Effect of Selection on the Failure Rate Function

Abstract

Effect of selection procedures such as truncation and genotypic selection, are studied using selection differentials. These studies are mainly restricted to the study of mean or percentiles of the characteristics of interest. However, in situations where improvement on longetivity is itself of interest, in addition to studying mean or percentiles, one may study the reliability characteristics such as Failure Rate, Mean Residual Life etc., of the lifetimes of individuals. In this paper, we study the effect of genotypic selection when the distribution function of the lifetime is governed by a single locus with 2 alleles. We compute the difference in the failure rate function from one generation to the next generation for different values of n, the number of generations. We also obtain the limiting values of the failure rate function as n and compute the number of generations required for the failure rate to reach a value close enough to the limiting failure rate function. We also consider an example in a two-loci case and study the effect of selection on the failure rate function.