Common fallacies of lot acceptance sampling schemes.
Using a “c=0” (accept a sample with only zero defects) rule with an AQL sampling plan means that there will be no defects in the lot/batch.
Remember that we are making the decision whether to accept the lot by making an inference to the lot from the sample results.
If “c=0” is required, then consider using one of the standard plans available. See Zero Acceptance Number Sampling Plans (Squeglia).
Know what the O-C curve for the resulting plan looks like.
Taking a sample based on the percentage of the total lot size offers consistent protection.
See the examples comparing AQL standard sample size results with results from a "10%" method provided at Sample Size based on Fixed Percentage.
When using a single sampling plan, if the lot is rejected based on results of the sample, then it is OK to take another sample and call it "double sampling".
This approach is based on the “continue to sample and test until you pass” scheme.
Per The Handbook of Applied Acceptance Sampling (Stephens), this is a “bastardization” of the double/multiple sampling scheme and should be discouraged.
Legitimate methods exist for allowing double or multiple samples under certain defined conditions. These are published in the sampling standards, such as Mil-Std-105E, ANSI Z1.4, ISO 2859, or BS 6000.
It is OK to adjust the sample size of a sampling plan, but still use the “Ac” (“accept”) and “Re” (“reject”) values associated with the plan.
The result is an O-C curve with unknown properties. The O-C curve can be fitted, but until this is done the amount of risk associated with the modified sampling plan is unknown.
The AQL value represents the highest level of nonconforming material that the customer will experience.
The AQL value is only an index that is used to organize the various sampling plans.
The AOQL is the sampling plan characteristic that represents the Average Outgoing Quality Level for a specific sampling plan.
For AQL-based sampling plans, the AQL value is more closely associated with Pa = 95% and Type 1 error (producer’s risk … the risk of rejecting an acceptable lot).
For protection for the customer, it is more useful to focus on Pa = 10% (or another, similar benchmark) to assess Type 2 error (consumer’s risk … the risk of accepting an unacceptable lot).