From: Stan Hilliard
Date: 07 Sep 2000
Time: 21:06:04
YOUR QUESTION: "The subject is quite tough, should one get deep inside the statistical theory, right?"
MY ANSWER: I think that what makes it seem tough is the terms. To me, a term that is left vague and not defined exactly is confusing. It is also confusing when different sources of information use different meanings for the same term.
For example, Mil-Std-105 uses the term AQL differently than the statistical meaning of AQL. The difference is explained here: www.samplingplans.com/aqlprimer.htm
The statistical meaning is concise and cannot be misinterpreted, whereas in Mil-Std-105, the meaning is vague and leads to multiple interpretations and misconceptions.
YOUR QUESTION: "I would like to know, exactly, the meaning of the AQL percentages in the 105E table. For instance: let's say I have a lot of 4,000 pcs, inspection level II, and an AQL of 2.5%, and so an Ac of 10. What does it means with words?"
MY ANSWER: That plan has a sample size, n = 200 and an acceptance number, Ac = 10. I entered 200,10 into software program TP105 and determined two points on the oc curve. The producer's point was alpha=5%, AQL=3.11%. The consumer's point was beta=5%, RQL=8.33%. (Actually, the program uses decimal fractions instead of percentages.)
Also, the oc curve produced by the software indicates that for a lot containing exactly 2.5% defective, this plan (200,10) has a probability of acceptance of 98.25%. The probability of rejecting a 2.5% lot is 100-98.25=1.75%. Obviously, Mil-Std-105E did not use a 5% producers risk here.
YOUR QUESTION: "Also, I find those tables (105E) quite strange for a change of lot size of a very small amount (3200 to 3201) dramatically increases the sample size... Is it possible to get some more detailled tables?"
MY ANSWER: The way that Mil-Std-105E changes the sample size with lot size is to use different oc curves for different lot sizes. Basically, Mil-Std-105E uses the lot size and "inspection level" to vary the consumer's point, forcing the larger lots to require larger samples sizes. This resulted in the situation that you describe.
You can avoid this problem by using software program TP105. See: www.samplingplans.com/software.htm
TP105 does not involve the lot size or the esoteric "inspection levels". Instead, it gives you control over the consumer's point directly -- the consumer's risk (beta risk) and the rejectable quality level (RQL). All four parameters (alpha, beta, AQL, and RQL) can be changed in as small a step-size as is desired. Since these are the only parameters that effect the n and Ac, there are no dramatic jumps in sample size. See: www.samplingplans.com/software.htm
I hope this answers your question. If not, please post a follow-up message.
Sincerely, Stan Hilliard