Multi-objective imperfect maintenance for dependent competing risk systems with multiple degradation processes and random shocks

Multiple competing risks are one of the important topics in reliability field, especially degradation processes and random shocks. This research aims to relax the independent assumption by considering that there exist dependent relationships not only among multiple degradation measures but also between degradation measure and random shocks. In reality, many systems have multiple components with more than one degradation measure which is dependent with each other due to their interplaying functions or common usage history. Independent assumption may underestimate system reliability estimation under many cases. Random shocks will also contribute to the system failure through two ways: (1) one is working directly on the degradation processes; (2) the other is causing immediate failure to the system.;We develop a new methodology to formulate the reliability prediction model for the gradually degradating systems subject to multiple dependent competing risks of degradation processes and random shocks. Two kinds of random shocks are considered: (1) fatal shocks, which fail the system immediately; (2) non-fatal shocks, which exhibit two effects on the system degradation process, including sudden degradation increment and degradation rate acceleration. The dependency between degradation processes and random shocks are modulated by a time-scaled covariate factors while the dependency among degradation processes are fitted by copula method. Also the reliability and state probability estimation for the systems are derived under the research scope of multi-state system using both analytical and Monte Carlo simulation for the dependent competing-risk systems.;Different maintenance policy models involving imperfect preventive maintenance for this dependent model are introduced and compared with each other. Multi-objective optimization is applied to consider two important targets simultaneously in maintenance issues, including long-run expected cost rate and system availability.