Reliability modeling for competing failure processes considering degradation rate variation under cumulative shock

Most systems experience both random shocks (hard failure) and performance degradation (soft failure) during service span, and the dependence of the two competing failure processes has become a key issue. In this study, a novel dependent competing failure processes (DCFPs) model with a varying degradation rate is proposed. The comprehensive impact of random shocks, especially the effect of cumulative shock, is reasonably considered. Specifically, a shock will cause an abrupt degradation damage, and when the cumulative shock reaches a predefined threshold, the degradation rate will change. An analytical reliability solution is derived under the concept of first hitting time (FHT). Besides, a one-step maximum likelihood estimation method is established by constructing a comprehensive likelihood function. Finally, the reasonability of the closed form reliability solution and the feasibility and effectiveness of the proposed DCFPs modeling methodology are demonstrated by a comparative simulation study.