自保护相依多部件系统的预防维修建模及策略优化

自保护技术作为自愈技术的一种,能够使系统在环境或工况条件变化的干扰下以较高可靠性运行。本文构建了一个新的具有相依主要部件和辅助部件的系统可靠性模型,其中主要部件的退化速率与工作中的辅助部件的数量有关。此外,基于定期检测和预防维修策略,本文利用半再生过程技术求解了系统的长期运行平均成本,并以长期运行平均成本最小化为目标给出了系统的最优预防维修策略。最后,以镗刀系统为例,利用所提方法给出了预防更换阈值和检测周期的最优值,以期望为实际维修行为决策提供理论参考。     

Preventive maintenance for inspected systems with additive subexponential shock magnitudes

We examine the long-run average availability and cost rate of a maintained system which deteriorates according to a random-shock process. Shocks arrive according to a Poisson process. The system fails whenever the cumulative damage exceeds a given threshold. The system's failures are not self-announcing, hence, failures must be detected via inspections. The system is inspected at periodic or exponentially distributed intervals. Systems are replaced by preventive maintenance or after failure (corrective maintenance), whichever occurs first. When the distribution function of the shock magnitudes belongs to the class of subexponential distributions, we obtain simple approximations for the availability and the cost rate. Copyright © 2007 John Wiley & Sons, Ltd.     

A sequential condition‐based repair/replacement policy with non‐periodic inspections for a system subject to continuous wear

This paper studies a condition‐based maintenance policy for a repairable system subject to a continuous‐state gradual deterioration monitored by sequential non‐periodic inspections. The system can be maintained using different maintenance operations (partial repair, as good as new replacement) with different effects (on the system state), costs and durations. A parametric decision framework (multi‐threshold policy) is proposed to choose sequentially the best maintenance actions and to schedule the future inspections, using the on‐line monitoring information on the system deterioration level gained from the current inspection. Taking advantage of the semi‐regenerative (or Markov renewal) properties of the maintained system state, we construct a stochastic model of the time behaviour of the maintained system at steady state. This stochastic model allows to evaluate several performance criteria for the maintenance policy such as the long‐run system availability and the long‐run expected maintenance cost. Numerical experiments illustrate the behaviour of the proposed condition‐based maintenance policy. Copyright © 2003 John Wiley & Sons, Ltd.     

Modeling past-dependent partial repairs for condition-based maintenance of continuously deteriorating systems

We are interested in the stochastic modeling of a condition-based maintained system subject to continuous deterioration and maintenance actions such as inspection, partial repair and replacement. The partial repair is assumed dependent on the past in the sense that it cannot bring the system back into a deterioration state better than the one reached at the last repair. Such a past-dependency can affect (i) the selection of a type of maintenance actions, (ii) the maintenance duration, (iii) the deterioration level after a maintenance, and (iv) the restarting system deterioration behavior. In this paper, all these effects are jointly considered in an unifying condition-based maintenance model on the basis of restarting deterioration states randomly sampled from a probability distribution truncated by the deterioration levels just before a current repair and just after the last repair/replacement. Using results from the semi-regenerative theory, the long-run maintenance cost rate is analytically derived. Numerous sensitivity studies illustrate the impacts of past-dependent partial repairs on the economic performance of the considered condition-based maintained system.     

A condition-based order-replacement policy for a single-unit system

This paper presents a condition-based order-replacement policy for a single-unit system, aiming to optimize the condition-based maintenance and the spare order management jointly. The concerned system deteriorates stochastically and gradually, and is inspected periodically. Under the proposed policy, both the preventive replacement and the spare order are decided based on the observed deterioration level of the system. Therefore, the decision variables for this order-replacement problem include the inspection interval, the ordering threshold, and the preventive replacement threshold. The analytical modeling of the condition-based order-replacement policy is presented in detail in this paper. The policy performance is evaluated in terms of the long-run average cost per unit time, the mean availability, and the rate of preventive replacement, for which the mathematical models are also derived. Numerical examples illustrate the performance of the condition-based order-replacement policy, especially the influences of the lead time of the spare order over the different performance criteria.     

Coordinated maintenance in a multi-component system with compound Poisson deterioration

This paper proposes a coordinated maintenance model in a multi-component system with compound Poisson deterioration. The main contribution is a policy-iteration approach for Semi-Markov processes that optimizes the threshold at which the component is eligible for preventive maintenance if another component requires corrective maintenance. The methodology is novel as we develop explicit expressions for the policy evaluation and prove these expressions to satisfy the set of linear equations which characterize traditional policy evaluation. By doing so, long-run average cost savings are achieved, since setup costs can be shared.     

Optimal maintenance of two stochastically deteriorating machines with an intermediate buffer

We consider a manufacturing system in which an input generating installation transfers a raw material to a subsequent production unit. Both machines deteriorate stochastically with usage and may fail. For each machine the deteriorating process is described by some known transition probabilities between different degrees of deterioration. A buffer has been built between the two machines in order to cope with unexpected failures of the installation. A discrete-time Markov decision model is formulated for the optimal preventive maintenance of both machines. The maintenance times are geometrically distributed and the cost structure includes operating costs, storage costs, maintenance costs and costs due to the lost production. It is proved that for fixed buffer content and for fixed deterioration degree of one machine, the average-cost optimal policy initiates a preventive maintenance of the other machine if and only if its degree of deterioration exceeds some critical level. We study, by means of numerical results, the effect of the variation of some parameters on the optimal policy and on the minimum average cost. For the case in which the maintenance times follow continuous distributions, an approximate discrete-time Markov decision model is proposed.     

考虑非周期检测的视情维修与备件订购联合策略优化

针对单部件系统/关键部件提出视情维修与备件订购联合策略,其中系统退化服从两阶段延迟时间过程且采用非周期检测策略,退化初期以检测间隔T₁检查系统状态,而在第一次识别缺陷状态时,缩短检测周期为T₂、订购备件且进行不完美维修;若系统在随后的退化中被识别处于缺陷状态,执行不完美维修直至超过阈值次数N_max并采取预防性更换,但若在检测周期内发生故障则进行更换。根据系统状态和备件状态分析各种可能更新事件及相应的联合决策,利用更新报酬理论构建最小化单位时间内期望成本的目标函数,优化T₁,T₂, N_max。与对比模型策略相比,算例结果表明所提出的联合策略能有效降低单位时间内的期望成本。     

Stationary availability of a semi‐Markov system with random maintenance

We consider a reparable system with a finite state space, evolving in time according to a semi‐Markov process. The system is stopped for it to be preventively maintained at random times for a random duration. Our aim is to find the preventive maintenance policy that optimizes the stationary availability, whenever it exists. The computation of the stationary availability is based on the fact that the above maintained system evolves according to a semi‐regenerative process. As for the optimization, we observe on numerical examples that it is possible to limit the study to the maintenance actions that begin at deterministic times. We demonstrate this result in a particular case and we study the deterministic maintenance policies in that case. In particular, we show that, if the initial system has an increasing failure rate, the maintenance actions improve the stationary availability if and only if they are not too long on the average, compared to the repairs ( a bound for the mean duration of the maintenance actions is provided). On the contrary, if the initial system has a decreasing failure rate, the maintenance policy lowers the stationary availability. A few other cases are studied. Copyright © 2000 John Wiley & Sons, Ltd.     

Hybrid block replacement and inspection policies for a multi-component system with heterogeneous component lives

Novel replacement policies that are hybrids of inspection maintenance and block replacement are developed for an n identical component series system in which the component parts used at successive replacements arise from a heterogeneous population. The heterogeneous nature of components implies a mixed distribution for time to failure. In these circumstances, a hybrid policy comprising two phases, an early inspection phase and a later wear-out replacement phase, may be appropriate. The policy has some similarity to burn-in maintenance. The simplest policy described is such a hybrid and comprises a block-type or periodic replacement policy with an embedded block or periodic inspection policy. We use a three state failure model, in which a component may be good, defective or failed, in order to consider inspection maintenance. Hybrid block replacement and age-based inspection, and opportunistic hybrid policies will also arise naturally in these circumstances and these are briefly investigated. For the simplest policy, an approximation is used to determine the long-run cost and the system reliability. The policies have the interesting property that the system reliability may be a maximum when the long-run cost is close to its minimum. The failure model implies that the effect of maintenance is heterogeneous. The policies themselves imply that maintenance is carried out more prudently to newer than to older systems. The maintenance of traction motor bearings on underground trains is used to illustrate the ideas in the paper.     

带有多重休假及预防维修的冲击模型二维更换策略

研究了修理工带有多重休假且定期检测的累积冲击模型.为了延长系统的运行时间,在检测时考虑了预防维修.将事后维修和预防维修结合起来运用于可修系统,且假定预防维修能够"修复如新",而事后维修为"修复非新".以系统的检测周期和故障次数为二维决策变量,选取系统经长期运行单位时间内期望费用为目标函数.并通过数值分析,求出了最优策略.     

The availability model and parameters estimation method for the delay time model with imperfect maintenance at inspection

The delay time model (DTM) is widely used to model the two-stage failure process and is helpful for developing cost-effective inspection/maintenance plans. Imperfect maintenance is common in practice, but seldom considered in DTM. An improved DTM with imperfect maintenance at inspection has been developed based on the assumption of imperfect inspection maintenance and perfect failure maintenance. The model of the long-run availability for the improved DTM is established. Parameters estimation method and the test for goodness of fit method are given. Numerical simulations are performed to study the influence of imperfect maintenance on the long-run availability and to validate the credibility of the parameters estimation method. The results show that imperfect maintenance will decrease the long-run availability. The existence of the optimal inspection interval regarding the maximum long-run availability is tightly related to the improvement factor, which denotes the maintenance effect. The parameters estimation method proves credible. The maximum likelihood estimations of the reliability parameters can be easily achieved by the Genetic Algorithms (GAs) searching tool.     

Optimal maintenance of a production-inventory system with idle periods

In this paper we consider a production-inventory system in which an input generating installation supplies a buffer with a raw material and a production unit pulls the raw material from the buffer with constant rate. The installation deteriorates in time and the problem of its optimal preventive maintenance is considered. It is assumed that the installation after the completion of its maintenance remains idle until the buffer is evacuated. Under a suitable cost structure it is shown that the average-cost optimal policy for fixed buffer content is of control-limit type, i.e. it prescribes a preventive maintenance of the installation if and only if its degree of deterioration is greater than or equal to a critical level. Using the usual regenerative argument, the average cost of a control-limit policy is computed exactly and then, the optimal control-limit policy is determined. Furthermore, the stationary probabilities of the system under the optimal policy are computed.     

A novel replacement policy for a linear deteriorating system using stochastic process with dependent components

In this study, a mechanical system with linear deterioration and preventive maintenance is considered. The state of the system over time is represented by a semicontinuous stochastic process with dependent components. The system cycles through on and off periods during its lifetime. The state of the system deteriorates linearly as a function of the usage time during on periods. When the system is offline, preventive maintenance is conducted, which improves the system state by a random amount. The system's on and off times and random improvement amounts are assumed to have general distributions. For such a system, our objective is to determine the expected value and variance for the number of preventive maintenance activities needed during the system lifetime and to propose a novel replacement policy for the system based on delay‐time modeling. Finally, the effectiveness of the obtained asymptotic results and the proposed replacement policy are tested through simulation.     

基于可用度的复杂结构装备检修时机决策模型

为最大限度地提高装备的可用度水平,检修工作十分必要,而检修时机的确定即成为一个重要的决策问题。对于复杂结构装备,组成部件的数量、寿命分布及对应的维修策略等都是可用度的影响因素。在采取预防性维修和修复性维修相结合策略的基础上,推导出了单装备任务周期内可用度关于检修时机的表达式,以此获得了装备群系统的检修时机决策模型,并充分考虑了部件工作年龄的影响。通过实例分析,验证了模型的合理性和实用性。     

基于可用度的复杂结构装备检修时机决策模型

为最大限度地提高装备的可用度水平,检修工作十分必要,而检修时机的确定即成为一个重要的决策问题。对于复杂结构装备,组成部件的数量、寿命分布及对应的维修策略等都是可用度的影响因素。在采取预防性维修和修复性维修相结合策略的基础上,推导出了单装备任务周期内可用度关于检修时机的表达式,以此获得了装备群系统的检修时机决策模型,并充分考虑了部件工作年龄的影响。通过实例分析,验证了模型的合理性和实用性。     

考虑不完美检测的两阶段点检与备件订购策略联合优化

针对设备维修与备件管理相互影响与制约的问题, 在基于延迟时间理论的基础上, 提出了两阶段点检与备件订购策略联合优化。点检是不完美的, 当点检识别设备的缺陷状态时, 进行预防更新; 设备故障时, 进行故障更新。结合设备更新时备件的状态, 采用更新报酬理论建立了以第一阶段点检时间、第二阶段点检周期和备件订购时间为决策变量, 以最小化单位时间期望成本为目标的模型。最后, 通过人工蜂群算法对模型求解, 并在数值分析中将两阶段点检策略与定期点检策略进行比较, 结果表明:两阶段点检策略始终优于定期点检策略, 验证了所建模型的有效性。     

A preventive maintenance policy for a continuously monitored system with correlated wear indicators

A continuously monitored system is considered, that gradually and stochastically deteriorates according to a bivariate non-decreasing Lévy process. The system is considered as failed as soon as its bivariate deterioration level enters a failure zone, assumed to be an upper set. A preventive maintenance policy is proposed, which involves a delayed replacement, triggered by the reaching of some preventive zone for the system deterioration level. The preventive maintenance policy is assessed through a cost function on an infinite horizon time. The cost function is provided in full form, and tools are provided for its numerical computation. The influence of different parameters on the cost function is studied, both from a theoretical and/or numerical point of view.     

Optimally maintaining a Markovian deteriorating system with limited imperfect repairs

We consider the problem of optimally maintaining a periodically inspected system that deteriorates according to a discrete-time Markov process and has a limit on the number of repairs that can be performed before it must be replaced. After each inspection, a decision maker must decide whether to repair the system, replace it with a new one, or leave it operating until the next inspection, where each repair makes the system more susceptible to future deterioration. If the system is found to be failed at an inspection, then it must be either repaired or replaced with a new one at an additional penalty cost. The objective is to minimize the total expected discounted cost due to operation, inspection, maintenance, replacement and failure. We formulate an infinite-horizon Markov decision process model and derive key structural properties of the resulting optimal cost function that are sufficient to establish the existence of an optimal threshold-type policy with respect to the system’s deterioration level and cumulative number of repairs. We also explore the sensitivity of the optimal policy to inspection, repair and replacement costs. Numerical examples are presented to illustrate the structure and the sensitivity of the optimal policy.     

两部件冷备系统的可靠性分析及其最优更换策略

本文研究了两个不同部件、一个修理工组成的冷贮备可修系统,假定它们的寿命分布和维修分布均匀为指数分布,但故障后均不能修复如新时,我们利用几何过程和补充变量法求得了一些可靠性指标,并以故障次数为策略,以长期运行单位时间内的期望效益为目标函数,确定了最优的故障次数,便得目标函数达到最大值,从而保证了系统的可用度。