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Shocks have attracted considerable interest in reliability and maintenance engineering because of their impact on vulnerable systems. Most industrial systems suffer from both internal degradation caused by fatigue and wear-out, and external shocks that often occur randomly due to harsh weather conditions, overloading, etc. Developing maintenance optimization models without taking these stochastic shocks into account is often ineffective. This paper develops a model to optimize the maintenance alarm threshold for a single-component continuously monitored system which is exposed to both fatal and non-fatal shocks in the presence of lead time for hard time maintenance. The shocks occur randomly according to a homogeneous Poisson process during the whole degradation process and have a stochastic impact on the degradation level, while the system resistance to shocks decreases as the system approaches failure. We propose a new numerical maintenance optimization model to find the solution without Monte-Carlo simulation and the model is compared to the Wiener process. A numerical example and a real-time experimental case study on roller bearings are used to demonstrate the effectiveness of the model. The results show that the model is capable of improving maintenance decision-making in terms of failure probability and risk perspective.
Tajiani et al. (Sat,) studied this question.