The censored delta shock model with non‐identical intershock times distribution and an optimal replacement policy

Abstract

In this article, we consider the censored model in which the distribution of intershock times do not have the same distribution, but it is assumed that a change occurs in the distribution of the intershock times due to an environmental effect and hence this distribution changes after a random number of shocks. For this shock model, several reliability characteristics are evaluated by assuming that the random change point has a discrete phase‐type distribution. Analytical results for evaluating the reliability function of the system for several continuous as well discrete distributions of the interarrival times, are also given. Also, the optimal replacement policy that is based on a control limit is proposed for a mixed censored ‐shock model in which both the distributions of the magnitudes of shocks and the distributions of the interarrival times of shocks change after a random number of shocks. Finally, several numerical examples are given to illustrate our results.