Optimal schemes for resubmitted lot acceptance using previous defect count data

• Optimal inspection schemes are derived by minimizing the expected sampling effort.
• The Poisson model is used to describe the number of nonconformities per sampled unit.
• The use of a few resubmissions often significantly reduces the expected sample size.
• A computational method is proposed to find the best resubmitted lot acceptance plan.
• The inclusion of past data and information provides substantial savings in sample size.

Optimal defects-per-unit inspection schemes for screening batches of manufactured material are obtained by minimizing the expected sampling effort. Nonaccepted lots may be resubmitted for resampling inspection, whereas the Poisson model is used to describe the random behavior of the number of nonconformities per sampled unit. A coefficient is presented to assess the similarity degree between the available previous information and the current inspection, and truncated gamma distributions are adopted to quantify the natural prior uncertainty about the defect rate using past count data and expert opinions. A step-by-step computational procedure is proposed to solve the underlying integer nonlinear programming problem in order to find the best resubmitted lot sampling plan with controlled expected producer and consumer risks based on previous objective and subjective knowledge. In many practical cases, the inclusion of lot resubmissions and past information into the inspection process provides substantial savings in sample size, as well as more reliable evaluations of the existing producer and consumer risks. The proposed approach allows the practitioners to consider a restricted interval for the defect rate, which is reasonable in practice and unfeasible under the frequentist perspective. Moreover, a mechanism is suggested to update the prior distribution based on past performance of the inspection plan. For illustrative purposes, the methodology developed is applied to the manufacturing of glass.