Reliability assessment under continuous fatigue degradation and shock based on Markov renewal process

In this paper, the Markov renewal process is developed to characterize the system subjected to multiple failure mechanisms. The evolution of the system state is defined as a semi-Markov process whose kernels are derived considering two shock scenarios. One is the mixed shock scenario, combining the extreme shock model and the δ-shock model, while the other is the cumulative shock scenario. Throughout the derivation, the mutual interactions between continuous fatigue degradation and shock are taken into account. Shocks lead to degradation increment and nonlinear fatigue damage accumulation, while the fatigue process intensifies damage due to shocks. Notably, the nonlinear fatigue damage accumulation involves retardation effects. In this study, a reliability model focused on the mutual interaction among failure modes is derived from the kernel of the semi-Markov process. The mean time to failure (MTTF) is also calculated. Moreover, the impacts of the shock thresholds on MTTF are discussed. Finally, two case studies based on real fatigue testing data of steel 350WT and aluminum alloy 2024-T351 are provided to illustrate the implementation and effectiveness of the proposed model.