Hybrid stochastic process-based reliability modeling considering two-phase dependence degradation patterns

Reliability modeling based on stochastic processes is an efficient approach to explore the internal degradation principle and random fluctuation of complex systems. Degradation models may transform when phase shifts occur, primarily due to changes in degradation mechanisms and environmental fluctuations. Motivated by the observed phenomena, we developed two hybrid degradation models with constant and random transition points. Specifically, Model 1 employs a Wiener process in the first phase and a Gamma process in the second phase, whereas, Model 2 reverses the order of the two kinds of stochastic process. Both the constant and random transition points are incorporated into the two models to account for the two-phase characteristic caused by the influence of the internal aging law and external environments, such as the cumulative effect of shocks. The system experiences a shock process where the shock effect is novel instantiated in that the shock damage could be absorbed in the first phase. In the second phase, however, the degradation increment will occur. Then, the system reliability is obtained for Model 1 and the simulation approach is applied in Model 2. Finally, some examples are shown to verify the models.