Reliability and maintenance analysis of a system with dependent main and auxiliary components

In this paper, the reliability and maintenance modelling of a system with dependent main and auxiliary components is studied. The system consists of one main degrading component that takes charge of the system functionality and several protective auxiliary components. Two types of failure interactions are considered: within the auxiliary components, whenever one component fails, failure rates of the survival auxiliary components increase. To the main degrading component, the failure of an auxiliary component may act as an shock and induce random damages to it. The auxiliary components are heterogeneous that follow general lifetime distributions. A periodical inspection and condition-based maintenance policy is developed to ensure the system functionality and control the maintenance budget. The maintenance problem is casted into a Markov decision process framework where the total expected discounted cost in the long-run horizon is taken as the assessment function. The value iteration algorithm is implemented to evaluate the maintenance policies and costs. Through a numerical example, the applicability of the proposed model and some sensitivity analysis are discussed.