Reliability of performance-based system containing multiple load-sharing subsystems with protective devices considering protection randomness

•Build a performance-based system including subsystems with protective devices (PDs).•Propose a new triggering condition of PDs based on units’ internal degradation rate.•Consider the degradation of PDs of load-sharing subsystems before running firstly.•Study the real case that the PDs in poor states may fail to function.•Formulate an efficient method of MPIA and UGF to get the system reliability. Existing studies on the systems with protective devices (PDs) all consider that the components are independent, and the PDs are activated to work in a perfect state and always realize their functions successfully until failures. However, it can be found that the above assumptions have some limitations, motivated by actual engineering cases. To fill the research gaps, this paper proposes a new system which contains multiple load-sharing subsystems with PDs. The PDs are subject to internal degradation with a lower rate before working, and may be unable to protect the components in poor states. The PD in each subsystem is triggered when the internal degradation rate of the working components reaches the preset value. The PDs can decrease the probability of the valid shocks and the internal degradation rate of the components. Each subsystem has multiple states, determined by the number of failed components and the subsystem in each state takes certain performance. The state of entire system is divided into multiple levels according to the total performance of subsystems. The Markov process imbedding approach and universal generating function technique is combined to analyze the system reliability. Finally, the applicability of the proposed model is validated using numerical examples.