
I hope that this has been some help. Sincerely, Stan Hilliard