Design of a two-stage procedure for three-class screening

A two-stage screening procedure is developed for a situation where an item is sold in one of two markets or scrapped. The items selling price and product specifications are different in both markets. In the first stage of the procedure, each item is inspected on a surrogate variable that is correlated with the performance variable of interest. If a decision is not reached at this point, the item is subjected to the second stage of the procedure where it is inspected on the performance variable, and a classification decision is made. A loss in revenue is incurred by the producer when an item that meets the specifications of the higher-price market is sold in the lower-price market. The producer also sustains a cost when an item that does not conform to the product specifications of a market is sold in that market. The economic factors considered in the model, therefore, are the selling prices and the cost consequences resulting from decision errors. The optimal screening specification limits for known-parameter and unknown-parameters situations are derived by maximizing the expected profit per item.