The optimum target value under single and two-stage screenings

In this paper we consider the problem of determining the optimum target value of the quality characteristic of interest and the screening limits for a correlated variable under single and two-stage screenings. In single-stage screening, inspection is performed directly on the quality characteristic of interest or on a variable that is correlated with the characteristic. In two-stage screening, the correlated variable is inspected first to decide if an item should be accepted, rejected, or whether additional observations should be taken. If additional observations are required, the quality characteristic is then directly observed in order to classify the undecided items. Models are constructed that involve selling and discounted prices as well as production, inspection, and penalty costs for both single and two-stage screenings. Methods for finding the optimum process mean and the screening limits are presented when the quality characteristic and the correlated variable are assumed to be jointly normally distributed. A numerical example is presented.