Controlling posterior producer and consumer risks in lot reinspection

Assuming that maximum tolerable posterior risks are specified for both producer and consumer, an integer nonlinear programming problem is formulated and solved in order to determine the optimal defects-per-unit acceptance sampling plan when lots found unacceptable may be resubmitted for reinspection. The number of nonconformities per inspected item follows a Poisson distribution. A computational algorithm is proposed to solve the underlying constrained minimization problem. The suggested procedure simplifies and quickens the determination of the inspection scheme for resubmitted lot acceptance with limited posterior risks that minimizes the expected number of sampled items per lot. An application to the manufacturing of paper is considered to illustrate the methodology developed. The generalized truncated gamma distribution is used to describe the prior uncertainty about the incoming defect rate per unit. The degree of similarity between the available previous information and the current study is also evaluated. Suitable ways are provided to assume a reduced parameter space for the defect rate and to update the prior model using past performance of the acceptance plan. The incorporation of lot resubmissions, as well as previous defect count data and expert opinions, into the decision process often yields appreciable savings in sampling effort.