Antoine Grall

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.

A condition-based maintenance policy with non-periodic inspections for a two-unit series system

This paper considers a condition-based maintenance policy for a two-unit deteriorating system. Each unit is subject to gradual deterioration and is monitored by sequential non-periodic inspections. It can be maintained by good as new preventive or corrective replacements. Every inspection or replacement entails a set-up cost and a component-specific unit cost but if actions on the two components are combined, the set-up cost is charged only once. A parametric maintenance decision framework is proposed to coordinate inspection/replacement of the two components and minimize the long-run maintenance cost of the system. A stochastic model is developed on the basis of the semi-regenerative properties of the maintained system state and the associated cost model is used to assess and optimize the performance of the maintenance model. Numerical experiments emphasize the interest of a control of the operation groupings.

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.

A maintenance policy for two-unit parallel systems based on imperfect monitoring information☆

In this paper a maintenance policy is optimised for a two-unit system with a parallel structure and stochastic dependences. Monitoring problems are taken into account in the optimisation scheme: the failure time of each unit can be not detected with a given probability. Conditions on the system parameters (unit failure rates) and on the non-detection probabilities must be verified to make the optimisation scheme valid. These conditions are clearly identified. Numerical experiments allow to show the relevance of taking into account monitoring problems in the maintenance model.

Optimization of replacement times using imperfect monitoring information

We propose a state-based PM policy based on a stopping rule for an imperfectly monitored two-unit parallel system consisting of s-dependent units. The observed failure rate of the system is proposed as an efficient tool to integrate the imperfect monitoring information in the maintenance decision process : the possible nondetection of the failure of a unit and the monitoring quality are explicitly taken into account when optimizing the maintenance decisions. Using classical martingale results, a stochastic cost model is developed to assess the performance of the monitoring-maintenance policy for this system. Numerical experiments show that the PM policy based on the observed failure rate of the system is more robust to defective monitoring information and that it performs better than a policy which discards completely this imperfect information.

A methodology for probabilistic model-based prognosis

This paper deals with the prognosis of complex systems using stochastic model-based techniques. Prognosis consists in this case in computing the distribution of the Remaining Useful Life (RUL) of the system conditionally to available information. In so doing, three main challenges arise from the industrial context. First, the model should unify the two classical approaches to describing complex systems: the bottom-up and the top-down approaches. The former uses elementary interacting components whilst the latter models the system’s physical behavior by means of a set of differential equations. Second, the prognosis must integrate online information to provide a specific result for each system depending on their life events. Online information can take different forms (e.g. inspections, component faults, non detection or false alarm, noisy signal) which must all be considered. Third, the prognosis must supply ready, meaningful numerical results, the error of which must also be under control. This paper proposes a method addressing those challenges. The method is illustrated with two different examples: a simplified spring-mass system and a pneumatic valve for aeronautical application.

Assessment of a maintenance model for a multi-deteriorating mode system

Abstract This paper deals with maintenance policies for stochastically deteriorating systems which are subject to sudden changes in their degradation processes. The main aim is to assess the interest of using change mode monitoring information from a maintenance decision making point of view. Two condition-based maintenance policies are considered and compared, each of them adapted to a specific level of available information, with or without change mode monitoring. Numerical examples show that the time distribution of the change of deterioration rate and the difference between the two possible deterioration rates strongly influence the choice of the best decision rule structure.