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Let’s imagine that a consumer receives some lots of products from a supplier. A sample of parts from the lot is taken and the number of defective items counted, if there is. If the number of defective items is low, the entire lot will be accepted, but if the number of defective items is high, the entire lot is rejected. Deciding on accepting a good-quality lot and rejecting a poor-quality lot is referred to in quality as acceptance sampling

Acceptance sampling is a statistical technique utilized in quality control, allowing a manufacturer to determine the quality level of a batch of products from a specific production run by selecting a predetermined number for testing. The quality of the sample selected during sampling becomes the quality level for the entire group of products.

The primary objective of acceptance sampling is to determine the quality level of a batch with a specified degree of statistical certainty without having to test every single unit of that batch. After completing the sampling exercise or testing, the manufacturer decides whether to accept a lot or reject it based on how many of the predetermined number of samples passed or failed the test.

The concept of acceptance sampling was originally applied by the U.S. military to the testing of bullets during World War II and became very popular throughout that time and beyond. The concept was developed by Harold Dodge, a veteran of the Bell Laboratories quality assurance department, who was acting as a consultant to the Secretary of War.

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Why Sampling?

Random sampling is conducted for the following reason:

  • Sensitive of Products:  Comprehensive testing might damage the product or make it unfit for sale in some way. An example is testing a food or pharmaceutical products. This is an especially important point to consider when testing method is a destructive one.
  • Cost & Time:  Inspecting too many products at a reasonable cost or within a reasonable timeframe poses another challenge. Much time is spent in the course of testing and more inspectors might be needed which amounts to more cost.
  • Cumbersomeness of Lot Size: It is practically unrealistic to test every single product of a particular lot of very large size at the same time due to the level of cumbersomeness of the batch which makes handling quite difficult.

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Acceptance Sampling Methods

The following are two methods listed below: 

  • Singular Sampling: This is the simplest which involves testing a single unit at random, per say X units produced (sometimes called an (n, c) plan). The acceptance is thereafter evaluated based on the number of defective units say, C, found in the sample size, say, N.
  • Multiple Sampling: This method involves multiple sampling, which relies on several such (N, C) evaluations. This method of sampling is more costly, but may be more accurate.


When Acceptance Sampling should be used

Since acceptance sampling relies on statistical inference made from a small sample, thus not as accurate as more comprehensive measures of quality control, it should only be used when so many products are made that are impractical to test a large percentage of its units; or when inspection of a unit would result in its destruction or render it unusable.

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Designing a Sampling Plan

Since sampling involves selection of only a part of the lot, the probabilities of errors in decisions need to be considered. This is because the error of rejecting a good-quality lot creates a problem for the producer. The probability of this error can be called the producer’s risk. Likewise, the error of accepting a poor-quality lot equally creates a problem for the buyer or consumer of the product; in this case, the probability of is called the consumer’s risk. 

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Designing an acceptance sampling plan involves first determining a sample size n and an acceptance criterion c, where c is the maximum number of defective items that can be found in the sample and the lot still be accepted. One key way of gaining proper understanding of both the producer’s risk and the consumer’s risk assuming that a lot of product has some known percentage of defective items and computing the probability of accepting such a lot for a given sampling plan

When the assumed percentage of defective items in a lot is varied, many different sampling plans can be evaluated and a sampling plan is thereafter selected in such a way that both the producer’s and consumer’s risks are reasonably low.

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About the Author

Adebayo is a thought leader in continuous process improvement and manufacturing excellence. He is a Certified Six Sigma Master Black Belt (CSSMBB), Digital Manufacturing Professional and ISO Management Systems Lead Auditor (ISO 9001, 45001 & ISO 22000) with strong experience leading various continuous improvement initiative in top manufacturing organizations. 

You can reach him here.

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