System performance of damage self-healing systems under random shocks by using discrete state method

Systems with self-healing mechanism have been successfully applied in many practical fields. However, the self-healing action has less been considered when discussing the reliability performance of systems subject to degradation or shocks. In this paper, we study a damage self-healing system subject to random shocks where the shock arrival times are described by a Poisson process with different intensities due to the accumulated system damage. When the system is majorly damaged, i.e., the state of the system is worse than a specified state, it loses the ability of self-healing. By using the discrete state method, the evolution of the system state can be modeled by a Markov renewal process. Then the system performance indexes, for example, the system reliability, the remaining lifetime distribution, the expected number of shocks and the availabilities are derived in the analytical forms. Finally, a numerical example is illustrated to demonstrate the framework we derived in this paper and show the influence of self-healing mechanism.