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# acceptance sampling

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A method of quality control. A random sample is taken from a batch of output and the decision to accept or reject the batch is based on either the number of defectives in the sample (inspection by attributes) or on some summary statistic such as the sample mean (inspection by variables).

In the case of inspection by attributes, the probability of accepting a batch is a function of the proportion, p, of defectives in the batch. Any acceptance sampling scheme that does not sample 100% of a batch will lead to the occasional rejection of batches with very low proportions of defectives (the producer's risk), and to the occasional acceptance of batches with very high proportions of defectives (the consumer's risk).

As p increases, so the probability that a batch will be rejected increases. The lot tolerance percent defective (LTPD) is the value of p (expressed as a percentage) that the sampling scheme would expect to reject on a given proportion (usually 90%) of occasions.

The maximum proportion of defectives that is regarded as desirable by the consumer is called the acceptable quality level (AQL). The graph relating the probability of acceptance to p is called the operating characteristic curve (OC-curve). The average quality level of the items in the batches released after inspection is the average outgoing quality (AOQ). The AOQ is usually calculated under the assumption that defective items found during testing will be replaced before the batch is released. The AOQ has minima at p=0 and p=1 and its maximum is termed the average outgoing quality limit (AOQL).

Suppose that the proportion of defectives remains constant from batch to batch. Eventually a batch will be rejected. The average run length (ARL) is the average number of batches inspected up to and including the one that is rejected. See quality control.

Subjects: Probability and Statistics.

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