Acceptance Sampling Plans

Acceptance sampling plans are probably the most ubiquitous quality tool. Acceptance sampling is the process of evaluating a lot or shipment of product based on an evaluation of a sample of that product. Various acceptance sampling plans have been created over the years, but the Mil-Std plan, later adopted as ANSI Z1.4 is by far the most common. Within Z1.4 are several variations of sampling plans such as double and multiple sampling plans. Additional plans have been created for sequential and continuous sampling. A variation of Z1.4, Zero Acceptance plans are growing in popularity.

An acceptance sampling will have a specified risk of accepting the lot given some unknown level of lot quality. To use the plan a company first determines an AQL or acceptable quality level. For medical devices typical quality levels are 0.65% or less for critical components. Less critical features, 1.0% and 2.5%, with 4.0% for purely cosmetic features. To determine the proper sample size, one looks in the tables for a given lot size and AQL. The table is set up such that larger lot sizes will have larger sample sizes. This is to equalize the risk of accepting a bad lot. The larger the lot the costlier the mistake in accepting lots with bad quality. Once a sample size is obtained the sample is collected, typically spread out over the lot. If the number of nonconformances in the lot exceeds the acceptance number, the lot is rejected.

The decision to accept or reject the lot carries two types of risk. Producers risk is the risk that due to sampling variation more than the expected number of nonconformances were found in the sample causing the lot to be rejected, when the lot actually contains fewer nonconformances than permitted by the AQL. Consumers risk is the risk that due to sampling variation fewer nonconformances were found in the sample than expected causing the lot to be accepted. When released these nonconformances will show up in the consumers products hence the name consumers risk.

The switching rules in Z1.4 require a tightened inspection when 2 of 5 consecutive lots have been rejected. And Reduced inspection if the preceding 10 lots have been accepted. In the table for reduced inspection; acceptance and reject numbers are not sequential which may require multiple sampling which can be very difficult to administer. Switching rules can be also difficult to administer as ready knowledge of detailed inspection history is required.

Double & Multiple Plans

Even more difficult to administer are double and multiple sampling plans. Double and multiple sample sizes are smaller than single sampling plans thereby reducing sampling costs. To use these plans the sample is drawn, if the number of nonconformances is smaller than the acceptance number the lot is accepted. If the number of rejects exceeds the reject number the lot is rejected. If a sample contains more nonconformances than the acceptance number but less than the reject number an additional sample is collected. This continues until the number of nonconformances is less than the acceptance number or greater than the reject number.

The instructions for Z1.4 make plain that for a sampling plan to conform to Z1.4 the switching rules must be used. Individual plans selected from the standard without the use of switching rules “simply represent a repository for a collection of individual plans indexed by AQL.”

Zero Acceptance Plans

Zero acceptance plans are an alternative to Z1.4. Zero acceptance plans avoid two problems associated with Z1.4: the switching rules discussed above which can be difficult to administer; and the fact that Z1.4 allows nonconformances to be accepted. The zero acceptance plans contain a single table with sample sizes increasing with lot sizes, as in Z1.4, with columns associated with varying level of acceptable quality levels, AQL. But all lots are rejected if a single defect is found in the sample.

A common misunderstanding of all Acceptance Sampling Plans is that these plans screen out bad quality. This is not really correct. Acceptance Sampling plans are designed to accept the majority, around 95%, of lots with quality at or near the AQL. The Rejectable Quality Level, RQL, is that level of nonconformances that has a given low probability, generally 15%, of being accepted and therefore an 85% probability of being rejected. Zero Acceptance plans are no different, they are designed to accept the majority, again about 95%, of lots with quality at or near the AQL. It is a gross misunderstanding of Zero Acceptance plans to conflate the statements “these plans do not accept nonconformances” with “these plans prevent nonconformances from being accepted.” To help understand it is helpful to look at what is becoming a new way of judging evaluating sampling plans, the LQ.

The concept of an AQL prioritizes the risk to the producer over that of the consumer. Limiting Quality, or LQ, turns this around to provide better focus on the consumer. The LQ is similar to the RQL, i.e. that level of adverse quality that has a given probability of being rejected, typically 10% or 5%. The LQ for Z1.4 and zero acceptance plans are not very different, meaning both plans have a low level of accepting lots with poor quality. As of yet, defining sampling plans by their LQ is not widely used. In the future expect it to become more commonplace.

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