Continuous-time predictive-maintenance scheduling for a deteriorating system

TLDR

Classical maintenance strategies such as periodic inspection/replacement, systematic periodic replacement, and corrective policies can be replicated by selecting specific inspection schedules and replacement thresholds. The paper proposes a predictive‑maintenance framework for a continuously deteriorating single‑unit system. The authors develop a decision model that jointly optimizes a preventive‑replacement threshold and an inspection schedule to minimize failure and unavailability costs over an infinite horizon, using regenerative and semi‑regenerative process theory to compute the maintained‑system cost. Numerical experiments demonstrate that jointly optimizing the replacement threshold and inspection times minimizes the long‑run expected maintenance cost, outperforms classical preventive policies, adapts automatically to wear‑process characteristics and cost structures, and converges to systematic periodic replacement when inspections and replacements are costly.

Abstract

A predictive-maintenance structure for a gradually deteriorating single-unit system (continuous time/continuous state) is presented in this paper. The proposed decision model enables optimal inspection and replacement decision in order to balance the cost engaged by failure and unavailability on an infinite horizon. Two maintenance decision variables are considered: the preventive replacement threshold and the inspection schedule based on the system state. In order to assess the performance of the proposed maintenance structure, a mathematical model for the maintained system cost is developed using regenerative and semi-regenerative processes theory. Numerical experiments show that the s-expected maintenance cost rate on an infinite horizon can be minimized by a joint optimization of the replacement threshold and the a periodic inspection times. The proposed maintenance structure performs better than classical preventive maintenance policies which can be treated as particular cases. Using the proposed maintenance structure, a well-adapted strategy can automatically be selected for the maintenance decision-maker depending on the characteristics of the wear process and on the different unit costs. Even limit cases can be reached: for example, in the case of expensive inspection and costly preventive replacement, the optimal policy becomes close to a systematic periodic replacement policy. Most of the classical maintenance strategies (periodic inspection/replacement policy, systematic periodic replacement, corrective policy) can be emulated by adopting some specific inspection scheduling rules and replacement thresholds. In a more general way, the proposed maintenance structure shows its adaptability to different possible characteristics of the maintained single-unit system.