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As the key of the prevalent prognostics and health management, remaining useful life prediction has attracted considerable attentions during the past decades. However, almost all of the existing remaining useful life prediction methods were implemented under the premise that the deteriorating systems were not maintained over the whole life cycle. For the deteriorating systems experiencing maintenance activities during their life profiles, this paper presents a simulation-based remaining useful life prediction method taking the influence of maintenance activities into account. Specifically, the Wiener process with jumps is employed to model the degradation path of a deteriorating system, where the jump parts are used to characterize the influence of maintenance activities on the system degradation. The parameters in the degradation model are estimated by the maximum likelihood estimation method. To acquire the remaining useful life distributions of the deteriorating system, we design a simulation-based algorithm on the basis of the Markov Chain Monte Carlo method. Accordingly, the interested statistics associated with the remaining useful life can be obtained numerically. Finally, a numerical example is provided to show the implementation of the newly proposed remaining useful life prediction method.

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This article proposes a novel preventive replacement policy based on condition monitoring and imperfect manual inspection for systems subject to a two-stage deterioration process, where the two-stage deterioration process is modeled by the white noise process and Brownian motion with a drift, respectively. The proposed preventive replacement policy is implemented using two thresholds: a failure threshold and a preventive threshold. Specifically, if the condition monitoring measurement is observed to cross the failure threshold, then the failure replacement will be carried out; and, if the condition monitoring measurement is observed to cross the preventive threshold while lower than the failure threshold, then the system needs to be checked by manual inspection, and the preventive replacement will be carried out once the system is found to be in the defective state. In this article, we consider that manual inspection is imperfect, namely, there is a probability that the defect will be unnoticed. By minimizing the expected cost per unit time, we obtain the optimal condition monitoring interval and preventive threshold. A numerical example is provided to demonstrate the performance of the proposed condition-based replacement policy. Comparisons are made with the existing work, which shows the effectiveness and superiority of the proposed policy.