Journal Article

On a terminating shock process with independent wear increments

Abstract

In extreme shock models, only the impact of the current, possibly fatal shock is usu-ally taken into account, whereas in cumulative shock models, the impact of the pre-ceding shocks is accumulated as well. In this paper, we combine an extreme shock model with a specific cumulative shock model. It is shown that the proposed setting can also be interpreted as a generalization of the well-known Brown-Proschan model that describes repair actions for repairable systems. For a system subject to a specific process of shocks, we derive the survival probability and the corresponding failure rate function. Some meaningful interpretations and examples are discussed.