Reliability modelling for systems degrading in Markovian environments with protective auxiliary components

Systems with dependent main and auxiliary components have been extensively investigated in the reliability field recently, but the influence of the changing environment has been less taken into consideration. Motivated by some real applications, when the protective auxiliary component fails, the degradation/failure rate of the main component varies as it is exposed to different environments. To bridge the gap between research and practice, in this paper the influences of the dynamic environments and the component dependencies are both incorporated to develop a new reliability model for systems with main and auxiliary components. A continuous-time homogeneous Markov process is used to model the evolution of the environments. When the auxiliary component works, it could protect the main component from the negative impact of the environment. Once the auxiliary component fails, the main component would degrade at different rates according to different environment states. Based on the proposed model, first the reliability of the system is derived in a recursive way. Besides, an opportunistic inspection and maintenance policy is designed for the system, and some important indexes such as the limiting average availability and the long-run average cost are derived. Finally, through numerical examples, the applicability of the proposed model and sensitivity analysis of the model parameters are discussed.