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

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 minimise 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.     

Optimum Maintenance and Availability of Series Systems Subject to Imperfect Repair

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Reliability analysis for a circular consecutive-2-out-of-n:F repairable system with priority in repair

A circular consecutive-2-out-of-n:F repairable system with one repairman is studied in this paper. When there are more than one failed component, priorities are assigned to the failed components. Both the working time and the repair time of each component is assumed to be exponentially distributed. Every component after repair is as good as new. By using the definition of generalized transition probability and the concept of critical component, we derive the state transition probability matrix of the system. Methodologies are then presented for the derivation of system reliability indexes such as availability, rate of occurrence of failure, mean time between failures, reliability, and mean time to first failure.     

Effect of maintenance policies on the just-in-time production system

Using simulation, experimental design, and regression analysis, mathematical models are developed here to describe the effect that maintenance policy, machine unreliability, processing time variability, ratio of preventive maintenance time to processing time, ratio of minimal repair time to preventive maintenance time, and production line size have on various measures of performance, namely total production line output and production line variability of the just-in-time production system. The analysis of the data shows that under different situations, different maintenance policies do not have the same effect on the production line performance. The following conclusions were obtained; when the number of production machines is low (five machines or less), and/or when the ratio of minimal repair time to preventive maintenance time is high, maintenance policy III leads to a higher performance than maintenance policy II. Otherwise maintenance policy II, which is more sensitive to the change of the ratio of minimal repair time to preventive maintenance time, leads to a higher performance. The results of the study can be utilized in choosing a maintenance policy as a function of the production process parameters. Once a policy is chosen, the practitioner can select the most important factors to control under that policy in order to minimize the machine idle time, maximize the production process reliability, improve productivity, and therefore increase the production line performance.     

Linear consecutive-k-out-of-n: F system reliability with common-mode forced outages

This paper presents a model of consecutive-k-out-of-n: F system subject to common-mode forced outages, whose interarrival times are independent and exponentially distributed. The objective is to analytically derive the mean operating time between failures for a non-repairable component system. The average system failure time and the system availability are also considered. Then, the model is extended to a system with repairable components and unrestricted repair, in which service times are exponentially distributed.     

Reliability of a k-out-of-n: G system with common-mode outages

This paper presents the model of a k-out-of-n: G system with common mode outages. The objective is to analytically derive the mean operating mode between failures for a non-repairable component system. The average system failure time and the system availability are also considered. Then, the model is extended to a system with repairable components and unrestricted repair, in which service times are exponentially distributed.     

Optimal restarting distribution after repair for a Markov deteriorating system

We consider a repairable system such that different completeness degrees are possible for the repair (or corrective maintenance) that go from a ‘minimal’ up to a ‘complete’ repair. Our question is: to what extent must the system be repaired in case of failure for the long-run availability to be optimal? The system evolves in time according to a Markov process as long as it is running, whereas the duration of repairs follows general distributions. After repair, the system starts again in the up-state i with probability d(i). We observe from numerical examples that the optimal restarting distribution d^opt (such that the long-run availability is optimal) is generally random and does not correspond to a new start in a fixed up-state. Sufficient conditions under which the optimal restarting distribution is non-random are given. Also, the optimal restarting distribution is provided for two classical structures in reliability.     

Performance analysis and optimization of a machine repair problem with warm spares and two heterogeneous repairmen

In this paper, we study a machine repair problem with warm spares and two heterogeneous repairmen from the view points of both queueing and reliability. In this system, the first repairman is always available for serving the failed units, while the second repairman leaves for a vacation of random length when the number of failed units is less than N. We obtain expressions for the steady-state probabilities of the system by solving the steady-state probability equations iteratively. Then, we obtain some performance measures for the system. We also obtain some performance measures of reliability for the system such as the steady-state availability, the steady-state failure frequency and the mean time between the system failures. Moreover, we present derivations of the mean time taken until the first failure of the system. A cost model is developed to determine the optimum value N while the system availability is maintained at a certain level. A sensitivity analysis is also performed.     

On the availability of a k-out-of-N system given limited spares and repair capacity under a condition based maintenance strategy

This paper considers a k-out-of-N system with identical, repairable components. Maintenance is initiated when the number of failed components exceeds some critical level. After a possible set-up time, all failed components are replaced by spares. A multi-server repair shop repairs the failed components. The system availability depends on the spare part stock level, the maintenance policy and the repair capacity. We present a mathematical model supporting the trade-off between these three parameters. We present both an exact and an approximate approach to analyse our model. In some numerical experiments, we provide insight on the impact of repair capacity, number of spares and preventive maintenance policy on the availability.     

基于修理设备可更换和修理延迟策略的两不同型部件冷贮备可修系统

考虑具有修理设备可失效可更换和修理延迟策略且由两个不同型部件组成冷贮备可修系统,利用Markov更新过程理论和全概率分解技术,得到了系统的稳态可用度、首次故障前平均时间、稳态故障频度以及系统等待修理的概率,并且通过引入修理设备的“广义忙期”,获得了修理设备的稳态不可用度和稳态更换频度．最后以数值实例分析了修理延迟时间和修理设备的失效率对系统可靠性指标的影响．在工程应用中特别感兴趣的是稳态可靠性数量指标,希望本文所得结果对系统的优化设计和更换维修提供有用的信息．     

A cost‐based selective maintenance decision‐making method for machining line

Machine line is a type of manufacturing system in which machines are connected in series or in parallel. It is significant to ensure the reliability as well as to reduce the total cost of maintenance and failure losses in the maintenance programs of such systems. Cost‐based selective maintenance decision‐making, which is the best method for a selected group of machines in machine line is presented under limited maintenance durations. Fault losses and maintenance costs of a single machine under different maintenance actions i.e. minimal repair, preventive maintenance and overhaul on the fault rate of the machine are calculated. An algorithm combining the heuristic rules and tabu search is proposed to solve the presented selective maintenance model. Finally, a case study on the maintenance decision‐making problem of a connecting rod machining line in the automobile engine workshop is presented to illustrate the applicability of the proposed method. The end result shows that the fault losses can be further reduced by the optimization of maintenance interval and maintenance duration. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimum policies for a system with general imperfect maintenance

This study considers periodic preventive maintenance policies, which maximizes the availability of a repairable system with major repair at failure. Three types of preventive maintenance are performed, namely: imperfect preventive maintenance (IPM), perfect preventive maintenance (PPM) and failed preventive maintenance (FPM). The probability that preventive maintenance is perfect depends on the number of imperfect maintenances conducted since the previous renewal cycle, and the probability that preventive maintenance remains imperfect is not increasing. The optimum preventive maintenance time that maximizes availability is derived. Various special cases are considered. A numerical example is given.     

Impact of the use-based maintenance policy on the performance of cellular manufacturing systems

In this paper, a multi-objective integer programming approach is developed to investigate the impact of the use-based preventive maintenance (UPM) policy on the performance of the cellular manufacturing system (CMS). Under the UPM policy a maintenance schedule is established which provides for the performance of preventive maintenance (PM) only after a predetermined number of operating hours of machine use. This research indicates how PM and failure repair (FR) actions affect the effective availability of the machines and accordingly the machine and inter/intra-cell material handling costs under the UPM policy. The objective is to minimise the machine cost, inter- and intra-cell material handling and PM/FR costs. The proposed model is solved by an interactive fuzzy programming (IFP) approach to determine the best compromise solution from the decision maker point of view. IFP assumes that each objective function has a fuzzy goal and focuses on minimising the worst upper bound to obtain an efficient solution which is close to the best lower bound of each objective function. Compromise solutions are prioritised by two efficiency criteria, i.e. grouping efficiency and system availability. The performance of the proposed model is verified by a comprehensive numerical example.     

Production Rate of Transfer Lines Without Buffer Storage

We consider transfer lines without buffer storage in between the machines and with synchronous transfer. The processing time of each machine is a constant but machines are unreliable. Our analysis is based on the overall completion time of the transfer line, which is the time between successive transfers of parts within the line. Two techniques are presented. The first one provides lower and upper bounds on the production rate. These bounds can be made as tight as desired. The second technique provides an approximation of the production rate. It is based on the approximation of some distributions by simpler distributions having the same mean and coefficient of variation. We first consider the case of transfer lines with identical processing times and exponential times to failure and times to repair. Extensions to different processing times and general repair times are also discussed.     

The robustness of markov reliability models

Markov models are an established part of current systems reliability and availability analysis. They are extensively used in various applications, including, in particular, electrical power supply systems. One of their advantages is that they considerably simplify availability evaluation so that the availability of very large and complex systems can be computed. It is generally assumed, with some justification, that the results obtained from such Markov reliability models are relatively robust. It has, however, been known for some time, that practical time to failure distributions are frequently non-exponential, particular attention being given in much reliability work to the Weibull family. Morover, recently additional doubt has been case on the validity of the Markov approach, both because of the work of Professor Kline and others on the non-exponentiality of practical repair time distribution, and because of the advantages to be obtained in terms of modelling visibility of the alternative simulation approach. In this paper we employ results on the ability of the k-out-of-n systems to span the coherent set to investigate the robustness of Markov reliability models based upon a simulation investigation of coherent systems of up to 10 identical components. We treat the case where adequate repair facilities are available for all components. The effects upon the conventional transient and steady-state measures of Weibull departures from exponentiality are considered. In general, the Markov models are found to be relatively robust, with alterations to failure distributions being more important than those to repair distributions, and decreasing hazard rates more critical than increasing hazard rates. Of the measures studied, the mean time to failure is most sensitive to variations in distributional shape.     

Optimal preventive maintenance strategy using two repair crews having different efficiencies: a quasi renewal process based modelling approach

This paper considers randomly failing, single-unit equipment subject to a periodic preventive maintenance (PM) policy. In case of failure between successive perfect PM actions (renewals), imperfect repairs are performed following a decreasing quasi-renewal process. One of two different maintenance crews can perform the repairs. One team is more experienced, and consequently more efficient than the other, but more costly. A mathematical model is developed in order to determine the PM period, T, and the kth repair, during a PM period, after which the repair team should be changed, minimising the average total cost per time unit over an infinite time span. It is also proved that an optimal solution in terms of the PM period always exists for any given system lifetime distribution and any set of maintenance costs. Numerical examples are presented and the obtained results are discussed.     

On the optimal scheduling of periodic tests and maintenance for reliable redundant components

Periodically, some m of the n redundant components of a dependable system may have to be taken out of service for inspection, testing or preventive maintenance. The system is then constrained to operate with lower (n−m) redundancy and thus with less reliability during these periods. However, more frequent periodic inspections decrease the probability that a component fail undetected in the time interval between successive inspections. An optimal time schedule of periodic preventive operations arises from these two conflicting factors, balancing the loss of redundancy during inspections against the reliability benefits of more frequent inspections.Considering no other factor than this decreased redundancy at inspection time, this paper demonstrates the existence of an optimal interval between inspections, which maximizes the mean time between system failures. By suitable transformations and variable identifications, an analytic closed form expression of the optimum is obtained for the general (m, n) case. The optimum is shown to be unique within the ranges of parameter values valid in practice; its expression is easy to evaluate and shown to be useful to analyze and understand the influence of these parameters.Inspections are assumed to be perfect, i.e. they cause no component failure by themselves and leave no failure undetected. In this sense, the optimum determines a lowest bound for the system failure rate that can be achieved by a system of n-redundant components, m of which require for inspection or maintenance recurrent periods of unavailability of length t.The model and its general closed form solution are believed to be new [2] and [5]. Previous work [1], [4] and [10] had computed optimal values for an estimation of a time average of system unavailability, but by numerical procedures only and with different numerical approximations, other objectives and model assumptions (one component only inspected at a time), and taking into account failures caused by testing itself, repair and demands (see in particular [6], [7] and [9]).System properties and practical implications are derived from the closed form analytical expression. Possible extensions of the model are discussed. The model has been applied to the scheduling of the periodic tests of nuclear reactor protection systems.     

Joint optimisation of production rate and preventive maintenance in machining systems

This paper studies an integrated control strategy of production and maintenance for a machining system which produces a single type of product to meet the constant demand. Different from previous research, we assume in this study that during the production, the production rate not only influences the life of cutting tool, but also the reliability of the machine. Both the replacement of cutting tool and the preventive maintenance (PM) of machine are considered in this paper. The machine is preventively maintained at the Nth tool replacement or correctively repaired at the machine failure, whichever occurs first. PM and corrective repair may cause shortage which can be reduced by controlling inventory. There are two decision variables p and N, where p denotes the production rate and N denotes the number of cutting tool replacement before the PM is performed. An integrated model is developed to simultaneously determine the optimal production rate and PM policy that minimise the total expected cost per unit item produced. Finally, an illustrative example and sensitivity analysis are given to demonstrate the proposed model.     

Simultaneous determination of preventive maintenance and replacement policies in a queue-like production system with minimal repair

This paper addresses the joint effects of preventive maintenance and replacement policies on a queue-like production system with minimal repair at failures. We consider a policy which calls for a preventive maintenance operation whenever N parts have been processed. If a failure occurs and at least K preventive maintenance operations have been carried out, the system is replaced by a new one. Otherwise, a failure is handled by minimal repair. An analytical model is developed and the argument of renewal–reward theory is used to provide long-run expected profit per unit time for a given maintenance and replacement policy. Numerical examples are given to provide some managerial insights.