Reliability analysis of a system including multi-state demand-based subsystems supported by protective devices considering two types of triggering errors

•Build a system with demand-based subsystems supported by protective devices (PDs).•Propose two possible triggering errors of PDs according to engineering practices.•Study the case that internal degradations of units and PDs are affected by shocks.•Propose a general state division method for the multi-state subsystems with PDs.•Jointly apply MPIA and UGF method to derive the reliability of the proposed model. Protective devices (PDs) can improve system reliability and extend its lifespan. Existing research on PDs primarily focused on their ability to reduce the internal degradation rate of the system or mitigate the impact of external shocks. In engineering practice, a type of widely applied PD is responsible for isolating failed components from the systems. Only one prior study investigated the above function of PDs and the error scenario of PDs that they cannot be successfully activated. However, there is another triggering error of PDs in reality that they may be falsely triggered when no component failures occur. To fill the research gap, a reliability model for a system with multi-state subsystems equipped with PDs is constructed, where two possible triggering errors of the PDs are considered. The degradation of the subsystems and PDs is caused by internal degradation and external shocks. The dependence between the two impacts lies in the fact that the increase in internal degradation is caused by the cumulative number of shocks reaching a threshold. Additionally, considering the engineering applications of these PDs, assume that the subsystems must meet random demands and that the supply of the subsystems varies according to their different states. System failure occurs when the number of subsystems unable to meet the demand exceeds the threshold. The reliability indices of the proposed system are derived by a combination of the Markov process imbedding approach and the universal generating function technique. Finally, the effectiveness and applicability of the proposed model are validated through a case study of a power system composed of multiple wind turbines.