A Screening Method for Increasing Acceptable Product with Some Parameters Unknown

Abstract

The problem is considered of screening on a random variable correlated with the performance variable to increase acceptable product. Consider a stockpile with a given proportion meeting a set quality standard and the necessity to upgrade the stockpile by testing on a variable correlated with the variable of interest. For example, stcppose lifetime is the variable of interest. Clearly it would be useless to try to screen on the lifetime variable itself. However, if a variable correlated with lifetimes is available and a bivariate normal model is assumed then much can be done. If all of the paramctcrs are known, the solution is given by Owen, McIntire and Seymour [12], but if some of the parameters are unknown then some procedures for handling the problem are given here.

Ptlost of the previous work in the area of selection by a correlated variate is concerned with personnel selection and animal improvement. As such, it is widely scattered. Fol example, Owen [9], p. XLIV, contains a bibliography which contains many items on personnel selection. Papers having to do with genetic selection and related areas are those by Cox [4], Binet [l], Searle [13], VanVleck [15], Chapman [2], Cochran [3], and Thompson [14]. This is not a complete bibliography, but, will give the reader some idea of the previous work. This previous work does not have exactly the same model as is considered here. The work here is closely related to tolerance limits.

KEY WORDS:

• Screening Variables
• Normal Probabilities
• Bivariate and Trivariate
• Selection Procedures IJsing Correlated Variables
• Toleranre Limits