An optimal Bayesian acceptance sampling plan using decision tree method

Acceptance sampling plans are widely used inspection policies for the quality assurance models in supply chain management systems. In this paper, the authors propose a decision-making model to obtain the optimal decision about a lot undergoing an acceptance sampling plan. In the first stage, the proportion of defectives is assumed to follow the Poisson distribution. Bayesian inference is used to model the decision outcomes of the sampling plan, which are acceptance, rejection or further inspection policies. The decision tree method along with backward induction is used in the second stage to determine the expected cost of various decisions about the lot. An optimal decision on a lot is evaluated based on minimal rejections allowed such that the cost incurred is minimum. The efficiency of the proposed model is compared with sampling models under identical conditions and numerical examples are provided to illustrate the application of the decision model.