Laurence Dieulle

A condition-based maintenance policy for stochastically deteriorating systems

Abstract We focus on the analytical modeling of a condition-based inspection/replacement policy for a stochastically and continuously deteriorating single-unit system. We consider both the replacement threshold and the inspection schedule as decision variables for this maintenance problem and we propose to implement the maintenance policy using a multi-level control-limit rule. In order to assess the performance of the proposed maintenance policy and to minimize the long run expected maintenance cost per unit time, a mathematical model for the maintained system cost is derived, supported by the existence of a stationary law for the maintained system state. Numerical experiments illustrate the performance of the proposed policy and confirm that the maintenance cost rate on an infinite horizon can be minimized by a joint optimization of the maintenance structure thresholds, or equivalently by a joint optimization of a system replacement threshold and the aperiodic inspection schedule.

Continuous-time predictive-maintenance scheduling for a deteriorating system

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.

Sequential condition-based maintenance scheduling for a deteriorating system

Abstract This paper deals with a continuously deteriorating system which is inspected at random times sequentially chosen by help of a maintenance scheduling function. The deterioration is modeled by a Gamma process. The system is considered as failed if its condition jumps above a pre-set failure level. Two types of replacement can take place at each inspection date depending on whether the current system state is above a pre-set critical threshold but not failed or in the failed state. This paper is focused on the development of a new probabilistic method based on the semi-regenerative property of the evolution process in order to calculate the long-time expected cost per unit of time. We use a recent result generalizing the well-known theorem usually used which says that the cost criterion is equal to the ratio of the expected cost on a renewal cycle over the expected cycle duration. Numerical experiments show that there exists a set of parameters (the critical threshold and the parameters of the maintenance scheduling function) which lead to a minimal cost.

MAINTENANCE POLICY FOR A CONTINUOUSLY MONITORED DETERIORATING SYSTEM

We consider a continuously monitored system that gradually and stochastically deteriorates. An alarm threshold is set on the system deterioration level for triggering a delayed preventive maintenance operation. A mathematical model is developed to find the value of the alarm threshold that minimizes the asymptotic unavailability. Approximations are derived to improve the numerical optimization.

Online maintenance policy for a deteriorating system with random change of mode

Most of maintenance policies proposed in the literature for gradually deteriorating systems, consider a stationary deterioration process. This paper is an attempt to take into account stochastically deteriorating systems which are subject to a sudden change in their degradation process. A technical device subject to gradual degradation is considered. It is assumed that the level of degradation can be resumed by a single scalar variable. An online maintenance decision rule is proposed, which makes it possible to take into account in real time the online information available on the operating mode of the system as well as its actual deterioration level. We show the efficiency of considering online decision rules for maintenance with respect to traditional maintenance policies based on a static alarm threshold. Numerical simulations are given, to assess and optimize the performance of the maintained system from its asymptotic unavailability point of view. It is compared to the results obtained with classical control-limit maintenance policies.

On the use of on-line detection for maintenance of gradually deteriorating systems

This paper deals with condition-based maintenance and non-stationary degradation process due to sudden changes. This is an attempt to propose an adaptive maintenance policy based on the on-line change detection procedure which can help to detect switches from a nominal mode to an accelerated mode in a non-informative context about the change mode time.

Asymptotic failure rate of a continuously monitored system

This paper deals with a perfectly continuously monitored system which gradually and stochastically deteriorates. The system is renewed by a delayed maintenance operation, which is triggered when the measured deterioration level exceeds an alarm threshold. A mathematical model is developed to study the asymptotic behavior of the reliability function. A procedure is proposed which allows us to identify the asymptotic failure rate of the maintained system. Numerical experiments illustrate the efficiency of the proposed procedure and emphasize the relevance of the asymptotic failure rate as an interesting indicator for the evaluation of the control-limit preventive replacement policy.

A condition-based maintenance policy for multi-component systems with Lévy copulas dependence

Abstract In this paper, we propose a new condition-based maintenance policy for multi-component systems taking into account stochastic and economic dependences. The stochastic dependence between components due to common environment is modelled by Levy copulas. Its influence on the maintenance optimization is investigated with different dependence degrees. On the issue of economic dependence providing opportunities to group maintenance activities, a new maintenance decision rule is proposed which permits maintenance grouping. In order to evaluate the performance of the proposed maintenance policy, we compare it to the classical maintenance policies.

Continuous time predictive maintenance scheduling for a deteriorating system

A predictive maintenance structure for a gradually deteriorating system (continuous time/continuous state) is proposed in this paper. 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 renewal processes theory. Numerical experiments show that the maintenance cost rate on an infinite horizon can be minimized by a joint optimization of the replacement threshold and the aperiodic inspection times and that the proposed maintenance structure performs better than classical preventive maintenance policies which can be treated as particular cases.

On the combined maintenance and routing optimization problem

This work focuses on the problem of planning and scheduling maintenance operations for a set of geographically distributed machines, subject to non-deterministic failures with a set of technicians that perform preventive maintenance and repair operations on the machines at the customer sites within a specific time window. This study presents a two-step iterative approach. In the first step, a maintenance model determines the optimal time until the next preventive maintenance operation, its frequency, and the time window for each customer, while minimizing the total expected maintenance costs. In the second step, a routing model assigns and schedules maintenance operations to each technician over the planning horizon within the workday. This two-step iterative process balances the maintenance cost, the failure probabilities, and waiting times at each customer. The novelty of this work lies in the integration of maintenance scheduling and a routing model that considers several machines.