Efficient truncated repetitive lot inspection using Poisson defect counts and prior information

Abstract

Optimal truncated repetitive sampling plans for inspecting lots of manufactured material using Poisson defect count data and prior information are obtained by minimizing the expected sampling effort. The proposed plans outperform the repetitive and single inspection schemes and they are shown to be better in reducing the number of sample units drawn from the lot. In truncated repetitive plans, the lots can be reinspected, at most, an optimal number of times when their acceptance or rejection cannot be concluded from the original inspection. Assuming a gamma prior model to describe the uncertainty about the unknown defect rate, a computational procedure is proposed to determine the truncated repetitive sampling plans with minimum expected sampling effort by solving integer nonlinear programming problems. The inclusion of lot reinspections, as well as previous information into the decision criteria, also provides the practitioners with a more precise evaluation of the expected producer’s and consumer’s risks. The results obtained illustrate that truncated repetitive plans with expected risks produce important savings in inspection time and cost with respect to conventional sampling schemes based on the classical requirements of quality levels and risks. An application concerning the manufacturing of glass is provided for illustrative purposes.