A condition-based maintenance policy considering failure dependence and imperfect inspection for a two-component system

In this paper, a condition-based maintenance of a two-component system under imperfect inspection is studied: component 1 is repairable and only two states (working and failed) are observable. Component 2 degrades with time. The degradation of component 2 is modelled by a Wiener process with different drift and volatility parameters depending on the working state of component 1. Component 2 fails if its degradation level exceeds a pre-defined threshold. A dual periodical inspection policy is proposed to monitor the system condition: component 1 is imperfectly inspected and the whole system is perfectly inspected with a longer period. Upon inspection, component 1 is replaced if a failure is detected. The whole system is renewed if the degradation of component 2 exceeds its preventive maintenance threshold. The problem is very complex due to the failure dependence between the two components and the partial revealed information within the system inspection period. Component 1 is impacted by the imperfect inspection. Component 2 may experience multiple changes of its degradation regime while only imperfect, partial change information is available. In this study, we intend to address these problems. The expression of the maintenance cost rate in the long-run is given to evaluate the maintenance policy. An algorithm is proposed to achieve the maintenance optimization. Numerical examples show the applicability of the model. It can provide reference to the decision-maker for optimizing the maintenance budget.