不确定失效阈值影响下考虑设备剩余寿命预测信息的最优替换策略

为了进一步提升设备维修决策的科学性,通过建立综合设备剩余寿命预测数据与不确定失效阈值的最优维修决策模型,实现了不可维修设备的最优替换策略。构建基于非线性Wiener过程的设备性能退化模型,并采用极大似然法估计退化模型参数;提出一种基于期望最大(Expectation Maximization, EM)算法的不确定失效阈值分布系数估计方法,通过引入虚拟失效阈值数据实现对失效阈值分布系数的同步迭代更新;基于首达时的概念推导出不确定失效阈值条件下设备剩余寿命的概率密度函数,并基于更新报酬理论建立维修决策模型,从而实现设备的最优维修决策。算例分析表明,设备的失效阈值会对维修决策结果产生重要影响,考虑设备失效阈值的不确定性既有助于提升剩余寿命预测的准确性,又可以有效降低设备的寿命周期费用。     

On parallel machine replacement problems with general replacement cost functions and stochastic deterioration

The parallel machine replacement problem consists of finding a minimum cost replacement policy for a finite population of economically interdependent machines. In this paper, we formulate a stochastic version of the problem and analyze the structure of optimal policies under general classes of replacement cost functions. We prove that for problems with arbitrary cost functions, there can be optimal policies where a machine is replaced only if all machines in worse states are replaced (Worse Cluster Replacement Rule). We then show that, for problems with replacement cost functions exhibiting nonincreasing marginal costs, there are optimal policies such that, in any stage, machines in the same state are either all kept or all replaced (No‐Splitting Rule). We also present an example that shows that economies of scale in replacement costs do not guarantee optimal policies that satisfy the No‐Splitting Rule. These results lead to the fundamental insight that replacement decisions are driven by marginal costs, and not by economies of scale as suggested in the literature. Finally, we describe how the optimal policy structure, i.e., the No‐Splitting and Worse Cluster Replacement Rules, can be used to reduce the computational effort required to obtain optimal replacement policies. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Monotone optimal preventive maintenance policies for stochastically failing equipment

This paper examines various models for maintenance of a machine operating subject to stochastic deterioration. Three alternative models are presented for the deterioration process. For each model, in addition to the replacement decision, the option exists of performing preventive maintenance. The effect of this maintenance is to “slow” the deterioration process. With an appropriate reward structure imposed on the processes, the models are formulated as continuous time Markov decision processes. the optimality criterion being the maximization of expected discounted reward earned over an infinite time horizon. For each model conditions are presented under which the optimal maintenance policy exhibits the following monotonic structure. First, there exists a control limit rule for replacement. That is, there exists a number i* such that if the state of machine deterioration exceeds i* the optimal policy replaces the machine by a new machine. Secondly, prior to replacement the optimal level of preventive maintenance is a nonincreasing function of the state of machine deterioration. The conditions which guarantee this result have a cost/benefit interpretation.     

A dynamic nonlinear constrained optimal replacement model

A stochastically constrained optimal replacement model for capital equipment is constructed. Each piece of capital equipment, or machine, is characterized by its age and “utility” or “readiness” class. The readiness of a machine at any age is a stochastic function of its initial utility class and its age. The total discounted replacement cost of several replacement streams, each commencing with an initial machine, is minimized with respect to the replacement age and initial utility class of each machine, subject to a readiness constraint stating the lower bound on the expected number of machines in each utility class at any time. A general solution procedure is outlined and a specific case is solved in detail.     

基于年龄更换策略的威布尔分布备件需求计算方法

备件需求量预测在装备保障工作中发挥着重要作用。预防性维修可以消除装备潜在的故障或避免装备发生故障后所导致的严重后果,从而使装备始终处于期望状态。预防性维修策略下备件需求量建模能够以可预见的可靠性数据为基础进行,其关键问题是最佳更换间隔时间的确定。针对威布尔分布装备备件,采用年龄更换策略,确定最佳更换间隔时间,并在此基础上导出威布尔型备件需求计算模型,为备件需求量的预测提供了一种简单有效的方法。     

Optimal burn‐in procedure for periodically inspected systems

Burn‐in is a widely used method to improve the quality of products or systems after they have been produced. In this paper, we study burn‐in procedure for a system that is maintained under periodic inspection and perfect repair policy. Assuming that the underlying lifetime distribution of a system has an initially decreasing and/or eventually increasing failure rate function, we derive upper and lower bounds for the optimal burn‐in time, which maximizes the system availability. Furthermore, adopting an age replacement policy, we derive upper and lower bounds for the optimal age parameter of the replacement policy for each fixed burn‐in time and a uniform upper bound for the optimal burn‐in time given the age replacement policy. These results can be used to reduce the numerical work for determining both optimal burn‐in time and optimal replacement policy. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

使用检查维修工作模型的建立

RCMA是制订装备预防性维修大纲的系统方法,可用度是制订军械装备预防性维修周期的主要决策目标,对RCMA七种工作类型之一的使用检查工作建立了以可用度为决策目标的一般模型,举例给出了模型输出结果的特征和敏感性,对几种特殊情况进行了讨论,给出的模型可用于此类问题的维修决策。     

复杂系统复合维修间隔期优化模型

采用组合策略对复杂系统辅以功能检测的定期更换维修工作进行综合优化.在分析复杂系统维修费用结构和组成的基础上,建立了其无限使用期条件下单位时间期望费用的数学模型,从而获得系统最佳的功能检测间隔期、定期更换周期内的检测次数和最优总费用.最后通过一个算例验证了该策略和模型的有效性.     

An optimum group maintenance policy

In this article we present an optimum maintenance policy for a group of machines subject to stochastic failures where the repair cost and production loss due to the breakdown of machines are minimized. A nomograph was developed for machines with exponential failure time distributions. The optimal schedule time for repair as well as the total repair cost per cycle can be obtained easily from the nomograph. Conditions for the existence of a unique solution for the optimum schedule and the bounds for the schedule are discussed.     

Maintaining systems with heterogeneous spare parts

We consider the problem of optimally maintaining a stochastically degrading, single‐unit system using heterogeneous spares of varying quality. The system's failures are unannounced; therefore, it is inspected periodically to determine its status (functioning or failed). The system continues in operation until it is either preventively or correctively maintained. The available maintenance options include perfect repair, which restores the system to an as‐good‐as‐new condition, and replacement with a randomly selected unit from the supply of heterogeneous spares. The objective is to minimize the total expected discounted maintenance costs over an infinite time horizon. We formulate the problem using a mixed observability Markov decision process (MOMDP) model in which the system's age is observable but its quality must be inferred. We show, under suitable conditions, the monotonicity of the optimal value function in the belief about the system quality and establish conditions under which finite preventive maintenance thresholds exist. A detailed computational study reveals that the optimal policy encourages exploration when the system's quality is uncertain; the policy is more exploitive when the quality is highly certain. The study also demonstrates that substantial cost savings are achieved by utilizing our MOMDP‐based method as compared to more naïve methods of accounting for heterogeneous spares.     

Planning horizon procedures for machine replacement models with several possible replacement alternatives

This paper develops a forward algorithm and planning horizon procedures for an important machine replacement model where it is assumed that the technological environment is improving over time and that the machine-in-use can be replaced by any of the several different kinds of machines available at that time. The set of replacement alternatives may include (i) new machines with different types of technologies such as labor- and capital- intensive, (ii) used machines, (iii) repairs and/or improvements which affect the performance characteristics of the existing machine, and so forth. The forward dynamic programming algorithm in the paper can be used to solve a finite horizon problem. The planning horizon results give a procedure to identify the forecast horizon T such that the optimal replacement decision for the first machine based on the forecast of machine technology until period T remains optimal for any problem with horizon longer than T and, for that matter, for the infinite horizon problem. A flow chart and a numerical example have been included to illustrate the algorithm.     

An optimum multiechelon repair policy and stockage model

Currently, sophisticated multiechelon models compute stockage quantities for spares and repair parts that will minimize total inventory investment while achieving a target level of weapon system operational availability. The maintenance policies to be followed are input to the stockage models. The Optimum Allocation of Test Equipment/Manpower Evaluated Against Logistics (OATMEAL) model will determine optimum maintenance as well as stockage policies for a weapon system. Specifically, it will determine at which echelon each maintenance function should be performed, including an option for component or module throwaway. Test equipment requirements to handle work load at each echelon are simultaneously optimized. Mixed-integer programming (MIP) combined with a Lagrangian approach are used to do the constrained cost minimization, that is, to minimize all costs dependent on maintenance and stockage policies while achieving a target weapons system operational availability. Real-life test cases are included.     

一种双参数批更换系统的优化问题

研究了一种在更换时间有限的情况下 ,基于交替更新过程的双参数批更换系统的优化问题 ,这一问题的目标是平均费用率的极小化。给出了一种特殊情况的讨论结果。     

依据供应标准获取装备维修器材需求分布的方法

依据当前装备维修器材供应标准和装备维修器材保障程度模型,建立了求解装备维修器材需求分布的几种典型模型,并给出了相应的求解方法和举例,所给模型与方法具有一般意义,有较大的推广价值,对实际工作中装备维修器材的评估及科学保障具有指导意义。     

基于维修器材离散随机需求最佳库存量确定研究

结合装备维修器材保障工作,就维修器材离散随机需求最佳库存量确定进行研究,对其建模进行系统分析,结合修理厂维修器材最佳库存量进行实例计算,以指导维修器材最佳库存量的确定.     

装备维修系统的组织模型研究

综述了组织模型的研究现状,用维修组织的存在环境、构成要素、维修目标、维修策略和存在时间建立了复杂装备维修系统的形式化模型,分析并研究了维修组织要素之间的交互、隶属与协作关系,定义了维修系统的元组织。该方法可描述动态复杂条件下的维修系统,有利于装备维修保障信息系统的计算机建模与实现。     

Optimal control of entry to an M/Ek/1 queue serving several classes of customers

The individual and social optimum control policies for entry to an M/M//1 queue serving several classes of customers have been shown to be control-limit policies. The technique of policy iteration provides the social optimum policy for such a queue in a straightforward manner. In this article, the problem of finding the optimal control policy for the M/E_k/1 system is solved, thereby expanding the potential applicability of the solutions developed. The Markovian nature of the queueing system is preserved by considering the service as having k sequential phases, each with independent, identically distributed, exponential service times, through which a customer must pass to be serviced. The optimal policy derived by policy iteration for such a system is likely to be difficult to use because it requires knowledge of the number of phases rather than customers in the system when an arrival occurs. To circumvent this difficulty, a heuristic is used to find a good usable (implementable) solution. In addition, a mixed-integer program is developed which yields the optimal implementable solution when solved.     

Optimal maintenance policy for stochastically failing equipment: A diffusion approximation

A system receives shocks at random points of time. Each shock causes a random amount of damage which accumulates over time. The system fails when the accumulated damage exceeds a fixed threshold. Upon failure the system is replaced by a new one. The damage process is controlled by means of a maintenance policy. There are M possible maintenance actions. Given that a maintenance action m is employed, then the cumulative damage decreases at rate r^m. Replacement costs and maintenance costs are considered. The objective is to determine an optimal maintenance policy under the following optimality criteria: (1) long-run average cost; (2) total expected discounted cost over an infinite horizon. For a diffusion approximation, we show that the optimal maintenance expenditure rate is monotonically increasing in the cumulative damage level.     

Optimal replacement of military aircraft: an economic approach

A nonlinear optimization model is developed in this paper to identify the optimal replacement strategy for military aircraft. In the model, the aircraft operating and maintenance (O&M) costs per available year are estimated as a function of age during the aircraft life cycle. After determining the optimal replacement policy, the model is applied to the CF Long-Range Patrol CP-140A Arcturus fleet. A sensitivity analysis is also carried out to assess the impact of some key model parameters on the result.     

A replacement schedule for multicomponent life-limited parts

In previous papers [1], [2] the authors developed a maintenance policy for a single life-limited part. Using an opportunistic replacement approach a scheme was devised which utilized early replacement of equipment to offset more costly future expenditures. This paper will extend the results to the multicomponent case. Examples are given illustrating the benefits of this new technique.