Reliability modeling for degradation-shock dependence systems with multiple species of shocks

In this research, reliability models are developed for systems or devices subject to dependent competing soft and hard failure processes with degradation-shock dependences. The new models in this paper extend previous researches by considering novel shock effect patterns (SEPs) resulting from multiple species of external shocks. A soft failure occurs when overall degradation level exceeds the soft failure threshold. Meanwhile, a hard failure occurs when the transmitted shock size exceeds the hard failure threshold. The dependences between the soft and hard failure processes are considered in terms of two different SEPs, degradation level and degradation rate. For SEP I, the shocks can increase the degradation level. Thus, the soft failure is indicated by the overall degradation level comprising of the internal continuous degradation and the additional damage caused by shocks. For SEP II, the shocks can increase the degradation rate of the soft failure process. Specifically, in this research four reliability models focusing on different stochastic processes and SEPs are developed. Closed-form reliability formulas are derived for the general path models, while simulation methods are adopted to get the reliability for the Wiener process models. Finally, numerical examples are given to illustrate the models and the approaches.