Reliability modeling and optimal random preventive maintenance policy for parallel systems with damage self-healing

Materials with intrinsic self-healing phenomenon possess the ability to heal in response to external random shocks. Introducing a recovery factor to quantitatively measure the damage self-recovery efficiency, this paper designs a self-healing mechanism corresponding to both damage load and shock arrival numbers for a parallel redundant system consisting of multiple non-identical components. From the actual engineering perspective, each shock arriving on the system selectively affects one component or more but not necessarily all units in parallel, and consequently, random shocks are categorized according to their sizes, attributes and affected components. This study investigates novel reliability models and schedules optimal preventive maintenance policies, in which the closed-form reliability quantities are derived analytically and the optimum preventive replacement interval is demonstrated theoretically. In addition, a Nelder-Mead downhill simplex method is introduced to seek the optimal replacement age in minimizing the long-run average maintenance cost rate for the condition system failure distribution is rather complex. A micro-electro-mechanical system (MEMS) whose constitutional materials are integrated by microcrystalline silicon, where polymer binders with self-healing capability are always synthesized, is designed to verify the results we obtained numerically, illustrating the significance of considering damage self-healing phenomena.