A new Bayesian acceptance sampling plan considering inspection errors

A sampling plan is a statement of criteria of acceptance applied to a batch, based on appropriate examination of a required number of sample units by specific methods. In this paper, a new acceptance sampling plan is introduced in which it is assumed that every defective item cannot be detected with complete certainty. To model the problem, the probability distribution function of the number of defective items in the batch is determined through Bayesian inference, and based on this probability density function, the probability of correct decisions in different actions is evaluated. An objective function is defined for each decision that minimizes the ratio of the system cost to the system correct decision probability, including the cost of rejecting the batch, and the cost of defectives items remaining in an accepted batch. Three numerical examples are provided to illustrate the applications of the proposed models.