Optimum Maintenance Policy of a Periodically Inspected System under Imperfect Repair

AbstratThis paper presents a method to find the optimal production, repair/replacement and preventive maintenance policies for a degraded manufacturing system. The system is subject to random machine failures and repairs. The status of the system is considered to degrade with repair activities. When a failure occurs, the machine is either repaired or replaced. A replacement action renews the machine while a repair action brings it to a degraded operational state for which the next repair time increases as the number of repairs increases. A preventive maintenance action is considered to improve the reliability of the machine and therefore the disruptions caused by the machine failures are reduced. The decision variables are the production rate, the preventive maintenance rate and the repair/replacement switching policy upon machine failure. The objective of the study is to find the decision variables that minimize an overall cost, including repair, replacement, preventive maintenance, inventory holding and backlog costs over an infinite planning horizon. The proposed model is based on a semiMarkov decision process and the stochastic dynamic programming method is used to obtain the optimality conditions. A numerical example is given to illustrate the proposed model. A sensitivity analysis is considered to confirm the structure of the control policy and to illustrate the usefulness on the proposed approach.

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“…As state by Badia and Berrade (2009), many engineering systems are subject to the so-called unrevealed failures.…”

Section: Industrial Contextmentioning

confidence: 99%

Simultaneous control of production, repair/replacement and preventive maintenance of deteriorating manufacturing systems

Nodem

Kenné

Gharbi

2011

International Journal of Production Economics

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“…As demonstrated in the literature, a monotone process such as an arithmetic-geometric approach is considered to be relevant, realistic and appropriate to the modelling of a deteriorating system maintenance problem, i.e., for modelling the survival time after the ( 1) th n  repair and the repair time after the th n failure. For more details, we refer the reader to the work of Leung (2006), Zhang et al (2001) and Badia and Berrade (2009), where some examples of arithmetic-geometric processes are provided.…”

Section: Mttrmentioning

confidence: 99%

“…As state by Badia and Berrade (2009), many engineering systems are subject to the so-called unrevealed failures. The unrevealed failures are constituted of those that are detected only by special tests, inspection or monitoring.…”

Section: Industrial Contextmentioning

confidence: 99%

“…Wang and Zhang (2006) studied a case of deteriorating system in which preventive repair times followed a stochastically increasing geometric process and determined optimal replacement policy of the machine. Badia and Berrade (2009) assumed that the mean times of repair constituted an increasing sequence from one failure to another and developed a maintenance policy of a system subject to periodical inspections, aimed at detecting the occurrence of failures. Although those authors took into account deterioration in repair times, none of them considered reduction of repair times following maintenance.…”

Section: Introductionmentioning

confidence: 99%

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Preventive maintenance and replacement policies for deteriorating production systems subject to imperfect repairs

Nodem

Gharbi

Kenné

2011

International Journal of Production Research

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This paper presents a special case of integration of the preventive maintenance into the repair/replacement policy of a failure-prone system. The machine of the considered system exhibits increasing failure intensity and increasing repair times. To reduce the failure rate and subsequent repair times following a failure, there is an incentive to perform preventive maintenance on the machine before failure. When a failure occurs, the machine can be repaired or replaced by a new one. Thus the machine's mode at any time can be classified as either operating, in repair, in replacement or in preventive maintenance. The decision variables of the system are the repair/replacement switching age or number of failures at the time of the machine's failure and the preventive maintenance rate. The problem of determining the repair/replacement and preventive maintenance policies is formulated as a semi-Markov decision process and numerical methods are given in order to compute optimal policies which minimize the average cost incurred by preventive maintenance, repair and replacement over an infinite planning horizon. As expected, the decisions to repair or to replace the machine upon a failure are modified by performing preventive maintenance. A numerical example is given and a sensitivity analysis is performed to illustrate the proposed approach and to show the impact of various parameters on the control policies thus obtained.

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“…Within the maintenance optimization literature, determining a periodic inspection interval to detect hidden failures has received much attention. The majority of this literature, however, assumes error-free inspections; see, e.g., [8]- [14]. More specifically, for example, Badía and Berrade [8] analyze the problem of optimally determining the inspection interval for a system subject to imperfect repairs after a failure detection, and perfect repairs after the th detected failure.…”

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confidence: 99%

Scheduling Preventive Maintenance as a Function of an Imperfect Inspection Interval

Maillart

Prokopyev

2015

IEEE Trans. Rel.

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This paper considers a system with periodic inspections and periodic preventive maintenance (PM) to detect and correct hidden failures that generate a penalty cost per unit time undetected. Imperfect periodic inspections (IPIs) occur at a chosen interval , and detect hidden failures with probability . Both reactive maintenance (RM), performed when a hidden failure is detected by an IPI, and PM, performed at a chosen time , renew the system. The objective is to determine the optimal frequency and quantity of imperfect inspections between PM such that the expected cost (which includes the costs of undetected failures, IPIs, PM, and RM) per unit time is minimized over an infinite horizon. We analytically establish conditions for the existence of a finite optimal for a given value of , and discuss the asymptotic behavior of the objective function for large and . These results are further exploited to describe convergence properties of a proposed approach for finding a globally optimal solution. Also, for the special case of a Weibull time-to-failure distribution, we derive conditions that guarantee the uniqueness of a locally optimal solution for a given value of . Index Terms-Imperfect inspections, maintenance optimization, preventive maintenance (PM). ACRONYMS AND ABBREVIATIONSPM preventive maintenance IPI imperfect periodic inspection RM reactive maintenance cdf cumulative distribution function pdf probability density function TTF time to failure NOTATION probability that an IPI detects an underlying failure cost per PM or RM cost per IPI instantaneous cost of a hidden failure cost rate of a hidden failure when the length of the undetected time period is ,

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Optimum Maintenance Policy of a Periodically Inspected System under Imperfect Repair

Cited by 23 publications

References 8 publications

Simultaneous control of production, repair/replacement and preventive maintenance of deteriorating manufacturing systems

Simultaneous control of production, repair/replacement and preventive maintenance of deteriorating manufacturing systems

Preventive maintenance and replacement policies for deteriorating production systems subject to imperfect repairs

Scheduling Preventive Maintenance as a Function of an Imperfect Inspection Interval

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