The optimum target values for a production process with three-class screening

For situations where an item is sold in one of two markets with different profit/cost structures or scrapped, economic selections of target values for the mean of the quality characteristic Y of interest and the screening specification limits on a correlated variable X which is correlated with Y are proposed. Two profit models based on Y and X are constructed which involve four profit/cost components: profit, production, inspection, and penalty costs. Assuming that X and Y are jointly normally distributed, methods of finding the optimal process mean and the screening specification limits on X are presented and an illustrative example is given.