维修决策模型和方法的理论与应用研究
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摘要
维修对于各类工业生产设备、军事装备以及交通运输工具等系统的正常工作或安全运行具有重要作用。维修费用也是各类企业的主要支出之一。然而，一直以来多数企业认为维修是“必要但令人讨厌的工作”而不给予重视。不同于其他生产和管理问题，研究人员对维修问题的关注和研究也相对较少。因此，企业中盲目维修和维修过剩问题严重，据统计有三分之一的维修费用属于浪费。有鉴于此，维修管理问题被称为“企业管理领域最后一个未攻克的堡垒”。当前已有的维修管理理念(例如以可靠性为中心的维修和全员生产维护等)，其中的大多数维修决策都是基于专家或工程师的经验和定性判断，决策过程中缺少定量分析方法。从20世纪60年代开始发展的维修建模和优化技术(维修决策模型)作为运筹学和可靠性工程学的交叉领域，致力于综合衡量维修工作相关的支出和收益这两方面因素，给出最佳的维修时机。维修建模和优化技术侧重于对系统或设备的失效(或劣化过程)以及维修工作进行定量的描述和分析，从运筹学角度指导维修工作的进行。
早期关于维修建模和优化的研究主要针对定期计划维修工作展开。近年来随着传感技术和计算机技术的迅速发展，视情维修技术得到大力推广，视情维修决策问题受到广大研究人员的关注。本文重点研究了视情维修建模和优化问题，包括设备视情维修和备件定购决策联合优化问题以及视情机会维修决策问题；最后研究了如何为不同设备(或部件)选择不同维修方式，即维修方式选择问题。本文具体研究内容包括以下几个方面：
(1)针对一类单设备系统，提出了一种视情更换和视情定购策略，其中设备劣化建模为一类Gamma过程，并且周期性进行设备状态检查。为了计算该策略下系统的费用率、可靠性和可用度，建立了相关的数学解析模型。运用遗传算法对该定购更换策略进行优化，得到最优的设备状态检查周期、设备预防更换状态阈值和备件定购状态阈值。数值算例表明，费用率与可靠性和可用度之间不能同时达到最优，并且较大的备件定购交付时间提高了故障维修费用率，降低了系统可靠性和可用度。
(2)针对连续劣化的设备在不同的劣化水平下都可能失效的现象，基于根据设备实际劣化状态评定可靠性的思想，提出了状态可靠性理论。该理论在卡车发动机视情维修决策优化中的应用结果表明，状态可靠性适用于表征同类设备(或部件)的不同个体经历不同的劣化过程后的不同可靠性指标。
(3)针对一类多设备系统(设备相同且独立)，提出了两种视情更换和备件定购策略，其中设备劣化分别建模为连续Gamma过程和离散时间马尔可夫链，设备劣化水平可由周期检查确定，并且备件定购均采用(S，s)型策略(S是最大备件库存水平，s为再定购水平)。利用蒙特卡罗仿真方法估计系统的故障维修费用率，应用遗传算法或穷举法对包括状态检查周期、预防维修状态阈值以及最大备件库存水平和再定购水平等决策变量进行优化。基于实际的卡车发动机油液分析数据，给出了定购更换策略的应用实例，并进行了相关费用参数的灵敏度分析。结果表明，应用这两种维修策略对发动机进行视情维修决策优化，能够比原维修策略节省大约3％以上的费用(根据费用参数变化而变化)，并且可以有效降低较大的备件定购交付时间的不利影响。
(4)针对包含多个不同设备的劣化系统(如一个发电机组)，提出一种视情机会维修策略，其中设备的劣化过程建模为连续时间马尔可夫链。针对电力市场环境下发电机组中发电设备的视情维修决策优化问题，详细给出了该策略的蒙特卡罗仿真步骤。通过数值算例，解释了该视情机会维修策略在发电设备维修决策优化中的应用过程。
(5)提出应用模糊层次分析法来评价和选择维修方式，从而可以利用三角模糊数对不确定的判断进行更好的建模。针对传统模糊层次分析法的缺点，提出了一种新的权重确定方法，该方法能够基于模糊比较矩阵给出精确的权重，从而避免了模糊权重的排序问题。以火电厂锅炉某部件的维修方式选择为例，解释了该改进模糊层次分析法的应用过程。与标准层次分析法比较说明，该改进模糊层次分析法给出的维修方式选择结果合理可行。
最后是全文总结和展望。
Maintenance plays a key role in keeping availability and reliability levels of industrial equipment, weapons, and transportation facilities, etc. One of the main expenditure items for various manufacturing firms is maintenance cost. However, the importance of maintenance is often neglected, and maintenance is considered as a "necessary evil" by most plant managers. Being different from other production and management problems, researchers and practitioners pay little attention to maintenance. This may be one of the reasons that result in low maintenance efficiency in industry at present, and it is reported that one third of all maintenance costs is wasted as the result of unnecessary or improper maintenance activities. Some maintenance strategies including reliability centered maintenance and total productive maintenance are popular and highlighted by maintenance engineers at present. However, lacking quantitative methods and models, most of them are based on engineers' experience and qualitative analysis. As an interdisciplinary of reliability and operations, maintenance modeling and optimization (maintenance decision models) has been developed since 1960s, and it aims to derive optimal maintenance decisions based on quantitative analysis of revenue and expenditure associated with maintenance activities.
Early approaches of maintenance modeling and optimization are designed for performing time-based preventive maintenance. Recently, condition-based maintenance is becoming popular with the development of sensors and computers. This dissertation focuses mainly on condition-based maintenance modeling and optimization, in which three condition-based maintenance and spare provisioning policies and one condition-based opportunistic maintenance policy are proposed for one-unit or multi-unit deteriorating systems. On the other hand, the problem of selection of optimum maintenance strategies for different equipment/components are also addressed. The main contents of this dissertation are outlined as follows,
(1) A condition-based order-replacement policy is presented for a single-unit system, aiming to optimize the condition-based maintenance and the spare order management jointly. The deterioration of the unit is modeled using the theory of the gamma process, and it is inspected periodically. The analytical modeling of the condition-based order-replacement policy is presented in detail for evaluating cost rate, reliability and availability. The policy is optimized by genetic algorithms, deriving the optimal inspection interval, ordering threshold, and preventive replacement threshold. Numerical examples illustrate the relation between optimization criteria, and the influences of the lead time of the spare order over the different performance criteria.
(2) Considering the units that deteriorate continuously, it is found that 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. The theory of condition-based reliability is applied to maintenance optimization of haul truck motors, indicating that the condition-based reliability is able to characterize different reliability variations of different equipment with different deterioration histories.
(3) Two new policies, referred to as the condition-based replacement and spare provisioning policies, are proposed for deteriorating systems with a number of identical and independent units. They combines the condition-based replacement policy with periodical inspections and the (S, s) type inventory policy, where S is the maximum stock level and s is the reorder level. The deterioration level of each unit under the two policies are described by Gamma process and discrete-time Markov chain, respectively. The related simulation models are developed for the system operation under the proposed condition-based replacement and spare provisioning policies. Thus, via the simulation method, the decision variables of the policies can be jointly optimized for minimizing the cost rate. The case studies are given, showing the procedure of applying the proposed policies 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.
(4) A new condition-based and opportunistic maintenance policy is given for multi-unit systems (e. g. a generating unit). Under this maintenance policy, the deterioration processes of equipment are discrete and modeled using continuous-time Markov chains, and maintenance decisions are given based on deterioration states of equipment. The Monte Carlo simulation model of the maintenance policy is also given in detail. By a numerical example, the application of the proposed maintenance policy to the optimization of condition-based maintenance in a thermal power plant is illustrated.
(5) The problem of evaluating different maintenance strategies for different equipment/components is addressed. To deal with the uncertain judgment of decision makers, a fuzzy modification of the analytic hierarchy process (AHP) method is applied, where uncertain and imprecise judgments of decision makers are translated into fuzzy numbers. In order to avoid the fuzzy priority calculation and fuzzy ranking procedures in the traditional fuzzy AHP methods, a new fuzzy prioritization method is proposed. This fuzzy prioritization method can derive crisp priorities from a consistent or inconsistent fuzzy judgment matrix by solving an optimization problem with non-linear constraints. An example of selection of maintenance strategies in a power plant with the application of the proposed fuzzy AHP method is given.
The conclusions and future directions are given at the end of the dissertation.
早期关于维修建模和优化的研究主要针对定期计划维修工作展开。近年来随着传感技术和计算机技术的迅速发展，视情维修技术得到大力推广，视情维修决策问题受到广大研究人员的关注。本文重点研究了视情维修建模和优化问题，包括设备视情维修和备件定购决策联合优化问题以及视情机会维修决策问题；最后研究了如何为不同设备(或部件)选择不同维修方式，即维修方式选择问题。本文具体研究内容包括以下几个方面：
(1)针对一类单设备系统，提出了一种视情更换和视情定购策略，其中设备劣化建模为一类Gamma过程，并且周期性进行设备状态检查。为了计算该策略下系统的费用率、可靠性和可用度，建立了相关的数学解析模型。运用遗传算法对该定购更换策略进行优化，得到最优的设备状态检查周期、设备预防更换状态阈值和备件定购状态阈值。数值算例表明，费用率与可靠性和可用度之间不能同时达到最优，并且较大的备件定购交付时间提高了故障维修费用率，降低了系统可靠性和可用度。
(2)针对连续劣化的设备在不同的劣化水平下都可能失效的现象，基于根据设备实际劣化状态评定可靠性的思想，提出了状态可靠性理论。该理论在卡车发动机视情维修决策优化中的应用结果表明，状态可靠性适用于表征同类设备(或部件)的不同个体经历不同的劣化过程后的不同可靠性指标。
(3)针对一类多设备系统(设备相同且独立)，提出了两种视情更换和备件定购策略，其中设备劣化分别建模为连续Gamma过程和离散时间马尔可夫链，设备劣化水平可由周期检查确定，并且备件定购均采用(S，s)型策略(S是最大备件库存水平，s为再定购水平)。利用蒙特卡罗仿真方法估计系统的故障维修费用率，应用遗传算法或穷举法对包括状态检查周期、预防维修状态阈值以及最大备件库存水平和再定购水平等决策变量进行优化。基于实际的卡车发动机油液分析数据，给出了定购更换策略的应用实例，并进行了相关费用参数的灵敏度分析。结果表明，应用这两种维修策略对发动机进行视情维修决策优化，能够比原维修策略节省大约3％以上的费用(根据费用参数变化而变化)，并且可以有效降低较大的备件定购交付时间的不利影响。
(4)针对包含多个不同设备的劣化系统(如一个发电机组)，提出一种视情机会维修策略，其中设备的劣化过程建模为连续时间马尔可夫链。针对电力市场环境下发电机组中发电设备的视情维修决策优化问题，详细给出了该策略的蒙特卡罗仿真步骤。通过数值算例，解释了该视情机会维修策略在发电设备维修决策优化中的应用过程。
(5)提出应用模糊层次分析法来评价和选择维修方式，从而可以利用三角模糊数对不确定的判断进行更好的建模。针对传统模糊层次分析法的缺点，提出了一种新的权重确定方法，该方法能够基于模糊比较矩阵给出精确的权重，从而避免了模糊权重的排序问题。以火电厂锅炉某部件的维修方式选择为例，解释了该改进模糊层次分析法的应用过程。与标准层次分析法比较说明，该改进模糊层次分析法给出的维修方式选择结果合理可行。
最后是全文总结和展望。
Maintenance plays a key role in keeping availability and reliability levels of industrial equipment, weapons, and transportation facilities, etc. One of the main expenditure items for various manufacturing firms is maintenance cost. However, the importance of maintenance is often neglected, and maintenance is considered as a "necessary evil" by most plant managers. Being different from other production and management problems, researchers and practitioners pay little attention to maintenance. This may be one of the reasons that result in low maintenance efficiency in industry at present, and it is reported that one third of all maintenance costs is wasted as the result of unnecessary or improper maintenance activities. Some maintenance strategies including reliability centered maintenance and total productive maintenance are popular and highlighted by maintenance engineers at present. However, lacking quantitative methods and models, most of them are based on engineers' experience and qualitative analysis. As an interdisciplinary of reliability and operations, maintenance modeling and optimization (maintenance decision models) has been developed since 1960s, and it aims to derive optimal maintenance decisions based on quantitative analysis of revenue and expenditure associated with maintenance activities.
Early approaches of maintenance modeling and optimization are designed for performing time-based preventive maintenance. Recently, condition-based maintenance is becoming popular with the development of sensors and computers. This dissertation focuses mainly on condition-based maintenance modeling and optimization, in which three condition-based maintenance and spare provisioning policies and one condition-based opportunistic maintenance policy are proposed for one-unit or multi-unit deteriorating systems. On the other hand, the problem of selection of optimum maintenance strategies for different equipment/components are also addressed. The main contents of this dissertation are outlined as follows,
(1) A condition-based order-replacement policy is presented for a single-unit system, aiming to optimize the condition-based maintenance and the spare order management jointly. The deterioration of the unit is modeled using the theory of the gamma process, and it is inspected periodically. The analytical modeling of the condition-based order-replacement policy is presented in detail for evaluating cost rate, reliability and availability. The policy is optimized by genetic algorithms, deriving the optimal inspection interval, ordering threshold, and preventive replacement threshold. Numerical examples illustrate the relation between optimization criteria, and the influences of the lead time of the spare order over the different performance criteria.
(2) Considering the units that deteriorate continuously, it is found that 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. The theory of condition-based reliability is applied to maintenance optimization of haul truck motors, indicating that the condition-based reliability is able to characterize different reliability variations of different equipment with different deterioration histories.
(3) Two new policies, referred to as the condition-based replacement and spare provisioning policies, are proposed for deteriorating systems with a number of identical and independent units. They combines the condition-based replacement policy with periodical inspections and the (S, s) type inventory policy, where S is the maximum stock level and s is the reorder level. The deterioration level of each unit under the two policies are described by Gamma process and discrete-time Markov chain, respectively. The related simulation models are developed for the system operation under the proposed condition-based replacement and spare provisioning policies. Thus, via the simulation method, the decision variables of the policies can be jointly optimized for minimizing the cost rate. The case studies are given, showing the procedure of applying the proposed policies 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.
(4) A new condition-based and opportunistic maintenance policy is given for multi-unit systems (e. g. a generating unit). Under this maintenance policy, the deterioration processes of equipment are discrete and modeled using continuous-time Markov chains, and maintenance decisions are given based on deterioration states of equipment. The Monte Carlo simulation model of the maintenance policy is also given in detail. By a numerical example, the application of the proposed maintenance policy to the optimization of condition-based maintenance in a thermal power plant is illustrated.
(5) The problem of evaluating different maintenance strategies for different equipment/components is addressed. To deal with the uncertain judgment of decision makers, a fuzzy modification of the analytic hierarchy process (AHP) method is applied, where uncertain and imprecise judgments of decision makers are translated into fuzzy numbers. In order to avoid the fuzzy priority calculation and fuzzy ranking procedures in the traditional fuzzy AHP methods, a new fuzzy prioritization method is proposed. This fuzzy prioritization method can derive crisp priorities from a consistent or inconsistent fuzzy judgment matrix by solving an optimization problem with non-linear constraints. An example of selection of maintenance strategies in a power plant with the application of the proposed fuzzy AHP method is given.
The conclusions and future directions are given at the end of the dissertation.
引文
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