Process mean and screening limits for filling processes under two-stage screening procedure

We consider the problem of determining the optimum process mean and screening limits of a surrogate variable associated with product quality under a two-stage screening procedure. In this procedure, the surrogate variable is inspected first to decide whether an item should be accepted, rejected or additional observations should be taken. If additional observations are required, the performance variable of interest is then observed to classify the undecided items. Assuming that the performance and surrogate variables are jointly normally distributed, the optimum process mean and screening limits are obtained by maximizing the expected profit which includes selling price, production, reprocessing, inspection and penalty costs. A numerical example is presented.