Optimum process mean and screening limits for a production process with three-class screening

The optimum process mean and screening limits are provided for a production process where the accepted item is sold in one of two alternative markets and the rejected item is reworked. All items are subject to screening where the screening variable may be the major quality characteristic of interest (performance variable) or the surrogate variable, which is highly correlated with the performance variable. Each item is classified into three quality grades A, B, and C: grade A items are sold to primary market, grade B items are sold to secondary market, and grade C items are reworked by the same manufacturing process. Assuming that performance and surrogate variables are jointly normally distributed, two profit models are constructed which include selling price, production, inspection, rework and penalty costs. Methods of finding the optimum process mean and the screening limits are presented and an illustrative example is given.