Acceptance Sampling Plans

Acceptance sampling is a procedure used for sentencing incoming batches. The most widely used plans are given by the Military Standard tables, which were developed during World War II.

Types of acceptance sampling plans

Sampling plans can be categorized across several dimensions:

Sampling by attributes vs. sampling by variables: When the item inspection leads to a binary result (either the item is conforming or nonconforming) or the number of nonconformities in an item are counted, then we are dealing with sampling by attributes. If the item inspection leads to a continuous measurement, then we are sampling by variables.

Incoming vs. outgoing inspection: If the batches are inspected before the product is shipped to the consumer, it is called outgoing inspection. If the inspection is done by the consumer, after they were received from the supplier, it is called incoming inspection.

Rectifying vs. non-rectifying sampling plans: Determines what is done with nonconforming items that were found during the inspection. When the cost of replacing faulty items with new ones, or reworking them is accounted for, the sampling plan is rectifying.

Single, double, and multiple sampling plans: The sampling procedure may consist of drawing a single sample, or it may be done in two or more steps. A double sampling procedure means that if the sample taken from the batch is not informative enough, another sample is taken. In multiple sampling, additional samples can be drawn after the second sample.

Military Standard 105E (ISO 2859, ANSI/ASQC Z1.4)

The original version of the standard (MIL STD 105A) was issued in 1950. The last revision (MIL STD 105E) was issued in 1989, but canceled in 1991. The standard was adopted by the International Standards Organization as ISO 2859.The tables give inspection plans for sampling by attributes for a given batch size and acceptable quality level (AQL). An inspection plan includes: the sample size/s (n), sample of n items from the batch. Count the number of nonconforming items within the sample (or the number of nonconformities, if more than one non conformity is possible on a single item). If the number of nonconforming items is c or less, accept the entire batch. If it is r or more then reject it. In most cases r =c+1 (for double and multiple plans, there are several values for the sample sizes, acceptance, and rejection numbers).The standard includes three types of inspection (normal, tightened, and reduced inspection). The type of inspection that should be applied depends on the quality of the last batches inspected. At the beginning of inspection, normal inspection is used. The types of inspection differ as follows:

• Tightened inspection (for a history of low quality) requires a larger sample size than in under normal inspection.
• Reduced sampling (for a history of high quality) has a higher acceptance number relative to normal inspection (so it is easier to accept the batch)
• There are special switching rules between the three types of inspection, as well as a rule for discontinuation of inspection. These rules are empirically based.

Supplier and Consumer Risks

The supplier risk is the risk that a batch of high quality (according to the AQL) is rejected. The consumer risk is the risk that a batch of low quality will be accepted. The military standard plans assure a supplier risk of 0.01-0.1 (depending on the plan). The only way to control the consumer risk is by changing the inspection level.