Economic lot sampling inspection from defect counts with minimum conditional value-at-risk

Expected cost functions are often minimized to determine optimal inspection schemes for lot acceptance purposes. However, minimum mean cost sampling plans usually have high probabilities of suffering great losses. A risk management perspective based on minimizing the conditional value-at-risk (CVaR) is proposed in order to avoid unacceptably large costs. In essence, the CVaR associated with an inspection scheme is the expected cost of a given proportion of the most costly cases. Optimal defects-per-unit acceptance sampling plans with controlled producer and consumer risks for screening lots of incoming materials and outgoing products are determined by minimizing the CVaR for a given risk aversion degree. The decision criterion is based on the uniformly most powerful test. The Poisson distribution is used to model the number of nonconformities per sampled unit and the natural prior uncertainty on the defect rate Λ is described by a truncated gamma distribution. A computational algorithm is suggested to solve the underlying integer nonlinear programming problem. Practitioners can assume a restricted range for the defect rate and prior knowledge on Λ may be updated using past performance of the inspection plan. The developed methodology is applied to the manufacturing of paper for illustrative purposes.