A decision-theoretic approach to some screening problems

Summary

Suppose an item is acceptable if its measurement on the variable of interestY isY≦u. It may be expensive (or impossible) to measureY, and a correlated variableX exists which is relatively inexpensive to measure and is used to screen items, i.e., to declare them acceptable ifX≦w. We examine two situations in both of whichl acceptable items are needed. (i) Before use of the item,Y is measured directly to ensure acceptability: ShouldX be used for screening purposes before theY measurement or not? (ii)Y cannot be measured directly before use, but screening is possible to determine the items that are to be used. We assume thatX andY have a bivariate normal distribution for which the parameters are known. Some comments are made about the case when the parameters are not known.