Failure rate-based models for systems subject to random shocks

Shock process that can increase the failure rate of the systems working under a stochastic environment is known as the shot-noise process. In the existing literature focusing on the shot-noise process, it is usually assumed that the failure rate increments caused by shocks are the same constants or identically distributed variables. However, such an assumption has limitations if the external environment is constantly changing or the shocks can weaken the system gradually. This article proposes an extended shock model in which the failure rate increments of systems caused by shocks need not be identical or identically distributed. The reliability functions of the systems as well as some reliability indices are derived explicitly. Some special cases are discussed. Besides, a preventive maintenance model is also investigated in which the system is replaced when the number of shocks reaches a fixed threshold. Finally, an example on a refrigeration system is provided to illustrate the proposed model.