From: Stan Hilliard
Date: 07 Sep 2001
Time: 23:38:37
Greetings Bart,
> YOU SAID -- "The fact that we receive more than 10 deliveries for each project give us enough confidence that we do not accept an average quality less than the AQL."
I have my doubts about this. When you look at the oc curves in 2859-1 or 8422, don't you find that lots with fractions defective higher than AQL can still have a high probability of acceptance?
> YOU SAID --"The operating curves indicate that there is little chance to accept a quality less than the LQ. How can we have an idea of the quality those isolated lots really have?"
For any specific lot, the best estimate of its fraction defective is fraction defective of the sample:
p'=(X defectives)/(n sample size)
The lower and upper confidence limits will show the interval of plausible fraction defective in the lot. That calculation is performed for the binomial and poisson distribution by software program TP105.
www.samplingplans.com/software.htm
> YOU SAID -- The AQL with the corresponding Operating curve gives just an indication. A contractor could always try to deliver an isolated lot with more errors than twice the AQL. Do you have a suggestion for this fact ????"
The oc curve for individual lots tells you how the sampling plan will perform -- whether the lot is one of a kind or one in a series of lots. It cannot be used to estimate the quality of a lot. This is because the oc curve can only be read in one direction. That is, if you know the fraction defective (p') of a lot, you can determine with the oc curve the probability of the lot's acceptance (Pa). You cannot read an oc curve backwards (Pa to p') to estimate the quality.
> YOU SAID -- "Honestly I am alarmed there is little difference in the sample size we need in function of the lot size."
It is because the standards are based on the binomial and poisson distributions, both of which assume infinite population. Lot size doesn't effect the statistical calculations. Infinite population is another name for sampling with replacement.
The variation of sample size with lot size in the standards is an add-on construct. The designers of the AQL standards choose to assign steeper oc curves to larger lot sizes -- but the oc curves of the standards are still based on infinite population. When they change the oc curve, they try to hold AQL constant let LQ (=RQL) "float". I think that this AQL approach to specifying sampling plans is less reasonable than simply specifying the AQL and RQL (LQ) points.
You will find further discussion of this topic in the message on this forum entitled: Process/Quality Control & Acceptance Sampling for Small Unique Lots, John Walker, 19 Apr 2001
Stan Hilliard