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Acceptance Sampling

Acceptance sampling is a procedure used for product acceptance or rejection and is based on inspecting only a sampled number of units from the total number produced. In many situations in which the inspection is destructive, such as testing flashbulbs, it is not feasible to inspect all the bulbs produced. Acceptance sampling can be performed during incoming inspection of raw materials or components, in various phases of in-process operations, or during final inspection. Such a procedure may be applied to cases in which inspection is by attributes or by variables.

Acceptance sampling is a scheme that determines whether a batch or lot of product items should be accepted or rejected. It does not control or improve the quality level of the process. Although acceptance sampling offers some advantages associated with its feasibility in destructive testing, its economies in inspection cost, and its usefulness in improving quality, it also poses some risks because an entire batch may be rejected based on inspection of a few items.

Risks in Acceptance Sampling

Two types of risks are inherent in acceptance sampling plans: producer's risk and consumer's risk.

Producer's Risk

This is the risk (denoted by α) associated with rejecting a lot that is of “good” quality, and a numerical definition of a “good” lot is prescribed by the acceptable quality level (AQL). The AQL may be viewed as the maximum proportion of nonconforming items in a batch that can be considered satisfactory as a process average. Thus, the interpretation of the statement that the producer's risk is 5% for an AQL of 0.03 is as follows: Batches that are 3% nonconforming are considered satisfactory, and it is desirable that such batches, or those that are better, not be rejected more than 5% of the time.

Consumer's Risk

This is the risk (denoted by β) associated with accepting a “poor” lot. A numerical definition of a poor lot is indicated by the limiting quality level (LQL), also referred to as the lot tolerance percent defective. The statement that the consumer's risk is 10% for an LQL of 0.09 means that batches that are 9% or more nonconforming are considered poor. Consequently, such batches should be accepted no more than 10% of the time by the selected acceptance sampling plan.

Acceptance Sampling by Attributes and Variables

In attribute acceptance sampling, a product is classified as nonconforming or unacceptable if it contains one or more nonconformities or defects. For example, a hair dryer may be nonconforming if the speed control switch does not operate at each of the settings.

Alternatively, acceptance sampling may be used in the context of product-related variables, which can be measured and on the basis of which a decision about the product can be made. An example is the monitoring of the weight of cereal boxes. Suppose a minimum acceptable weight of 12 ounces is specified. By the selection of reasonable protection levels associated with errors that could be made in decision making using acceptance sampling, an acceptance limit is found. For sampled cereal boxes, sample statistics such as the mean and the standard deviation may be calculated. Using these measures, if the calculated sample mean is less than the acceptance limit, the batch of boxes could be rejected.

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