Extreme shock model with change point based on the Poisson process of shocks

Abstract

In this article, we introduce and study an extreme shock model in which the distribution of magnitude of shocks can change due to environmental effects. A new decision parameter is used to model the change point, and the non‐homogeneous Poisson process is employed to model the arrival of shocks. We derive the reliability function and mean time to system failure for the defined model. Furthermore, we propose an optimal age replacement policy. The results are illustrated when the change point follows the Erlang distribution.