Prediction Intervals for Screening Using a Measured Correlated Variate

At least I units are required whose values of a performance variable Y fall below the upper specification limit U. They are obtained by screening units on a correlated variable X until m units are obtained whose values of X meet the threshold W. The numbers I and m are specified in advance of screening, and W needs to be determined. Two cases are discussed: one with all parameters known and one with all parameters unknown. The analysis in this paper amounts to the application of a binomial model in addition to the bivariate normal screening model previously discussed in Owen, Mclntire, and Seymour (1975) and in Owen and Su (1977). When the bivariate distribution parameters are unknown, finding W is similar to the prediction interval problem discussed in the literature. Some illustrative tables and examples are included.