# Acceptance Sampling

## What is Acceptance Sampling?

Acceptance Sampling is a method used in the industry for quality control. This method uses statistical sampling to inspect or test a random sample for determining whether the quality of a batch of product or service is acceptable or not. This method is used for quality control of the products or services when the cost of 100% inspection or test is too high or time-consuming or when the test destroys the product. Acceptance sampling is considered to be an effective and efficient means to ensure the quality control of such products or services. There are mainly two different methods used for this purpose- sampling by attributes and sampling by variables.

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.

## History

Acceptance sampling procedures became common during World War II. Sampling plans, such as MIL-STD-105, were developed by Harold F. Dodge and others and became frequently used as standards.

Acceptance sampling is an important field of statistical quality control that was popularized by Dodge and Romig and originally applied by the U.S. military to the testing of bullets during World War II. If every bullet was tested in advance, no bullets would be left to ship. If, on the other hand, none were tested, malfunctions might occur in the field of battle, with potentially disastrous results.

Dodge reasoned that a sample should be picked at random from the lot, and on the basis of information that was yielded by the sample, a decision should be made regarding the disposition of the lot. In general, the decision is either to accept or reject the lot. This process is called Lot Acceptance Sampling or just Acceptance Sampling.

More recently, quality assurance broadened the scope beyond final inspection to include all aspects of manufacturing. Broader quality management systems include methodologies such as statistical process control, HACCP, six sigma, and ISO 9000. Some use of acceptance sampling still remains.

## How does Acceptance Sampling Work?

Acceptance sampling is a quality control procedure, which uses the inspection of small samples instead of 100 percent inspection in making the decision to accept or reject much larger quantities, called a lot. This is a statistical procedure, which uses random samples, that is, each item in the lot has an equal chance of being a part of the sample that is inspected.

In its simplest form, If the sample from a larger lot has an acceptable level of defects, it will be accepted. If not, the entire lot will be rejected. If acceptance sampling is used prior to accepting goods from a supplier (i.e., incoming inspection), then the acceptable level of defects must be agreed between the supplier and customer because the supplier may have to take back the entire lot if it fails acceptance sampling. A sampling plan establishes the rules guiding the sampling and the criteria for accepting or rejecting the lot.

In general, Acceptance Sampling is done when a product is finished and leaves the production plant, but in some cases, it may also be done within the factory. It is to be remembered that this method helps in determining whether or not to accept a batch of a product, but it does not estimate the quality of the lot. Usually, the manufacturer supplies a few samples from the lot to the consumer. If the number of defects is lower than the acceptable number, the lot is accepted by the consumer. There are two major types of acceptance sampling plans, one is by attributes and the other is by variables. Although the former is most common for acceptance sampling, the latter is also used in many cases.

## 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.

## Why Is It Called Acceptance Sampling?

As a measure of quality control, acceptance sampling inspects a small number of available products 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.

## What is an Attribute Acceptance Sampling Plan?

In this Acceptance Plan, a random sample size (which is less than the size of the lot) is selected from the lot. Then Acceptance Quality Level or AQL is determined. AQL is the maximum percent defective that can be tolerated as a process average. In other words, it is the maximum number or percentage of defective pieces in a good lot. Rejectable Quality Level or RQL signifies the percentage defectives in a lot that can be tolerated in only as a specified proportion of lots. For example, a company receives a shipment of 10,000 pieces of the product X. The receiving company cannot afford to inspect each of the products received. They can apply an attribute sampling plan to determine how many pieces of the products need to be inspected (sample size) and how many defective products are allowed in that sample (acceptance number). Suppose the AQL is 1.5% and the RQL is 5.0% and it is assumed that alpha=0.05 and beta=0.1. Then the sampling plan indicates 209 pieces need to be examined and if 6 or less than 6 of the examined pieces are defective, the shipment is to be accepted and if more than 6 is defective the entire shipment is to be rejected.

## What is a Variables Acceptance Sampling Plan?

It is comparatively a complex method and requires an understanding of the statistical model of normal distribution. In this method, variables or measurement data are used instead of attribute data and the defective rate and the defective rate varies with the mean, standard deviation, and distribution shape.

## 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).