Reliability analysis of self-healing systems equipped with multi-component protective devices operating in a shock environment

Many industrial systems, possess the self-healing abilities owing to the use of self-healing materials, such as the pipelines with the self-healing coatings. Furthermore, protective devices are installed for the self-healing systems due to the severity of the shock environment. However, no prior studies have evaluated the reliability of self-healing systems equipped with protective devices. To bridge this research gap, this study first investigates the reliability of self-healing systems supported by multi-component protective devices in a shock environment. When a run of invalid shocks with a certain size occurs, the self-healing mechanism of the system is activated to repair the damage resulting from previous valid shocks. Multi-component protective devices have been utilized for the systems in the hostile shock environments to reduce the risk of failure. When the self-healing mechanism and protection from the devices exert a joint influence on the system, a scenario where the protective devices switch between operating and standby states may occur. The reliability indexes of the self-healing system with multi-component protective devices are analyzed in the case of the shock length and continuous time by a combined method. The applicability of the proposed model and efficacy of the method are demonstrated by numerical examples.