From: Stan Hilliard
Date: 9/18/2004
Time: 11:38:47 AM
Here are the statements that you can make, but first the relationships:
(low) AQL ------- Ac/n ------- RQL (high)
That is, the maximum acceptable sample fraction defective is greater than AQL and less than RQL -- expressing all three as decimal fractions.
STATEMENTS BASED ON THE PRODUCER'S AND CONSUMERS' POINTS:
1) If the number of defectives in the sample is equal to Ac, then the probability that the lot fraction defective is as high as RQL is equal to beta -- the consumers risk, (typically 5 0r 10 percent)
2) If the number of defectives in the sample is greater than Ac, then the probability that the lot fraction defective is as low as AQL is equal to alpha -- the producer's risk.
Neither of these statements answers your question. but in acceptance sampling methodology, probability statements are made about AQL when a lot is REJECTED (X>Ac), and about RQL (not AQL) when a lot is accepted (X+<Ac).
I suggest that you study the following page about the misinterpretation of AQL and the negative consequences of that:
www.samplingplans.com/aqlprimer.htm
A more thorough tutorial is at:
www.samplingplans.com/modern3.htm
And last but not least, your goal seems more like you need to make a statement of the interval estimate of how high and how low a lot could be -- based on a particular sample. That requires calculating the confidence limits for that lot from that sample. One way to do that is with our attribute sampling program, TP105, which calculates confidence limits in addition to designing attribute sampling plans based on Alpha,Beta,AQL,RQL.
www.samplingplans.com/programtp105.htm
If you post a particular sample result here (n,X), I will post the 95% confidence limits for the lot that it came from.
I hope that this is of help.
Stan Hilliard