Development of the optimal screening procedures for normal and logistic models

When the nature of measuring a performance variable is destructive or expensive to inspect, a surrogate variable which is strongly correlated with the performance variable can be used. Most of the models of screening procedures reported in the literature assume that rejected items are scrapped, and that performance and surrogate variables follow a bivariate normal distribution. In many industrial settings, however, the rejected items are often reprocessed or recycled for cost reduction and/or environmental protection purposes. In this situation, conventional models of screening procedures become ineffective. In this paper, we propose new economic screening procedures with dichotomous performance variable T and continuous surrogate variable X in situations where the rejected items are reprocessed. Two models – normal and logistic models – are developed. Profit models are constructed which include four price/cost components: selling price, cost from an accepted non-conforming item, and reprocessing and inspection costs. Methods of finding the optimal screening procedures are presented and numerical examples are given.