Optimal Triggering Policy of Protective Devices Considering Self-Exciting Mechanism of Shocks

Safety-critical systems are commonly required to complete specific missions in shock environments, and their failures may lead to severe economic losses and significant safety hazards. To enhance system reliability, protective devices are commonly equipped to resist external shocks. The existing literature focuses mainly on the maintenance policy of safety-critical systems, ignoring the system reliability analysis considering the effect of protective devices and the self-exciting mechanism of shocks. This paper considers multi-state systems equipped with a protective device in shock environments where valid shocks and invalid shocks occur stochastically. The system state degenerates due to valid shocks or the self-exciting behavior of invalid shocks. The self-exciting mechanism is triggered when the number of cumulative or consecutive invalid shocks suffered by the system exceeds a certain threshold, leading the system to a worse state. The protective device can be triggered to protect the system from the damage of external shocks when the state is worse than a predetermined threshold. The protective effect is characterized by reducing the probability of valid shocks. A finite Markov chain embedding approach is used to evaluate the system reliability index. In addition, an optimization model is constructed to determine the optimal triggering threshold of the protective device. The numerical results indicate that protective devices can significantly improve the reliability of the system and incorporating the self-exciting mechanism of shocks into reliability modeling contributes to accurate reliability evaluation.