On the interaction between maintenance,spare part inventories and repair capacity for a k-out-of-N system with wear-out

In this paper we consider a k-out-of-N system with identical, repairable components under a condition-based maintenance policy. Maintenance consists of replacing all failed and/or aged components. Next, the replaced components have to be repaired. The system availability can be controlled by the maintenance policy, the spare part inventory level, the repair capacity and repair job priority setting. We present two approximate methods to analyse the relation between these control variables and the system availability. Comparison with simulation results shows that we can generate accurate approximations using one of these models, depending on the system size.     

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.     

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 replacement and spare provisioning policy for deteriorating systems with uncertain deterioration to failure

A new policy, referred to as the condition-based replacement and spare provisioning policy, is presented for deteriorating systems with a number of identical units. It combines the condition-based replacement policy with periodical inspections and the (S,s$S\text{,}s$) type inventory policy, noted as the (T,S,s,_Lp$T\text{,}S\text{,}s\text{,}{L}_{\text{p}}$) policy, where T is the inspection interval, S is the maximum stock level, s   is the reorder level, and _Lp$L_{\text{p}}$ is the preventive replacement threshold for the deterioration levels of units. The deterioration level of each unit in the system can be described by a scalar random variable, which is continuous and increasing monotonically. Furthermore, the deterioration level just when the unit failure occurs, termed deterioration to failure, is uncertain. Therefore, the condition-based reliability is proposed in order to characterize various and uncertain deterioration levels when unit failure occurs. A simulation model is developed for the system operation under the proposed condition-based replacement and spare provisioning policy. Thus, via the simulation method and the genetic algorithm, the decision variables T, S, s  , and _Lp$L_{\text{p}}$ can be jointly optimized for minimizing the cost rate. A case study is given, showing the procedure of applying the proposed policy and the condition-based reliability methodology to optimizing the maintenance scheme of haul truck motors at a mine site based on oil inspections, and proving beneficial for plant maintenance managers to reduce maintenance cost.     

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。     

Analysis of the reliability and the maintenance cost for finite life cycle systems subject to degradation and shocks

This paper deals with a deteriorating system subject to two different causes of failure: internal continuous degradation and sudden shocks. The degradation process is modelled using a gamma process. It is assumed that the system fails when the deterioration level reaches a critical threshold. Furthermore, sudden shocks arrive at the system at random times following a non-homogeneous Poisson process. When a sudden shock takes place, the system fails. To control the system reliability, a condition-based maintenance is applied. Under this maintenance policy, availability measures of the system are obtained. It is shown that these measures fulfil Markov renewal equations. A recursive method is developed to compute these measures. Furthermore, the maintenance cost of this system is analysed. Traditionally, the maintenance cost is analysed assuming an infinite time span. However, most systems have a finite life cycle and the application of the asymptotic approach is questionable. In this paper, the maintenance cost is analysed considering a finite life cycle. A recursive method, which combines numerical integration and Monte Carlo simulation, is developed to obtain the expected cost rate in the finite life cycle and its associated standard deviation.     

A preventive maintenance policy with sequential checking procedure for a Markov deteriorating system

We consider a repairable system subject to a continuous-time Markovian deterioration while running, that leads to failure. The deterioration degree is measured with a finite discrete scale; repairs follow general distributions; failures are instantaneously detected. This system is submitted to a preventive maintenance policy, with a sequential checking procedure: the up-states are divided into two parts, the “good” up-states and the “degraded” up-states. Instantaneous (and perfect) inspections are then performed on the running system: when it is found in a degraded up-state, it is stopped to be maintained (for a random duration that depends on the degradation degree of the system); when it is found in a good up-state, it is left as it is. The next inspection epoch is then chosen randomly and depends on the degradation degree of the system by time of inspection. We compute the long-run availability of the maintained system and give sufficient conditions for the preventive maintenance policy to improve the long-run availability. We study the optimization of the long-run availability with respect to the distributions of the inter-inspection intervals: we show that under specific assumptions (often checked), optimal distributions are non-random. Numerical examples are studied.     

基于视情维修的质保政策设计研究

随着产品同质化程度不断提升,完善的质保服务已成为厂商提升品牌形象、刺激用户购买需求和全面反馈市场信息的主要途径。本文以具有退化特性的耐用品为研究对象,建立了视情维修条件下性能退化的维纳过程模型,考虑产品价格、质保期长度和维修费用承担比例对产品需求的影响,以最大化厂商利润为目标,确定了最优的质保期长度和维修费用承担比例。结合算例,比较了无视情维修和提供视情维修两种情形下对应的厂商利润,并分析了产品退化速率、成本参数和产品价格对利润的影响。研究结果表明,在质保服务范围内提供合理的视情维修服务既可将产品可靠性维持在一个较高水平,又可显著提升厂商利润。     

An integrated model of statistical process control and condition-based maintenance for deteriorating systems

This paper proposes an integrated model of statistical process control and condition-based maintenance for a deteriorating system. We study a system that will not be as good as new after a preventive maintenance and can only survive a certain number of preventive maintenances. The system is modeled as a geometric process and monitored by an \(\bar{X}\) control chart. By analyzing the evolution of the system in different scenarios, we establish a mathematical model to minimize the expected cost during the expected cycle time that can be used to make an optimal replacement policy in applications. A computational scheme is presented and illustrated through a numerical example. A sensitivity analysis is performed to investigate the effect of statistical constraint, mean shift, and the parameters of the system.     

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.     

An application of DPCA to oil data for CBM modeling

In multivariate time series analysis, dynamic principal component analysis (DPCA) is an effective method for dimensionality reduction. DPCA is an extension of the original PCA method which can be applied to an autocorrelated dynamic process. In this paper, we apply DPCA to a set of real oil data and use the principal components as covariates in condition-based maintenance (CBM) modeling. The CBM model (Model 1) is then compared with the CBM model which uses raw oil data as the covariates (Model 2). It is shown that the average maintenance cost corresponding to the optimal policy for Model 1 is considerably lower than that for Model 2, and when the optimal policies are applied to the oil data histories, the policy for Model 1 correctly indicates almost twice as many impending system failures as the policy for Model 2.     

Optimal maintenance policy in a multistate deteriorating standby system

An optimal maintenance policy for a multistate deteriorating standby system is proposed in this study. Traditionally, a system could only presume two operational states: success or failure, and the maintenance policy is to determine the optimal number of standby components, subject to factors such as maintenance capability, cost of the standby items, etc., so as to minimize the operational cost. This study considers a more general production system in which progressive deterioration is incurred during the operating time, hence resulting in degrading performance. By modeling the system as a multistate deteriorating system, an optimal maintenance policy is obtained by determining the optimal number of standby components required in the system and the optimal state in which the replacement of deteriorating components shall be made.     

Condition-based maintenance with imperfect inspections for continuous degradation processes

A condition-based maintenance (CBM) strategy is now recognized as an efficient approach to perform maintenance at the best time before failures so as to save lifetime cycle cost. For continuous degradation processes, a significant source of variability lies in measurement errors caused by imperfect inspections, and this may lead to “false positive” or “false negative” observations, and consequently to inopportune maintenance decisions. To the best of our knowledge, researches on CBM optimization with imperfect inspections remain limited for continuous degradation processes, even though the subject is of practical interest for the implementation of a CBM policy. Imperfect inspections are indeed imperfect but still return interesting information on the system degradation level, and making them perfect can be expensive. Therefore, we analyze the economic performance of a maintenance policy with imperfect inspections, and compare it with the classical policy with perfect inspections to see which policy offers the best benefit in a given situation. Furthermore, a CBM policy with a two-stage inspection scheme is proposed to take benefit of mixing both perfect and imperfect inspections in the same maintenance policy. Through numerical experiments and a real case study, it is shown that the policy with imperfect inspections can be better than the classical one, and that the proposed policy with a two-stage inspection scheme always leads to the minimum long run maintenance cost rate.     

Optimal component replacement decisions using vibration monitoring and the proportional-hazards model

This paper describes a case study in which the Weibull proportional-hazards model is used to determine the optimal replacement policy for a critical item which is subject to vibration monitoring. Such an approach has been used to date in the context of monitoring through oil debris analysis, and this approach is extended in this paper to the vibration monitoring context. The Weibull proportional-hazards model is reviewed along with the software EXAKT used for optimization. In particular the case considers condition-based maintenance for circulating pumps in a coal wash plant that is part of the SASOL petrochemical company. The condition-based maintenance policy recommended in this study is based on histories collected over a period of 2 years, and is compared with current practice. The policy is validated using data that arose from subsequent operation of the plant.     

Availability Analysis of Repairable <Emphasis Type="Italic">N</Emphasis>-Server <Emphasis Type="Italic">n</Emphasis><Subscript><Emphasis Type="Italic">i</Emphasis></Subscript>-Replicated Systems

We develop an exact closed-form expression for the steady-state availability of a repairable, N-server system in which the ith server contains n _i identical, reconfigurable, breakdown-prone units. Our approach, which follows from the Markov chain balance equations and the recursive properties of Hessenberg matrix determinants, is simpler than previously proposed matrix geometric approaches, and can readily be adapted to the availability analysis of more complicated structures. We illustrate this by computing the steady-state availability of a mixed parallel-serial gracefully degrading replicated system.     

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.     

机会维修策略下的系统可用度分析

机会维修是针对多部件系统提出的一类新的维修策略,主要解决部件间存在经济相关性的问题.利用更新过程理论建立了机会维修策略下的系统模型,并给出了系统瞬态和稳态可用度的求解方法.通过分析比较可知,利用更新过程稳态下的某些特性,可以不必求解更新方程而比较简便地求解系统稳态可用度.     

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。     

Availability and maintenance of series systems subject to imperfect repair and correlated failure and repair

The series system is one of the most important and common systems in reliability theory and applications. This paper investigates availability, maintenance cost, and optimal maintenance policies of the series system with n constituting components under the general assumption that each component is subject to correlated failure and repair, imperfect repair, shut-off rule, and arbitrary distributions of times to failure and repair. Imperfect repair is modeled through the basic idea of the quasi renewal processes introduced by H. Wang, H. Pham, A quasi renewal process and its applications in imperfect maintenance, International Journal of Systems Science 27(10) (1996) 1055–1062; 28(12) (1997) 1329. System availability, mean time between system failures, mean time between system repairs, asymptotic fractional down time of the system, etc., are derived, and a numerical example is presented to compare with the existing models by R.E. Barlow, F. Proschan, Satistical Theory of Reliability of Life Testing, Holt, Renehart & Winston, NY, 1975. Then two classes of maintenance cost models are proposed and system maintenance cost rates are modeled. Finally, properties of system availability and maintenance cost rates are studied. Optimization models to optimize system availability and/or system maintenance costs are developed, and optimum system maintenance policies are discussed through a numerical example.