From: Stan Hilliard
Date: 19 May 2000
Time: 21:52:53
Greetings Viet, You said: > What is the risk if I accept that lot?
If you follow the plan then you won't accept the lot. If you accept the lot, the sampling risks no longer apply. The Pa of the oc curves are conditional probabilities, and only hold if you know the fraction defective of a specific lot -- which you never do. The horizontal axis of oc curves should be labeled "IF the fraction defective of the lot is ...".
Once you have taken the sample and have n=100, x=1, the problem becomes one of estimation. How high and how low might the population fraction defective be? This is answered by binomial confidence limits. The program TP105 can calculate one-sided and two-sided confidence limits at any chosen confidence coefficient.
For n=100, x=1, CC=95%, the two-sided confidence limits (in fraction defective) are LCL=0.000253 pBar=0.010000 UCL=0.054459.
The relationship of the confidence limits to AQL and RQL are as follows:
(For UCL) Find the oc curve of the sampling plan that has the sample outcome (n,x) as (n, c). (example: n=100, c=1). Find the RQL of that plan for a beta risk that corresponds to the confidence coefficient. For one sided confidence limit, use beta=alpha. For two-sided limits, use beta=alpha/2.
(For LCL) Find the oc curve that of the sampling plan with the same n but c=x-1. (example: n=100, c=0). Find the AQL of that plan for an alpha risk that corresponds to the confidence coefficient. For one sided confidence limit, use alpha=alpha. For two-sided limits, use alpha=alpha/2.
Sincerely, Stan Hilliard