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.