# Accepting Sampling Procedures

11/04/2021

Acceptance sampling is a statistical measure used in quality control. It allows a company to determine the quality of a batch of products by selecting a specified number for testing. The quality of this designated sample will be viewed as the quality level for the entire group of products.

A company cannot test every one of its products. There may simply be too high a volume or number of them to inspect at a reasonable cost or within a reasonable time frame. Or effective testing might result in the destruction of the product or making it unfit for sale in some way.

Acceptance sampling solves these problems by testing a representative sample of the product for defects. The process involves first, determining the size of a product lot to be tested, then the number of products to be sampled, and finally the number of defects acceptable within the sample batch.

Products are chosen at random for sampling. The procedure usually occurs at the manufacturing site the plant or factory and just before the products are to be transported. This process allows a company to measure the quality of a batch with a specified degree of statistical certainty without having to test every single unit. Based on the results how many of the predetermined number of samples pass or fail the testing the company decides whether to accept or reject the entire lot.

The statistical reliability of a sample is generally measured by a t-statistic, a type of inferential statistic used to determine if there is a significant difference between two groups that share common features.

Acceptance sampling uses statistical sampling to determine whether to accept or reject a production lot of material. It has been a common quality control technique used in industry. It is usually done as products leaves the factory, or in some cases even within the factory. Most often a producer supplies a consumer a number of items and a decision to accept or reject the items is made by determining the number of defective items in a sample from the lot. The lot is accepted if the number of defects falls below where the acceptance number or otherwise the lot is rejected.

In general, acceptance sampling is employed when one or several of the following hold:

• Testing is destructive;
• The cost of 100% inspection is very high; and
• 100% inspection takes too long.

A wide variety of acceptance sampling plans are available. For example, multiple sampling plans use more than two samples to reach a conclusion. A shorter examination period and smaller sample sizes are features of this type of plan. Although the samples are taken at random, the sampling procedure is still reliable.

Acceptance sampling for attributes

A single sampling plan for attributes is a statistical method by which the lot is accepted or rejected on the basis of one sample. Suppose that we have a lot of size M; a random sample of size  N<M is selected from the lot; and an acceptance number B is determined. If it is found the number of nonconforming is less than or equal to B, the lot is accepted; and if the number of nonconforming is greater than B, the lot is not accepted. The design of a single sampling plan requires the selection of the sample size N and the acceptance number B.

MIL-STD-105 was a United States defense standard that provided procedures and tables for sampling by attributes (pass or fail characteristic). MIL-STD-105E was cancelled in 1995 but is available in related documents such as ANSI/ASQ Z1.4, “Sampling Procedures and Tables for Inspection by Attributes”. Several levels of inspection are provided and can be indexed to several AQLs. The sample size is specified and the basis for acceptance or rejection (number of defects) is provided. MIL-STD-1916 is currently the preferred method of sampling for all Department of Defense (DoD) contracts.