Performance modeling for condition-based activation of the redundant safety system subject to harmful tests

Redundancy is a widely adopted measure for the enhancement of safety system performance. This fault-tolerance design can keep the system functioning through one unit if the other has failed. Besides the continuous aging degradation, mechanical units expose to random shocks, resulting in the dependence. In practice, it is often sufficient to activate only one unit in case of a shock so that the degradation will then be intensified. Unit-level failure occurs when the total degradation level reaches a certain level and will keep hidden. Thus, periodic tests are arranged to reveal the system state, accompanying the side effects on the existing degradation given the test-induced additional stress. A novel condition-based activation policy is proposed based on the system state, referring to how to preset the allocation of units to withstand potential shocks in the upcoming test interval. In this paper, analytical formulas are developed to evaluate system performance with the involvement of these aforementioned factors. Finally, numerical examples are presented to find an optimal test and activation policy to reach minimum system unavailability in a given service time horizon. This study is expected to provide clues for practitioners in the optimal test and operation of redundant structure.