Probabilities of true and false decisions in conformity assessment of a finite sample of items

Probability of conforming items of a finite sample of items is evaluated when conformity assessment (CA) of each item is based on comparison of measured item property values with their acceptance and/or tolerance limits. Two models of probabilities of false decisions on conformity of the whole sample are developed. The first model considers a specific sample of items that already underwent a CA process. A Poisson binomial distribution is applied to calculate the number of the sample items having good (conforming) true property values. The second model, applying a multinomial distribution, treats a generic sample of items potentially drawn from a common population. This model allows evaluating probabilities of false decisions on conformity of the sample items (false positives and negatives), as well as probabilities of correct decisions (true positives and negatives). Applicability of both the models is demonstrated using data of simulated and experimental case studies. These methods extend the existing framework for evaluation of probabilities of true and false decisions in the CA of individual items to the whole sample. The proposed approach provides quality indexes for such a sample, that can be applied in quality inspection and CA of products and objects in industry and trade, environmental monitoring, and other fields. In particular, this approach may be helpful for solving the inspection problem of a production lot, when the minimal number of non-conforming items in a sample for rejecting the whole lot is to be determined.