From: Stan Hilliard
Date: 13 Jun 2002
Time: 17:26:05
UP-ARROW WHEN YOU ALREADY HAVE THE LARGER SAMPLE: I assume that the series of AQLs of the color-codes covers the range of 0.10% to 4.0%, The 0.10% requiring a sample size for code letter N. My table shows the up-arrow at N, 4% - going to M 4%. As I understand your situation, you would have already taken a larger sample size -- so what to do?
You can adopt the strategy of passing the lot if the sample is significantly better than the RQL of the 4% code letter M plan. This is accomplished statistically if the upper confidence limit based on the "N" sample is less than the RQL of the "M" plan.
For example, my table VII-b shows 9.6% as the LQ at 5% Pa. (LQ=RQL). Thus if the upper one-sided 95% confidence limit (based on the binomial distribution) is less than 9.6% you can pass the lot. Thus you have a method to make a decision with a sample from code letter N based on the criterion for code letter M. This is what the standard is trying to do -- as if you hadn't taken the larger sample.
The calculation of the upper one sided 95% confidence limit is easy to determine with software program TP105. You just enter the sample size (n) and the number of defectives (X) and the program shows the confidence limit on screen. http://www.samplingplans.com/software_oc.htm
If you need a printed copy of a confidence limit report, you would need the software program Audit Sample Planner (ASP), which is oriented to confidence limits rather than oc curves. http://www.samplingplans.com/software_me.htm
For acceptance sampling applications, I would recommend TP105.
ATTRIBUTE SAMPLE SIZE REDUCTION: With attribute data by lots, a sequential sampling plan is the most efficient of the series: single, double, multiple, sequential. Since you are already using double sampling, the next "level" would be multiple.
EXCEPTION: For any case except a C=0 single plan, the sample size can be reduced in the series: single, double, multiple, sequential. You can't reduce n of a fixed=n (single) C=0 plan. That is why the mil standard calls for a larger n for AQL=0.1%, N-->M.
Stan Hilliard