A new acceptance sampling plan using Bayesian approach in the presence of inspection errors

Abstract

In acceptance sampling plans, the decisions on either accepting, rejecting the lot or inspecting all items in the lot is still a challenging problem. We developed a new acceptance sampling plan to decide about the received lot based on cost objective function in the presence of inspection errors. It is assumed that inspection is not perfect and type I and type II errors occur in the inspection process. The problem of acceptance sampling plan in the presence of inspection errors is modeled using decision tree approach, where the sample size and decision of accepting, rejecting or inspecting are decision nodes. Bayesian inference is used to update the probability distribution function of nonconforming proportion. Then the cost at terminal nodes is analysed and optimal decisions are determined using a backward recursive approach. A case study is solved for illustrating the application of the model and sensitivity analysis is carried out on the parameters of the proposed methodology and the behavior of model by changing the parameters is investigated. We also compared the proposed model with single sampling model. At the end, the model is generalized in order to consider different potential decisions that can be made in practice.