Reliability of a System Subjected to a Cumulative Shock Model With a Change Point

Shock models play a vital role in describing the lifetime behavior of the system working in a stochastic environment. The cumulative shock model is one of the widely studied models of system failure and describes the failure of a system as the accumulation of additive damage from shocks. In this paper, we study a new cumulative shock model when the magnitudes of shocks are non‐identical over time. The proposed model assumes that the magnitude of a shock changes after a random time, namely the change point. We discuss the mathematical expressions for the reliability function. While closed‐form expressions are unavailable, we further use a novel matrix‐based analytical approach to approximate the reliability of the system. We present numerical examples to illustrate our findings.