Explicit quasi-optimal inspection schemes from nonconformity count data with controlled producer and consumer risks

Assuming that maximum allowable risks are specified for both producer and consumer, an integer nonlinear programming problem is formulated in order to find the optimal inspection scheme for lot acceptance purpose based on defect count data and limited prior information. The number of nonconformities per unit is assumed to follow a Poisson distribution. Closed-form quasi-optimal inspection schemes for screening submitted lots of manufactured material are determined using normal transformations of chi-square distributions and second-order Taylor series expansions of the operating characteristic function. The full prior model on the process average is not needed. Instead only prior estimations of the means and variances for the quality levels of the acceptable and rejectable lots are necessary to derive explicit and accurate approximations of the smallest number of units to be tested per lot and the maximum tolerable number of nonconformities in the selected sample. The suggested methodology requires little prior information to judge the quality of the submitted material and greatly simplifies and quickens the determination of optimal acceptance sampling plans with controlled average risks. In general, the inclusion of prior knowledge yields substantial savings in sample size, as well as improved evaluations of the actual average producer and consumer risks. Moreover, our approach is quite robust against slight changes in the available prior knowledge and also provides a suitable way to properly combine multiple expert judgments. The developed procedure is applied to the manufacturing of paper and glass to show the accuracy of the proposed quasi-optimal plans and the corresponding average risks.