Failure-Correlated Opportunity-based Age Replacement Models

Abstract

In this paper, we extend the existing opportunity-based age replacement policies by taking account of dependency between the failure time and the arrival time of a replacement opportunity for one-unit system. Based on the bivariate probability distribution function of the failure time and the arrival time of the opportunity, we focus on two opportunity-based age replacement problems and characterize the cost-optimal age replacement policies which minimize the relevant expected costs, with the hazard gradient, which is a vector-valued bivariate hazard rate. Through numerical examples with the Farlie–Gumbel–Morgenstern bivariate copula and the Gaussian bivariate copula having the general marginal distributions, we investigate the dependence of correlation between the failure time and the opportunistic replacement time on the age replacement policies.