Screening on Correlated Variables: A Bayesian Approach

Abstract

Let X and Y be two correlated variables, where the measurement of X is easier or less expensive to make than the one on Y. Suppose that the Y measurement is required to meet a certain specification limit. Given that the joint distribution of (X, Y) is bivariate normal and given the sufficient statistics from a random sample from this distribution, we propose a Bayesian method for determining a cutoff limit on X so that, with a guaranteed probability, Y meets its specification limit. Monte Carlo simulations are used to evaluate the Bayesian procedure. It is seen to be less conservative than the method of Owen, Li, and Chou (1981), and it is fairly robust under nonnormality. An example using data from one time point to predict results at another time point illustrates the application of the method.