Acceptance Sampling and Binomial Distribution

Quality control, which often involves checking batches (called “lots”) of products for defects, is a very important part of production. One method of quality control that became commonly used during World War II is called acceptance sampling.^[1]

Acceptance Sampling is a quality control technique used to assess the quality of a product or a batch of products. It involves inspecting a random sample from the batch and deciding whether to accept or reject the entire batch based on the quality of the sampled items. Acceptance sampling is commonly used in manufacturing, especially when testing the entire batch would be time-consuming or costly. It is a practical and cost-effective way to ensure quality control, especially for large-scale production processes. It allows manufacturers to make decisions about the entire batch based on the evaluation of a smaller, manageable sample.

In acceptance sampling, a random sample is drawn from each lot of a product, and the items in the sample are tested. Each item in the sample is designated as either “conforming” to a set of standards or “nonconforming.” If the number of nonconforming items is above a pre-determined threshold, then the whole lot of the product is rejected.

Many industries today use multi-stage sampling plans if it is feasible, but we will focus on single-stage plans.^[2]