Economic design of a two-stage screening procedure with a prescribed outgoing quality

An economic two-stage screening procedure based on screening and performance variables is proposed. A screening variable is used first to decide whether an item should be accepted, rejected, or undecided. The performance variable is then used to classify the undecided items. The two variables are assumed to have a bivariate normal distribution. A cost model is constructed which involves costs due to screening and performance inspections and misclassification errors. Optimal cutoff values on the screening variable minimizing the expected cost are obtained subject to the constraint that the outgoing quality exceeds a prespecified level. Methods of finding the optimal cutoff values are presented for both parameters-known and parameters-unknown cases.