Acceptance Sampling

One of the powerful statistical techniques of quality control is Acceptance Sampling. This technique is generally used in those situations where items ate inspected in batches, generally known as lots. For example, you may receive a shipment of 10,000 electric bulbs and you may have to decide whether to accept the shipment or return it back to the supplier. The acceptability will depend on the acceptable quality of the lot, which in turn depends on the use and the price you are willing to pay for this quality. Suppose you decide to accept if the average fraction defective is less than 5 percent. Then to ascertain the actual quality you may decide to inspect each and every bulb. Such a strategy of 100 percent Inspection. however, may often be expensive and impractical. In such cases a more intelligent way is to use the concept of Sampling Inspection. 

The idea of sampling inspection is to inspect by a small portion of the lot and infer the quality of the lot, based on the quality of the sample. Acceptance is based on the inference made from the sample and hence the technique is known as Acceptance Sampling. Tepidly a lot is specified by its size (N)  and the fraction (f) of defectives that are expected to be present (at the most) in the lot. The principles of statistics are used in the inference process. 

Interestingly the concept of acceptance sampling is no different from the strategy adopted by a typical housewife who decides whether or not a pot-ful of rice is cooked by inspecting just a manful of grains. 

Two things must be kept in mind. In order that sampling inspection might work, the sample must be primitiveness of the lot. Typically this is ensured by choosing the sample at random so that every portion of the lot equal representation in the sample. Such a sampling is known as Random Sampling. Second, a sample is only representative and not identical (in characteristics) with the lot. In the inference process, therefore, a few good lots will be rejected and a few bad lots will be accepted. We can control such sampling errors, but they cannot be eliminated. In fact in the design of sampling plans we will ensure that the errors are kept below certain acceptable levels.