Condition-based maintenance for a K-out-of-N deteriorating system under periodic inspection with failure dependence

This paper deals with condition-based maintenance policy of a K-out-of-N deteriorating system with failure dependence. The intrinsic degradation of each component is modelled with a pure jump Lévy process. The idea of the failure dependence is motivated by complex engineering systems where the failure of one component may cause a momentary, transient shock to the system. The effect of the shock is modelled by a random magnitude of increment in the degradation level of each surviving component. Perfect periodic inspections are carried out on the system. Upon inspection, highly deteriorated or failed components are perfectly replaced and hence are restored to an as-good-as-new state. Nothing is done to the rest of the components. For such a system, the evaluation of the reliability and the assessment of the maintenance planning are quite complex due to the failure dependence as well as the imperfect maintenance at the system level. In this study, we address these problems by the implementation of Markov renewal theory. The maintenances costs in both the short-run and long-run horizons are derived and we validate these theoretical calculations by Monte-carlo simulations. Numerical example is given to illustrate the applicability of the proposed model. It can provide a reference for the decision-making when developing maintenance policies.