Bayesian Inference and Negative Binomial Distribution for Designing an Optimum Acceptance Sampling Plan

sampling plan is a statement of criteria of acceptance applied to a batch based on appropriate examinations 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 decision in different actions is evaluated. Decision making is based on the First and second type error probabilities. Based on these two criteria, the optimal decision is made. One numerical example is provided to illustrate the applications of the proposed models.