Reliability modeling for a two-phase degradation system with a change point based on a Wiener process

•A fixed change point model with a jump based on a Wiener process is developed.•The fixed change point model is extended to a random change point model.•Two phase changing patterns for the random change point model are proposed.•Analytical results of the system reliability indexes are given for Model 1 and the HPP case of PCP 2 in Model 2.