Acceptance Sampling

What Is Acceptance Sampling?

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 at all times. There may be too many to inspect at a reasonable cost or within a reasonable timeframe. Also, comprehensive testing might damage the product or make it unfit for sale in some way. Testing a small sample would be indicative without ruining the bulk of the product run.

Understanding Acceptance Sampling

Acceptance sampling tests 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, just before the products are to be shipped. The goal is 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 lot.

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

A History of Acceptance Sampling

Acceptance sampling in its modern industrial form dates from the early 1940s. It was originally applied by the U.S. military to the testing of bullets during World War II. The concept and methodology were developed by Harold Dodge, a veteran of the Bell Laboratories quality assurance department, who was acting as a consultant to the Secretary of War.

While the bullets had to be tested, the need for speed was crucial, and Dodge reasoned that decisions about entire lots could be made by samples picked at random. Along with Harry Romig and other Bell colleagues, he came up with a precise sampling plan to be used as a standard, setting the sample size, the number of acceptable defects, and other criteria.

Acceptance sampling procedures became common throughout World War II and afterward. However, as Dodge himself noted in 1969, acceptance sampling is not the same as acceptance quality control. Dependent on specific sampling plans, it applies to specific lots and is an immediate, short-term test — a spot check, so to speak. In contrast, acceptance quality control applies in a broader, more long-term sense for the entire product line; it functions as an integral part of a well-designed manufacturing process and system.

Special Considerations

When done correctly, acceptance sampling can be effective for quality control. Probability is a key factor in acceptance sampling, but it is not the only factor. If a company makes a million products and tests just 10 units with one default, an assumption would be made on the probability that 100,000 of the 1,000,000 are defective. However, this may be grossly inaccurate.

More reliable conclusions can be made by increasing the batch (lot) size to greater than 10 and increasing the sample size by doing more than just one test and averaging the results.

Frequently Asked Questions

Why Is It Called Acceptance Sampling?

As a measure of quality control, acceptance sampling inspects a small number of available product in order to infer the quality of all other units produced. This is the sampling part, where a small number of units are randomly selected from the population of available units. If the sampled units are acceptable, then the whole batch is accepted.

How Does Acceptance Sampling Work?

Several methods are utilized. The simplest involves testing a single unit at random, per x units produced (sometimes called an (n, c) plan). The acceptance is evaluated based on the number of defective units (c) found in the sample size (n). Other methods involve multiple sampling, which relies on several such (n, c) evaluations. While using multiple samples is more costly, it may be more accurate.

When Should Acceptance Sampling Be Used?

Because it relies on statistical inference made from a small sample, it's not as accurate as more comprehensive measures of quality control. Therefore, it should only be used in cases where so many products are made that is impractical or unfeasible to test a large percentage of units; or when inspection of a unit would result in its destruction or render it unusable again (e.g., testing a fire extinguisher).