How do I calculate AQL given a sample size, accept/reject numbers, and lot size?

The company I work for manufactures suspension assemblies for hard drives. We employ a 0.10 AQL sample plan for lot sizes 3201 - 10,000 for critical attribute defects (c = 0, n = 125) and, for cosmetic defects, the acceptance number is 2 (using the same 125 pc sample). This is not a standardized AQL based on the ANSI Z-1.4 standard and I would like to convert the plan used for cosmetic defects into an AQL. Any suggestions on how I can do this?

You could use the the binomial distribution to "work backwards" to see what sort of defect rates would create such a sampling plan. (I posted a spreadsheet here: Sampling Spreadsheet to help determine the sample size for sampling plans (http://elsmar.com/Forums/showthread.php?t=12836) that can help with the calculations).

Playing around with the numbers, I found that if you take a typical definition that AQL = "lots with this defect rate will be accepted 95% of the time", then for:


c=0 for 125 pieces ==> AQL = 0.04
c=2 for 125 pieces ==> AQL = 0.6

I should point out the the standard tables do no specifically try to meet the "will be accepted 95% of the time". It can be well below or well above 95% in the actual plans. So there is no way to definitive way to say what the AQL is if the plan is not on the tables.

Tim F

It would benefit you to actually plot the Operating Characteristic (OC) for a few sampling plans if you really are unfamiliar with the mechanism for determining AQL from a given sampling plan. All you need is a set of probability tables and some graph paper - and maybe a calculator if you are not to good at basic arithmetic. Doing this for yourself is more informative than simply looking at the curves an a textbook, or perhaps in documents similar to Mil Std 105

The comparison between curve shapes for differing values is also very informative.

Regarding the earlier comparison of C=0 and C= 2; Plotting the curve for each of these plans, on the same sheet, provides a view of the remote end of the curve, what happens when the product quality is actually way off the projected AQL.

Regarding the comment