Design of two-stage screening procedures with a prescribed outgoing quality

Abstract

This thesis is concerned with economic design of two-stage screening procedures based on the screening and performance variables which guarantee a prescribed outgoing quality. In a two-stage screening procedure, a screening variable is used first to decide whether an item should be accepted, rejected, or undecided and the performance variable is then used to classify the undecided items. Design of two-stage screening procedures involves determining cutoff values for a screening variable. A cost model is constructed which involves costs due to screening and performance inspections and type I and type II misclassification errors. Optimal cutoff values on the screening variable minimizing the expected cost are obtained subject to the constraint that the average outgoing quality exceeds a prespecified level. Methods of finding the optimal cutoff values are presented for both parameters-known and parameters-unknown cases. This thesis is divided into the following three parts. (i) Two-stage screening procedures are considered where the screening and performance variable are both continuous and a single specification limit is given on the performance variable. The two variables are assumed to have a bivariate normal distribution. (ii) Two-stage screening procedures with continuous screening and performance variables are considered for the case where both lower and upper specification limits are given on the performance variable. A cost model is constructed involving six cost components since each of type I and type II misclassification errors occurs in relation with both lower and upper specification limits. (iii) Two-stage screening procedures are designed where the screening variable X is continuous and the performance variable T is dichotomous. Two models are considered; i) the logistic model where P(T = 1│x) is assumed to be a logistic function of x and ii) the normal model where X given T is assumed to be normally distributed.