A Distribution-Based Systems Reliability Model Under Extreme Shocks and Natural Degradation

Abstract

Degradation, and shock are two common mechanisms accounting for product failures. This paper presents a convenient means of capturing both shock and degradation in a single model when the extent of degradation and the magnitude of shocks are not observable, but only the failure times and the corresponding failure modes are recorded. We assume that the lifetime of a degradation-oriented failure, which is regarded as some initial random resource, belongs to some distribution family. Shocks arrive according to a non-homogeneous Poisson process, and the destructive probability depends on the transformed remaining resource of the system. Under these assumptions, we propose the single failure time model, and the recurrent event model. This study complements the well-known Brown-Proschan model. The single failure time model has successfully been applied to a real time data set. We also conduct a simulation study to examine the accuracy of our model.