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.     

Availability optimisation for stochastic degrading systems under imperfect preventive maintenance

This paper deals with imperfect preventive maintenance (PM) optimisation problem. The system to be maintained is typically a production system assumed to be continuously monitored and subject to stochastic degradation. To assess such degradation, the proposed maintenance model takes into account both corrective maintenance (CM) and PM. The system undergoes PM whenever its reliability reaches an appropriate value, while CM is performed at system failure. After a given number of maintenance actions, the system is preventively replaced by a new one. Both CM as well as PM are considered imperfect, i.e. they bring the system to an operating state which lies between two extreme states, namely the as bad as old state and as good as new state. The imperfect effect of CM and PM is modelled on the basis of the hybrid hazard rate model. The objective of the proposed PM optimisation model consists on finding the optimal reliability threshold together with the optimal number of PM actions to maximise the average availability of the system. A mathematical model is then proposed. To solve this problem an algorithm is provided. A numerical example is presented to illustrate the proposed maintenance optimisation model.     

Optimal joint selective imperfect maintenance and multiple repairpersons assignment strategy for complex multicomponent systems

This paper addresses the joint selective maintenance and repairperson assignment problem (JSM–RAP) for complex multicomponent systems. The systems perform consecutive missions separated by scheduled finite duration breaks and are imperfectly maintained during the breaks. Current selective maintenance (SM) models usually assume that only one repair channel is available or that the repairperson assignment optimisation can be done at a subsequent stage. Using a generalised reliability function for k-out-of-n systems, we formulate the JSM–RAP for multicomponent systems more complex than the series-parallel systems commonly used in previous SM models. Two nonlinear formulations and their corresponding binary integer programming models are then proposed and optimally solved. Numerical experiments show the added value of the proposed approach and highlight the benefit of jointly carrying out the selection of the components to be maintained, the maintenance level to be performed and the assignment of the maintenance tasks to repairpersons. It is also shown that the flexibility provided by mixed skill cohorts of repairpersons over uniform cohorts can yield higher performance levels when the skillsets are significantly different.     

Optimum Maintenance and Availability of Series Systems Subject to Imperfect Repair

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On the performance quality of repairable systems

The quality of a system operation is characterized by decreases in time deterministic function or by a stochastic process with decreasing sample paths. Simple relations for the stationary characteristic of quality are derived in cases when the system is repairable after each failure. Methods of quality improvement are considered. The case of imperfect repair for a simplified setting is studied. Several examples are considered. Copyright © 2003 John Wiley & Sons, Ltd.     

Effects of maintenance policy on an imperfect production system under trade credit

The traditional production model development assumed that all products are perfect quality and did not consider maintenance, which is far from reality. In practice, the production process may shift randomly from an in-control state to an out-of-control state during a production run, i.e. process deterioration. This paper considers both preventive maintenance and corrective maintenance which are used to increase the system reliability. The objective of this paper is to determine the optimal production run time and maintenance frequency while minimising the total cost under process deterioration and trade credit. This paper develops a theorem and an algorithm to solve the problem described, provides numerical analysis to illustrate the proposed solution procedure, and discusses the impact of various system parameters. A real case of hi-tech manufacturer is used to verify the model. It predicts a 10.36% decrease in total cost if the preventive maintenance decision is considered.     

不完备生产与条件维护策略下的生产批量决策研究

构建了不完备生产与条件维护下的生产批量模型,采用威布尔分布的曲线分布宽度描述可靠性的退化性,考虑了曲线分布宽度为等比数列和等差数列2种模型,利用报酬更新理论求解了期望平均总成本的最小值。结果表明,第1种模型的期望平均总成本要高于设备不具有退化性的期望平均总成本,前者的条件维护的阈值、最优生产批量和维护次数都比后者的少;第2种模型的期望平均总成本总体要低于设备不具有退化性的期望平均总成本,前者的条件维护的阈值比后者的少,而前者的维护次数和最优生产批量都比后者的多。研究还发现,公比和公差是影响期望平均总成本的最重要因素,需求是影响条件维护的可靠性阈值的最重要因素。本文的相关启示可为管理者提供决策参考依据。     

A cost minimisation model for joint production and maintenance planning under quality constraints

In this paper, integrated planning of production, imperfect maintenance and process inspections in a multi-machine system is investigated. This system consists of parallel machines which deteriorate with time and they may shift from a primarily in-control state to a degraded state with a higher defective rate or to a failed state. Maintenance scheduling corresponds to a discrete time age-based imperfect maintenance with a large number of maintenance alternatives. Process inspections are considered to detect the current state of the system. Detecting a deteriorated condition initiates the quality check of the related sub-lots, rework of defective items and a process adjustment that brings the machine in its normal conditions. Production planning includes a capacitated lot-sizing problem with multiple products. We propose a joint approach that coordinates the decisions of the three functions, where the objective function minimises the total cost. Evaluation of costs and interacting factors is presented and two heuristic methods are proposed to solve the problem. The results of the joint model are compared to a non-integrated method and a sensitivity analysis is conducted.     

Renewal-type equations for a general repair process

We consider a component which undergoes instantaneous general repairs on failure. Suppose that V_i = ϕ(V_i−1 + Y_i), where V_i is the virtual age immediately after the ith failure, Y_i is the time between the (i − 1)th and ith failures, ϕ(·) is a specified repair functional, and V₀ = s. We derive integral equations for the repair density, and also for the joint density of repairs with respect to chronological age and virtual age on failure. In the asymptotic case, approximations are obtained for the mean and variance of virtual age on failure, virtual age after repair, and time between failures. Two policies are then considered. The first, an upgraded repair strategy employs minimal repairs until the component reaches a specified age, thereafter repairs restore the virtual age to that prescribed level. The second policy considered is the Kijima Type 2 model which is not amenable to the usual g-renewal analysis that is used in the Type 1 model. The repair density is obtained by numerical solution of the relevant integral equation. Finally, approximations for the asymptotic moments are found to be in close agreement with simulated results. © 1997 John Wiley & Sons, Ltd.     

Reliability‐based Optimal Maintenance Scheduling by Considering Maintenance Effect to Reduce Cost

A new reliability‐based optimal maintenance scheduling method is presented that considers the effect of maintenance in reducing costs. An ordering list of element maintenance effects with various maintenance‐interval types is constructed. By means of this ordering list, reliability‐based optimal maintenance scheduling for simple reliability structures and composite reliability systems is then carried out. The properties of the proposed method, such as the evaluation of maintenance cost reduction, the simplicity of the proposed method by sacrificing system availability within the allowance method, the operation decision based on the optimal maintenance schedule, etc., are discussed. With simulations, the effectiveness of the proposed method is verified. Copyright © 2005 John Wiley & Sons, Ltd.     

Reliability-centered predictive maintenance scheduling for a continuously monitored system subject to degradation

This paper tries to integrate sequential imperfect maintenance policy into condition-based predictive maintenance (CBPM). A reliability-centered predictive maintenance policy is proposed for a continuously monitored system subject to degradation due to the imperfect maintenance. It is assumed that the system hazard rate is a known function of the system condition and then can be derived directly through CBPM. A hybrid hazard rate recursion rule based on the concept of age reduction factor and hazard rate increase factor is built up to predict the evolution of the system reliability in different maintenance cycles. Whenever the system reliability reaches the threshold R, an imperfect preventive maintenance (PM) is performed on the system. The optimal reliability threshold R is determined by minimizing the cumulative maintenance cost per unit time in the residual life of the system which is based on simulation. Finally, a discussion is presented to show how the optimal results depend on the different cost parameters.     

考虑维修场所的动车组多部件双目标成组维修研究

为探究维修场所选择对动车组多部件维修策略制定的影响,综合考虑维修方式、维修场所类别和维修人员等因素,以减少维修成本和维修时间为目标,建立了考虑维修场所的动车组多部件双目标成组维修模型。首先,在两级非完美维修方式的基础上,引入维修场所对维修方式的约束,通过维修场所的选择进一步选择维修方式。然后,提出一种部件维修任务分配算法,实现了维修人员与部件维修任务的优化匹配,使得系统维修时间最短;同时,将该算法引入到遗传算法中,用于求解考虑维修场所和系统维修时间的成组维修模型。实例分析表明,所提出的维修策略在满足动车组部件可靠度要求的前提下,减少了系统的维修成本和维修时间。研究结果可为合理制定动车组维修策略提供理论参考。     

基于最小与缺陷维修的二维产品保证策略研究

通过对相关文献的研究,提出采用使用时间和使用程度二维变量把产品保证区域划分成三个子区域,对第二个子区域里发生的第一次故障采用缺陷维修策略,对在第一、第三个保证子区域里发生的故障和在第二个保证子区域内第一次故障后的所有故障都采用最小维修策略;通过建立该产品保证策略下产品保证成本模型并获得优化处理的结果,又与相关文献所提供数例处理结果比较后发现:当故障产品最小维修费用相对于更换维修费用较小时,本文提供的产品保证策略方案更优.     

Discrete Nonhomogeneous Poisson Process Software Reliability Growth Models Based on Test Coverage

To incorporate the effect of test coverage, we proposed two novel discrete nonhomogeneous Poisson process software reliability growth models in this article using failure data and test coverage, which are both regarding the number of executed test cases instead of execution time. Because one of the most important factors of the coverage‐based software reliability growth models is the test coverage function (TCF), we first discussed a discrete TCF based on beta function. Then we developed two discrete mean value functions (MVF) integrating test coverage and imperfect debugging. Finally, the proposed discrete TCF and MVFs are evaluated and validated on two actual software reliability data sets. The results of numerical illustration demonstrate that the proposed TCF and the MVFs provide better estimation and fitting under comparisons. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimal maintenance policies in incomplete repair models

We consider an incomplete repair model, that is, the impact of repair is not minimal as in the homogeneous Poisson process and not “as good as new” as in renewal processes but lies between these boundary cases. The repairs are assumed to impact the failure intensity following a virtual age process of the general form proposed by Kijima. In previous works field data from an industrial setting were used to fit several models. In most cases the estimated rate of occurrence of failures was that of an underlying exponential distribution of the time between failures. In this paper, it is shown that there exist maintenance schedules under which the failure behavior of the failure-repair process becomes a homogeneous Poisson process.