Algorithms for the free replacement warranty with phase-type lifetime distributions

Abstract

This paper addresses the stochastic process generated by the cash flows resulting from free replacement warranties. Considering the underlying renewal processes, expressions for the quantities of interest can be obtained in terms of the renewal function which, in general, is very difficult to compute. For this reason most reported results are implemented only for product lifetimes belonging to the exponential family. To date there has been no significant research into the impact of the lifetime distribution on product warranty decisions. In this paper we develop algorithms to evaluate various items of interest in decision making when the lifetimes follow phase-type probability distributions. Extensive numerical results are presented to describe the effect of various model parameters on product warranty decisions.