Economic screening procedures based on a correlated variable

Abstract

This thesis is concerned with economic design of screening procedures to improve outgoing product quality based on a correlated variable. Economic design of screening procedures involves determining optimal cutoff vale for a screening variable. Optimal cutoff value is obtained by minimizing the expected total cost. This thesis is divided into the following three parts. (i) Economic design of one-and two-sided screening procedures is considered. It is assumed that the performance and screening variables are jointly normally distributed. When some parameters of the distribution are unknown, methods for finding optimal based on normal conditioned on t-distribution are presented under the constant quality cost function. Assuming that costs are incurred by screening inspection and Type I and II misclassification errors. When all parameters are unknown, methods for obtaining optimal screening procedures based on the predictive distribution are presented under three quality cost functions - constant, linear and quadratic - assuming that costs are incurred by screening inspection, acceptance of an imperfect item and disposition of a rejected one. (ii) Economic design of screening procedures based on a continuous screening variable X in place of dichotomous performance variable T is considered. Optimal cutoff values on the screening variable minimizing the expected total cost are obtained for normal and logistic models ; it is assumed that X given T is normally distributed in normal model and the probability that an item is conforming in screening inspection is given by logistic function of X in logistic model. Costs are assumed to be incurred by screening inspection and two types of misclassification errors. Cases where some parameters are unknown are also considered. (iii) When the performance variable is dichotomous and the screening variable is continuous, optimal screening procedures are presented for assuring, with a specified degree of confidence, that at least $...