Reliability analysis of a system with two-stage degradation using Wiener processes with piecewise linear drift

We study a model of a two-stage degradation process in a dynamic environment. The two stages, the normal stage and the defective stage, are separated by the first hitting time of the alarm threshold by the degradation level. Wiener processes with piecewise linear drift are used in each stage to describe the degradation level in a dynamic environment. System failure is triggered in two ways: the system degradation level reaches the defect-based failure threshold; the duration in the defective stage is larger than the duration-based failure threshold. Explicit expressions for the system reliability for different duration-based failure thresholds are obtained. These include when the duration-based failure threshold is zero, when it is a positive constant and when it tends to infinity. A simulation procedure is described for the case in which the duration-based failure threshold is a random variable. Finally, some numerical examples are presented to illustrate the proposed reliability assessment method. The modelling method and the results can be used for reliability evaluation, residual life prediction and maintenance decision optimization of a system with two-stage degradation in a dynamic environment.