Economic designs of single and double screening procedures based on two screening variables

Abstract

This thesis is concerned with economic designs of single and double screening procedures and determination of optimal target value to improve outgoing product quality based on two screening variables. Optimal cutoff values for two screening variables and optimal target value are obtained by minimizing the expected cost. This thesis is divided into the following three parts. (i) Economic designs of single and double screening procedures based on two screening variables are considered for the cases of one-and two- sided specification limit. Two screening variables are observed simultaneously in the single screening procedure and are observed sequentially in the double screening procedure. It is assumed that the performance and screening variables are jointly normally distributed. Three quality cost functions - constant, linear, and quaractic - are considered. Cost models are constructed which involve two screening inspection costs, and costs of accepted and rejected item. Methods of finding the optimal cutoff values of single and double screening procedures are presented and a numerical example is given. (ii) Economic designs of single and double screening procedures based on two continuous screening variables in place of dichotomous performance variable T are considered. Optimal cutoff values of single and double screening procedures minimizing the expected total cost are obtained for normal model; it is assumed that the screening variables for given T are jointly normally distributed. Costs are assumed to be incurred by the two screening costs and the costs of Type I and II misclassification errors. An illustrative example is given and numerical studies are performed to compare single and double screening procedures based on two screening variables with the screening procedures based on one screening variable. (iii) The problem of selecting optimal target values for the mean of the quantity Y of material in a container and cutoff value on the screening varia...