An Economic Two-Stage Screening Procedure with a Prescribed Outgoing Quality in Logistic and Normal Models

Abstract

An economic two-stage screening procedure based on a dichotomous performance variable T and a continuous screening variable X is proposed. X is measured first to decide whether an item should be accepted, rejected, or additional observations should be taken. If no terminal decision is reached, T is then observed to classify the undecided items. Two models are considered; (i) the logistic model, where P(T = 1\X = 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. A simple economic model based on inspection and misclassification costs is constructed. Optimal cutoff values on the screening variable are obtained by minimizing the expected cost-subject to the constraint that the average outgoing quality attains a prespecified level. Solutions are provided for both known-parameter and unknown-parameter cases. (C) 1995 John Wiley & Sons, Inc.