Markov decision models for the optimal maintenance of a production unit with an upstream buffer

We consider a manufacturing system in which a buffer has been placed between the input generator and the production unit. The input generator supplies at a constant rate the buffer with the raw material, which is pulled by the production unit. The pull-rate is greater than the input rate when the buffer is not empty. The two rates become equal as soon as the buffer is evacuated. The production unit deteriorates stochastically over time and the problem of its optimal preventive maintenance is considered. Under a suitable cost structure it is proved that the optimal average-cost policy for fixed buffer size is of control-limit type, if the repair times are geometrically distributed. Efficient Markov decision process solution algorithms that operate on the class of control-limit policies are developed, when the repair times are geometrical or follow a continuous distribution. The optimality of a control-limit policy is also proved when the production unit after the end of a maintenance remains idle until the buffer is filled up. Furthermore, numerical results are given for the optimal policy if it is permissible to leave the production unit idle whenever it is in operative condition.     

加速冲击损伤退化系统剩余寿命预测及预测维修决策

随着检测传感技术的发展,诸如风力发电机叶片等可对其状态进行检测,并依据检测结果进行剩余寿命预测.但此类系统在运行中受环境冲击影响较大,如何对冲击影响下的系统剩余寿命进行预测,并结合预测结果进行经济可靠的维修决策是一个值得研究的问题.对此,针对状态可检测的连续退化系统,研究考虑加速冲击损伤特性下的系统剩余寿命预测及基于预测的维修决策.首先,考虑自然退化和与退化相关的冲击损伤,构建加速冲击损伤退化模型和剩余寿命预测模型;其次,制定基于周期检测的状态维修与预测维修相结合的混合维修策略,并推导不同维修活动的发生概率;然后,构建以长期平均费用率最小为目标,以检测间隔和故障率阈值为决策变量的决策模型,并给出了优化解法;最后,以风力发电机叶片为案例验证模型的适用性和有效性,对系统的参数进行灵敏度分析,并与未考虑加速冲击损伤和未考虑预测的维修决策结果进行对比分析.     

基于不同中修次数的设备维修费用模型

针对具有三级维修机构保障的复杂设备,在不同的中修次数下,以单位工作时间内的平均维修费用最低为目标,通过对设备使用和修理流程分析,给出了设备使用与修理状态转移图,建立了一个设备更新周期内维修间隔期与维修费用关系模型.并结合示例分析说明了模型的适用性与灵敏性,可为设备维修决策提供依据.     

Performance evaluation for manufacturing systems under control-limit maintenance policy

Maintenance decision-making in large manufacturing systems is complex as it requires the integration of various information. A control-limit policy is popular in practice, where maintenance is carried out when the degradation state of a machine reaches a threshold value. In this paper, by developing a framework based on discrete-time Markov chain models, we evaluate the system performance under the control-limit policy, in manufacturing systems that consist of multi-state machines and intermediate buffers. An exact analysis is performed for a two-machine-one-buffer system and an approximation method based on system decomposition is developed for multi-stage systems. Both steady-state and transient performance is analyzed. Numerical examples are presented to demonstrate the accuracy of the proposed method and the impact of different parameters (e.g., buffer capacity, uncertainty in the maintenance duration) on the system performance.     

Minor maintenance actions and their impact on diagnostic and prognostic CBM models

Minor maintenance actions can affect condition-monitoring measurements, which may in turn affect the accuracy of diagnostic and prognostic techniques used in condition-based maintenance (CBM). Outputs of a CBM model include the calculation of optimal maintenance decisions, conditional reliability, and the calculation of remaining useful life, among other measures. It is necessary to have a model for the manner in which the condition monitoring data changes over time to produce these output measures; many models have been developed to do so. It is also common to record minor maintenance actions carried out on critical assets, with lubricant changes being one of the most common, but it is unusual for models to consider the impact of such maintenance actions that affect the condition monitoring data. In this paper we discuss the impact of minor maintenance on CBM models. A dataset on a collection of gearboxes, consisting of reliability and oil analysis information, including data on oil changes and oil additions, is used to illustrate the benefit of modelling minor maintenance actions.     

An optimal replacement policy for repairable cold standby system with priority in use

In this article, a cold standby repairable system consisting of two nonidentical components and one repairman is studied. It is assumed that component 2 after a repair is “as good as new” while component 1 after a repair is not, but component 1 is given priority in use. Under these assumptions, by using the geometric process repair model, we consider a replacement policy N based on the number of failures of component 1 under which the system is replaced when the number of failures of component 1 reaches N. Our problem is to determine an optimal policy N* such that the long-run average cost per unit time (i.e. the average cost rate) of the system is minimized. The explicit expression of the average cost rate of the system is derived and the corresponding optimal replacement policy N* can be determined numerically. Finally, a special system with Weibull-distributed working time and repair time of component 1 is given to illustrate the theoretical results in this article.     

Preventive maintenance scheduling for repairable system with deterioration

Maintenance as an important part in manufacturing system can keep equipment in good condition. Many maintenance policies help to decrease the unexpected failures and reduce high operational cost such as conventional preventive maintenance. But these conventional preventive maintenance policies have the same time interval T that may easily neglect system’s reliability, because the system deteriorates with increased usage and age. Hence, this study has developed a reliability-centred sequential preventive maintenance model for monitored repairable deteriorating system. It is supposed that system’s reliability could be monitored continuously and perfectly, whenever it reaches the threshold R, the imperfect repair must be performed to restore the system. In this model, system’s failure rate function and operational cost are both considered by the effect of system’s corresponding condition, which helps to decide the optimal reliability threshold R and preventive maintenance cycle number. Finally, through case study, the simulation results show that the improved sequential preventive maintenance policy is more practical and efficient.     

Optimization analysis of an unreliable multi-server queue with a controllable repair policy

This article deals with an infinite-capacity multi-server queueing system, in which the servers are assumed unreliable and may fail at any time. To conserve energy while delivering reliable service, a controllable repair policy is introduced. With such a policy, the failed servers will be sent to the repair facility only when the number of failed machines in the system arrives at a preset threshold value. A quasi-birth-and-death process is used to model the complex system and the stability condition is examined. The rate matrix is calculated approximately and steady-state stationary distributions are obtained by a matrix-analytic approach. The closed-form expressions of important system characteristics are presented. A cost model is constructed to determine the optimal repair policy, the optimal value of service rate and the optimal value of repair rate. Three heuristic algorithms are employed to deal with the optimization problem. Some numerical results are provided to compare the efficiency of two methods.     

Condition based maintenance optimization considering multiple objectives

In condition based maintenance (CBM) optimization, the main optimization objectives include maximizing reliability and minimizing maintenance costs, which are often times conflicting to each other. In this work, we develop a physical programming based approach to deal with the multi-objective condition based maintenance optimization problem. Physical programming presents two major advantages: (1) it is an efficient approach to capture the decision makers’ preferences on the objectives by eliminating the iterative process of adjusting the weights of the objectives, and (2) it is easy to use in that decision makers just need to specify physically meaningful boundaries for the objectives. The maintenance cost and reliability objectives are calculated based on proportional hazards model and a control limit CBM replacement policy. With the proposed approach, the decision maker can systematically and efficiently make good tradeoff between the cost objective and reliability objective. An example is used to illustrate the proposed approach.     

集成状态监测和故障诊断的设备管理平台的建立

针对目前设备状态维修中故障诊断和维修管理相互脱节的问题，在状态维修思想的指导下，构建了实施状态维修的设备管理平台，给出了系统平台的集成架构。结合发电企业设备维修的实际，提出了状态维修实施的信息模型。运用IDEF方法对整个设备管理平台的总体功能进行了详细分析，建立了系统的功能模型。在构建系统模型的基础上，综合采用网络技术、计算机技术和数据库技术等开发出了集成状态监测和故障诊断的设备管理系统，为企业成功开展状态维修提供了有效的管理平台。     

武器装备基于状态的维修系统设计

为了减少武器装备的故障以及维修时间,提高武器装备的可用度和重要部件的使用寿命,采用基于状态的维修技术与方法已成为当前维修领域研究与应用的热点.从武器装备的维修需求与技术出发,分析了现行装备维修的主要方式及其优缺点,总结了当前基于状态的维修(CBM)研究与应用现状,在此基础上提出了武器装备基于案例的CBM系统框架,给出了CBM适用的条件,并对CBM系统的核心模块进行了分析,给出了CBM系统工作的流程.最后,结合某装备中一齿轮箱的状态检测信息,进行了基于声音的装备故障诊断与案例分析与决策.分析结果表明:基于案例的CBM系统简单实用,能够满足装备维修需求.     

A geometric process repair model with inspections and its optimisation

In this article, a deteriorating simple repairable system with inspections, is studied. We assume that the system failure can only be detected by inspections and the repair of the system is not as good as new. Further assume that the successive working times of the system form a decreasing geometric process whereas the consecutive repair times form an increasing geometric process. Under these assumptions, we present a bivariate mixed policy (T,?N), respectively, based on the time interval between two successive inspections and the failure-number of the system. Our aim is to determine an optimal mixed policy (T,?N)* such that the long-run average cost per unit time (i.e. the average cost rate) is minimised. The explicit expression of the average cost rate is derived, and the corresponding optimal mixed policy can be determined numerically. Finally, we provide a numerical example to illustrate our model, and carry through some discussions and sensitivity analysis.     

相依多模失效下冷贮备系统最优切换及视情维护决策

针对存在冲击影响的冷贮备系统,研究其最优切换及视情维护决策问题.首先,在系统结构和切换式运行和维护特性分析的基础上,制定基于周期切换和状态检测的切换式离线视情维护策略;其次,建立累积冲击过程影响下系统退化所致的软失效和极端冲击过程所致的硬失效竞争可靠性模型;再次,通过分析两类冲击过程影响下系统运行与备用设备交替使用、维修过程中的状态转移特性,重点推导各检测周期时刻系统状态概率分布的迭代计算模型;然后,以系统平均费用率最小为目标,建立解析决策模型,以求解系统的最优切换周期和维护阈值.最后,以矿井主通风系统为案例验证策略及模型的有效性,并分析模型对参数的灵敏度.结果表明,系统的最优维修策略随机冲击影响的不同而变化显著.     

A simulation model for the analysis of machine deterioration and repair

One particular methodology for machine replacement and repair analysis encompasses a Markov or semi-Markov model consisting of states reflecting various stages of machine deterioration. In this paper the “bathtub curve” of replacement analysis is used as the basis for modeling the time in each state of a state-dependent, control-limit replacement policy. A repair queue is also embedded in the model. Specifically, a Q-GERT network simulation is developed and demonstrated via a case example of the weaving operation of a textile company. Output statistics related to the state movement of machines, new machines acquired, and machine repair are presented and discussed.     

The Optimal Rejuvenation Schedule Driven by Maintenance Cost in Application Server

The unpredictable system crash in application server leads to huge maintenance cost. In order to reduce the maintenance cost and prevent the failure, the optimal rejuvenation schedule is put forward based on the degradation of application server. Further, the degradation process of application server is modeled and the long-term cost is analyzed by renewal process theory. Then the boundary condition of the optimal rejuvenation schedule is discussed. Finally, the numerical results show that the optimal rejuvenation schedule can further reduce the maintenance cost of application server.     

Robust production and maintenance planning in stochasticmanufacturing systems

In this paper the authors consider a preventive maintenance and production model of a flexible manufacturing system with machines that are subject to breakdown and repair. The preventive maintenance can be used to reduce the machine failure rates and improve the productivity of the system. The control variables are the rate of maintenance and the rate of production; the objective is to choose a control process that optimizes a robust cost of inventory/shortage, production, and maintenance. The value function is shown to be locally Lipschitz and to satisfy a Hamilton-Jacobi-Isaacs equation. A sufficient condition for optimal control is obtained. Finally, an algorithm is given for solving the optimal control problem numerically     

Optimal maintenance model for a multistate deteriorating system: a geometric process approach

A monotone process model is introduced for a deteriorating system with k+1 states (k working states and one failure state). We prove that the model is equivalent to a geometric process model for a two-state system, in the sense that both systems have the same long-run average cost per unit time and the same optimal maintenance policy. Finally, an optimal maintenance policy for the deteriorating system is determined analytically.     

A shock model with two-type failures and optimal replacement policy

In this paper, a shock model for a repairable system with two-type failures is studied. Assume that two kinds of shock in a sequence of random shocks will make the system failed, one based on the inter-arrival time between two consecutive shocks less than a given positive value δ and the other based on the shock magnitude of single shock more than a given positive value γ. Under this assumption, we obtain some reliability indices of the shock model such as the system reliability and the mean working time before system failure. Assume further that the system after repair is ‘as good as new’, but the consecutive repair times of the system form a stochastic increasing geometric process. On the basis of the above assumptions, we consider a replacement policy N based on the number of failure of the system. Our problem is to determine an optimal replacement policy N* such that the long-run average cost per unit time is minimised. The explicit expression of long-run average cost per unit time is derived, and the corresponding optimal replacement policy can be determined analytically or numerically. Finally, a numerical example is given.     

Optimal age-replacement time with minimal repair based on cumulative repair cost limit and random lead time

In this article, we consider an age-replacement model with minimal repair based on a cumulative repair cost limit and random lead time for replacement delivery. A cumulative repair cost limit policy uses information about a system's entire repair cost history to decide whether the system is repaired or replaced; a random lead time models delay in delivery of a replacement once it is ordered. A general cost model is developed for the average cost per unit time based on the stochastic behaviour of the assumed system, reflecting the costs of both storing a spare and of system downtime. The minimum-cost policy time is derived, its existence and uniqueness is shown, and structural properties are presented. Various special cases are included. Because the framework and analysis are general, the proposed model extends several existing results. Finally, a numerical example is provided for illustration.     

基于退化状态空间划分的风电机组视情维修决策

风场的运维成本约占其收入的三分之一之多,风电机组的最优维修问题一直是风电系统降低运维成本的主要途径.针对同一风场多台风力机组成的系统,制定基于状态检测的视情机会维修策略,提出基于退化状态空间划分的多设备系统状态维修决策建模方法,在此基础上建立维修成本最小的解析模型,以决策风力机最优的状态检测周期和维修阈值.实验结果表明,基于状态监测的风力机视情维修机会方案可以很好地节约系统运维成本.