Condition-based maintenance assessment for a deteriorating system considering stochastic failure dependence

In this article, the condition-based maintenance optimization of a K-out-of-N deteriorating system considering failure dependence is discussed. The degradation of each component is modelled by a pure jump Lévy process. Whenever one component fails, it can either induce instantaneous failures or lead to the increment of degradation levels of other components. Thus, this model has the flexibility to describe the phenomena of instantaneous failures of multiple components, which is known as the common cause failure. It can also model the accumulative, gradual propagation effect of the component failure to the system. A periodic inspection policy is considered to reveal the real state of the system, upon which, possible maintenance actions can be carried out according to the observations. The inspection and maintenance problem is formulated as a Markov decision process and the value iteration algorithm is employed to solve the problem. The proposed policy is assessed by the total expected discounted cost in the long-run horizon. Under mild conditions, some structural properties of the optimal maintenance policies are obtained. A numerical example is given to illustrate the applicability of the proposed model. It can provide theoretical reference for the decision-maker when developing maintenance policies.