We study a system that experiences damaging external shocks at stochastic intervals, continuous degradation, and self-healing. The motivation for such a system comes from real-life applications based on micro-electro-mechanical systems (MEMS). The system fails if the cumulative damage exceeds a time-dependent threshold. We develop a preventive maintenance policy to replace the system such that its lifetime is prudently utilized. Further, three variations on the healing pattern have been considered: (i) shocks heal for a fixed duration $\tau$; (ii) a fixed proportion of shocks are non-healable (that is, $\tau=0$); (iii) there are two types of shocks -- self healable shocks heal for a finite duration, and nonhealable shocks inflict a random system degradation. We implement a proposed preventive maintenance policy and compare the optimal replacement times in these new cases to that of the original case where all shocks heal indefinitely and thereby enable the system manager to take necessary decisions in generalized system set-ups.

翻译：我们研究一类在随机时间间隔下承受有害外部冲击、持续退化及自愈行为的系统。此类系统的动机源于基于微机电系统（MEMS）的实际应用。当累积损伤超过随时间变化的阈值时，系统将发生故障。我们提出了一种预防性维护策略，通过更换系统以实现其寿命的合理利用。进一步，我们考虑了三种自愈模式的变体：（i）冲击愈合持续固定时长$\tau$；（ii）固定比例的冲击不可愈合（即$\tau=0$）；（iii）存在两类冲击——自愈型冲击在有限时长内愈合，不可愈合型冲击则造成随机系统退化。我们实施了所提出的预防性维护策略，并将这些新情况下的最优更换时间与所有冲击可无限愈合的原始情况进行了比较，从而使系统管理者能够在通用系统框架下做出必要决策。