Simplified resubmitted lot inspection from defect counts

Nowadays, as low defect rates per item are often expected in practice, conventional single sampling for lot acceptance purposes is rendered inefficient or unduly expensive. For specific producer’s and consumer’s quality and risk requirements, resubmitted lot sampling usually needs, on the average, less inspection effort than single sampling to properly discriminate between satisfactory and unsatisfactory batches. An integer nonlinear programming problem is stated in order to determine the optimal resubmitted lot sampling plan based on defect count data with limited producer and consumer risks. Nonaccepted lots may be resubmitted for sampling inspection a certain number of times. The number of nonconformities per sampled unit is assumed to follow a Poisson distribution. Quasi-optimal inspection schemes for screening submitted lots of manufactured material are derived in closed-forms by using a normal approximation of the incomplete gamma ratio function. Explicit and quite accurate approximations of the smallest number of units to be tested per lot and the maximum tolerable number of nonconformities in the selected sample are presented. The number of resubmissions with minimal inspection effort and controlled risks is also computed. An application to the manufacturing of glass is provided for illustrative purposes.