多状态复杂系统可靠性建模及维修决策
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摘要
随着现代系统和设备日益朝着大型化、复杂化、精密化方向发展以及对系统的失效机理和潜在规律的逐渐深入的探究,人们发现系统及组成单元在寿命周期内的失效演化过程中往往呈现出多状态的特征,并且各个状态的失效规律和机理、工作性能和效率不尽相同。在这种情况下,若采用常规的二态可靠性理论将系统粗略地划分为“正常”和“失效”两个状态显然不符合实际情况,而且忽略系统本身所表现出的多状态特征是不能准确地描述系统和单元的复杂失效过程的,这就迫切需要开展多状态可靠性理论的研究,以解决现代工程中大型复杂装备和系统的可靠性问题。
近年来,随着工程需求的不断增加,多状态可靠性理论成为了学术界和工业界所共同关注的热点问题,并在众多领域得到了迅速发展,如：机械工程、计算机和网络系统、网格、通讯系统、能源系统、供给系统、城市基础设施、战略和防御等。本论文针对多状态复杂系统可靠性理论发展中亟待解决的难题和挑战,以解决复杂性和不确定性这两个核心问题为出发点,在多状态复杂系统可靠性建模与维修决策方面开展研究,其主要内容和创新性成果如下：
(1)提出了多状态复杂系统的选择性维修决策优化模型。在多状态复杂系统可靠性理论基础上开展了在有限维修资源约束下多状态复杂系统的选择性维修决策优化的研究。通过将二态元件的非完好维修模型引入到选择性维修决策模型中,并构造维修费用—维修效果的模型以反映非完好维修与其维修成本的函数映射关系,该方法可为选择性维修决策的制定提供更大的灵活度。研究结果表明,本论文所提出的选择性维修方案较以往的方法具有明显的优势,系统经维修后的任务完成概率显著提高。
(2)提出了多状态元件的非完好维修模型,建立了多状态复杂系统的“系统级”更换维修策略。在实际生产中,复杂系统维修计划的预测和制定往往是从“系统级角度”出发的。本论文提出了一种多状态元件非完好维修模型,用以描述维修措施对元件衰退规律的影响,弥补了目前非完好维修模型仅能适用于二状态元件的缺陷,并在该非完好维修模型基础之上提出了一种新的多状态系统“系统级角度”的更换维修策略,可保证系统在单位时间的平均效益最大。
(3)系统地研究了多状态复杂系统的“元件级”维修建模与更换策略。本论文以“元件级角度”的维修策略作为研究的出发点,系统地开展了在完好维修、非完好维修下的多状态复杂系统的元件更换维修决策及全寿命周期内的系统冗余优化等问题的研究。通过提出更具一般性的多状态元件的非完好维修模型,建立元件维修费用和非完好维修效果之间的映射关系,有效地实现了各元件维修费用的合理分配。研究结果显示,本论文提出的方法比传统的维修方案更有效。同时,本论文还提出系统冗余分配和元件更换策略的联合优化问题,通过集成系统的冗余设计优化和维修决策,实现了系统全寿命周期内的可靠性优化设计。
(4)提出了模糊多状态复杂系统可靠性建模理论以及模糊多状态元件的更换维修决策方法。本论文开展了模糊不确定性下的多状态复杂系统可靠性建模与性能评估理论的研究,提出了模糊马尔可夫模型和模糊马尔可夫报酬模型以计算在模糊不确定性存在情况下多状态元件的动态状态分布与累积性能,并且通过提出不同类型系统的模糊通用生成函数近似算法,有效地提高了计算模糊多状态系统的性能状态分布的速度。同时,本论文还提出了更为完备的模糊多状态系统可用度计算方法,克服了现有方法的不足。在上述模糊多状态可靠性理论基础之上,本论文进一步深入研究了模糊多状态元件的更换维修决策理论,通过构造模糊不确定性下的元件更换决策模型并利用现有的几种模糊决策方法,为模糊多状态元件的维修方案的选择和制定提供了理论指导。
(5)提出了多级层次型复杂系统的统计灵敏度分析方法,并能广泛应用于复杂系统可靠性分析和设计中,以辅助系统不确定分析和降低模型复杂度。统计灵敏度分析是研究系统输入变量的变化对系统输出量变化的影响程度的一种不确定性分析方法,它通过对系统的输入变量的重要度排序可有效地降低复杂系统不确定性下分析、可靠性建模和设计优化等问题的复杂度。本论文提出了共享变量下的层次型统计灵敏度分析方法,有效地克服了现有的层次型统计灵敏度分析法不能处理子模型存在共享输入变量的局限,使复杂系统的统计灵敏度分析法具有更普遍的适用性。由于该方法遵循了自上而下的基本分析方式,符合复杂产品或系统的典型设计过程,并能通过并行计算的方式大幅度降低复杂系统统计灵敏度分析的总时间。
As modern advanced engineering devices and systems designed towards larger size, more complex, and higher precision, as well as the understanding of system failure mechanism and physics developed continuously, it has been observed that multiple states occur during the deterioration process of engineering systems and components. The associated failure mechanism, performance rate, and efficiency vary across different states. Conventional reliability analysis methods are limited by their fundamental assumption that both systems and components can be characterized as one of only two possible states:working perfectly or completely failed. It is inappropriate to describe the complicated failure process using these two states while ignoring the multiple states that possibly exist in engineering systems. Therefore, there is an urgent need for developing reliability theories and reliability analysis methodologies to facilitate the reliability assessment and enhancement in sophisticated multi-state systems.
With an increasing demand in industry in recent years, multi-state reliability theory has become an emerging research topic in both industry and academia. It has been applied to a variety of industrial domains, including mechanical engineering, computer and network, grid systems, communication, energy, supply systems, municipal infrastructure, and defense strategy research, etc. The overall objective of this dissertation is to address key challenges and critical issues in multi-state reliability theory, with a special emphasis on two fundamental aspects:complexity and uncertainty. In particular, this dissertation is focused on the reliability modeling and maintenance decision making of multi-state complex systems. The primary research contributions and innovative outcomes are summarized as follows:
(1) Development of a selective maintenance optimization strategy for multi-state systems. With the consideration of the limitation of maintenance resources, a selective maintenance optimization methodology based upon the multi-state system reliability theory is proposed. To take into account the imperfect maintenance quality, an imperfect maintenance model for binary state components is incorporated into the maintenance decision model. In addition, a cost-maintenance quality functional relationship is developed to consider the age reduction factor as a function of allocated maintenance cost. Demonstrated by numerical studies and examples, the proposed methodology provides much more flexibility in assigning the maintenance cost and yields better results than the existing methods in literature.
(2) Development of an imperfect maintenance model for multi-state components and a "system perspective" replacement policy for multi-state systems. In practice, the maintenance planning of complex systems is usually carried out from the system-level perspective. The existing imperfect maintenance models are applicable only to binary state components. In this work, a novel imperfect maintenance model is proposed to quantify the impact of maintenance activities on the degradation trend of multi-state components. Based upon the proposed imperfect maintenance model, a new system replacement strategy is developed to achieve the maximum expected profit per unit time for the entire multi-state system.
(3) Systematic investigation of the component-level maintenance and replacement optimization strategies for multi-state systems. In this dissertation, the optimized component replacement strategy, and the lifecycle-based redundancy design optimization under perfect and imperfect maintenance are studied from the component-level perspective. Building upon a generalized imperfect maintenance model for multi-state components, a flexible and effective repair cost assignment among components is achieved by proposing a set of functional relationships between the assigned repair cost and the imperfect repair quality. Through the study, it has been demonstrated that the proposed method is more economically efficient than conventional methods. In addition, a joint optimization method for redundancy and component replacement strategy is put forth by considering the component maintenance planning in the design stage of multi-state systems. It enables the system reliability design optimization across the entire lifecycle.
(4) Development of fuzzy multi-state system reliability modeling methods and fuzzy multi-state component replacement strategy. The multi-state system reliability modeling and assessment methods are developed based on the fuzzy uncertainty theory. A fuzzy Markov model and a fuzzy Markov reward model are proposed to evaluate the dynamic state distribution and the cumulative performance of fuzzy multi-state components. By developing a set of composition rules for the fuzzy universal generation function of different types of systems, the system state distribution can be derived in a computationally efficient manner. In addition, a modified fuzzy multi-state systems availability assessment approach is developed to overcome the drawbacks of the existing methods in assessing the system availability. A replacement strategy for fuzzy multi-state components that are based on the proposed fuzzy multi-state system reliability theory is further investigated. By constructing the formulation of replacement decision and utilizing the existing fuzzy ranking methods, it provides a general framework and guideline of maintenance planning for fuzzy multi-state components.
(5) Development of a hierarchical statistical sensitivity analysis method to facilitate uncertainty analysis and reduce complexity in design and reliability assessment of complex multi-level hierarchical systems. Statistical sensitivity analysis is an effective tool to examine the impact of variation in model inputs on the variations in model outputs, and can relieve the computational burden and manage the complexity in complicated system design and reliability analysis under uncertainty. A hierarchical statistical sensitivity analysis method is developed to deal with the shared variable among submodels, which is not addressed in other existing statistical sensitivity analysis methods. The inherited advantages of the proposed method are that the top-down strategy used in the method matches better with a typical design process of complex systems and products. The global statistical sensitivity index is obtained by aggregating the local sensitivity indices of submodels across multi-level hierarchy. The associated computational time is significantly reduced using the concurrent computing fashion. Therefore, the proposed method has a broader range of applicability to complex engineering systems design than other existing sensitivity analysis methods.
近年来,随着工程需求的不断增加,多状态可靠性理论成为了学术界和工业界所共同关注的热点问题,并在众多领域得到了迅速发展,如：机械工程、计算机和网络系统、网格、通讯系统、能源系统、供给系统、城市基础设施、战略和防御等。本论文针对多状态复杂系统可靠性理论发展中亟待解决的难题和挑战,以解决复杂性和不确定性这两个核心问题为出发点,在多状态复杂系统可靠性建模与维修决策方面开展研究,其主要内容和创新性成果如下：
(1)提出了多状态复杂系统的选择性维修决策优化模型。在多状态复杂系统可靠性理论基础上开展了在有限维修资源约束下多状态复杂系统的选择性维修决策优化的研究。通过将二态元件的非完好维修模型引入到选择性维修决策模型中,并构造维修费用—维修效果的模型以反映非完好维修与其维修成本的函数映射关系,该方法可为选择性维修决策的制定提供更大的灵活度。研究结果表明,本论文所提出的选择性维修方案较以往的方法具有明显的优势,系统经维修后的任务完成概率显著提高。
(2)提出了多状态元件的非完好维修模型,建立了多状态复杂系统的“系统级”更换维修策略。在实际生产中,复杂系统维修计划的预测和制定往往是从“系统级角度”出发的。本论文提出了一种多状态元件非完好维修模型,用以描述维修措施对元件衰退规律的影响,弥补了目前非完好维修模型仅能适用于二状态元件的缺陷,并在该非完好维修模型基础之上提出了一种新的多状态系统“系统级角度”的更换维修策略,可保证系统在单位时间的平均效益最大。
(3)系统地研究了多状态复杂系统的“元件级”维修建模与更换策略。本论文以“元件级角度”的维修策略作为研究的出发点,系统地开展了在完好维修、非完好维修下的多状态复杂系统的元件更换维修决策及全寿命周期内的系统冗余优化等问题的研究。通过提出更具一般性的多状态元件的非完好维修模型,建立元件维修费用和非完好维修效果之间的映射关系,有效地实现了各元件维修费用的合理分配。研究结果显示,本论文提出的方法比传统的维修方案更有效。同时,本论文还提出系统冗余分配和元件更换策略的联合优化问题,通过集成系统的冗余设计优化和维修决策,实现了系统全寿命周期内的可靠性优化设计。
(4)提出了模糊多状态复杂系统可靠性建模理论以及模糊多状态元件的更换维修决策方法。本论文开展了模糊不确定性下的多状态复杂系统可靠性建模与性能评估理论的研究,提出了模糊马尔可夫模型和模糊马尔可夫报酬模型以计算在模糊不确定性存在情况下多状态元件的动态状态分布与累积性能,并且通过提出不同类型系统的模糊通用生成函数近似算法,有效地提高了计算模糊多状态系统的性能状态分布的速度。同时,本论文还提出了更为完备的模糊多状态系统可用度计算方法,克服了现有方法的不足。在上述模糊多状态可靠性理论基础之上,本论文进一步深入研究了模糊多状态元件的更换维修决策理论,通过构造模糊不确定性下的元件更换决策模型并利用现有的几种模糊决策方法,为模糊多状态元件的维修方案的选择和制定提供了理论指导。
(5)提出了多级层次型复杂系统的统计灵敏度分析方法,并能广泛应用于复杂系统可靠性分析和设计中,以辅助系统不确定分析和降低模型复杂度。统计灵敏度分析是研究系统输入变量的变化对系统输出量变化的影响程度的一种不确定性分析方法,它通过对系统的输入变量的重要度排序可有效地降低复杂系统不确定性下分析、可靠性建模和设计优化等问题的复杂度。本论文提出了共享变量下的层次型统计灵敏度分析方法,有效地克服了现有的层次型统计灵敏度分析法不能处理子模型存在共享输入变量的局限,使复杂系统的统计灵敏度分析法具有更普遍的适用性。由于该方法遵循了自上而下的基本分析方式,符合复杂产品或系统的典型设计过程,并能通过并行计算的方式大幅度降低复杂系统统计灵敏度分析的总时间。
As modern advanced engineering devices and systems designed towards larger size, more complex, and higher precision, as well as the understanding of system failure mechanism and physics developed continuously, it has been observed that multiple states occur during the deterioration process of engineering systems and components. The associated failure mechanism, performance rate, and efficiency vary across different states. Conventional reliability analysis methods are limited by their fundamental assumption that both systems and components can be characterized as one of only two possible states:working perfectly or completely failed. It is inappropriate to describe the complicated failure process using these two states while ignoring the multiple states that possibly exist in engineering systems. Therefore, there is an urgent need for developing reliability theories and reliability analysis methodologies to facilitate the reliability assessment and enhancement in sophisticated multi-state systems.
With an increasing demand in industry in recent years, multi-state reliability theory has become an emerging research topic in both industry and academia. It has been applied to a variety of industrial domains, including mechanical engineering, computer and network, grid systems, communication, energy, supply systems, municipal infrastructure, and defense strategy research, etc. The overall objective of this dissertation is to address key challenges and critical issues in multi-state reliability theory, with a special emphasis on two fundamental aspects:complexity and uncertainty. In particular, this dissertation is focused on the reliability modeling and maintenance decision making of multi-state complex systems. The primary research contributions and innovative outcomes are summarized as follows:
(1) Development of a selective maintenance optimization strategy for multi-state systems. With the consideration of the limitation of maintenance resources, a selective maintenance optimization methodology based upon the multi-state system reliability theory is proposed. To take into account the imperfect maintenance quality, an imperfect maintenance model for binary state components is incorporated into the maintenance decision model. In addition, a cost-maintenance quality functional relationship is developed to consider the age reduction factor as a function of allocated maintenance cost. Demonstrated by numerical studies and examples, the proposed methodology provides much more flexibility in assigning the maintenance cost and yields better results than the existing methods in literature.
(2) Development of an imperfect maintenance model for multi-state components and a "system perspective" replacement policy for multi-state systems. In practice, the maintenance planning of complex systems is usually carried out from the system-level perspective. The existing imperfect maintenance models are applicable only to binary state components. In this work, a novel imperfect maintenance model is proposed to quantify the impact of maintenance activities on the degradation trend of multi-state components. Based upon the proposed imperfect maintenance model, a new system replacement strategy is developed to achieve the maximum expected profit per unit time for the entire multi-state system.
(3) Systematic investigation of the component-level maintenance and replacement optimization strategies for multi-state systems. In this dissertation, the optimized component replacement strategy, and the lifecycle-based redundancy design optimization under perfect and imperfect maintenance are studied from the component-level perspective. Building upon a generalized imperfect maintenance model for multi-state components, a flexible and effective repair cost assignment among components is achieved by proposing a set of functional relationships between the assigned repair cost and the imperfect repair quality. Through the study, it has been demonstrated that the proposed method is more economically efficient than conventional methods. In addition, a joint optimization method for redundancy and component replacement strategy is put forth by considering the component maintenance planning in the design stage of multi-state systems. It enables the system reliability design optimization across the entire lifecycle.
(4) Development of fuzzy multi-state system reliability modeling methods and fuzzy multi-state component replacement strategy. The multi-state system reliability modeling and assessment methods are developed based on the fuzzy uncertainty theory. A fuzzy Markov model and a fuzzy Markov reward model are proposed to evaluate the dynamic state distribution and the cumulative performance of fuzzy multi-state components. By developing a set of composition rules for the fuzzy universal generation function of different types of systems, the system state distribution can be derived in a computationally efficient manner. In addition, a modified fuzzy multi-state systems availability assessment approach is developed to overcome the drawbacks of the existing methods in assessing the system availability. A replacement strategy for fuzzy multi-state components that are based on the proposed fuzzy multi-state system reliability theory is further investigated. By constructing the formulation of replacement decision and utilizing the existing fuzzy ranking methods, it provides a general framework and guideline of maintenance planning for fuzzy multi-state components.
(5) Development of a hierarchical statistical sensitivity analysis method to facilitate uncertainty analysis and reduce complexity in design and reliability assessment of complex multi-level hierarchical systems. Statistical sensitivity analysis is an effective tool to examine the impact of variation in model inputs on the variations in model outputs, and can relieve the computational burden and manage the complexity in complicated system design and reliability analysis under uncertainty. A hierarchical statistical sensitivity analysis method is developed to deal with the shared variable among submodels, which is not addressed in other existing statistical sensitivity analysis methods. The inherited advantages of the proposed method are that the top-down strategy used in the method matches better with a typical design process of complex systems and products. The global statistical sensitivity index is obtained by aggregating the local sensitivity indices of submodels across multi-level hierarchy. The associated computational time is significantly reduced using the concurrent computing fashion. Therefore, the proposed method has a broader range of applicability to complex engineering systems design than other existing sensitivity analysis methods.
引文
[1]B. Natvig, S. Sormo, A. T. Holen, et al. Multi-state reliability theory:a case study. Advances in Applied Probability,1986,18(4):921-932.
[2]A. Lisnianski, G. Levitin, H. Ben-Haim, et al. Power system structure optimization subject to reliability constraints. Electric Power Systems Research,1996,39(2):145-152.
[3]G. Levitin, A. Lisnianski, D. Elmakis. Structure optimization of power system with different redundant elements. Electric Power Systems Research,1997,43(1):19-27.
[4]G.. Levitin, A. Lisnianski. Structure optimization of power system with bridge topology. Electric Power Systems Research,1998,45(3):201-208.
[5]R. Billinton, W. Zhang. State extension for adequacy evaluation of composite power systems-application. IEEE Transactions on Power Systems,2002,15(1):427-432.
[6]M. J. Zuo, Z. G. Tian. Performance evaluation of generalized multi-state k-out-of-n systems. IEEE Transactions on Reliability,2006,55(2):319-327.
[7]A. Zeblah. Reliability maximization of power system using ant colony approach. International Journal of Electrical and Power Engineering,2008,2(3):192-201.
[8]Y. Ding, A. Lisnianski, P. Wang, et al. Dynamic reliability assessment for bilateral contract electricity providers in restructured power systems. Electric Power Systems Research,2009, 79(10):1424-1430.
[9]Y. Ding, P. Wang, A. Lisnianski. Optimal reserve management for restructured power generating systems. Reliability Engineering and System Safety,2006,91(7):792-799.
[10]H. A. Taboada, J. F. Espiritu, D. W. Coit. Design allocation of multi-state series-parallel systems for power systems planning:a multiple objective evolutionary approach. Journal of Risk and Reliability,2008,222(3):381-391.
[11]E. Zio, P. Baraldi, E. Patelli. Assessment of the availability of an offshore installation by Monte Carlo simulation. International Journal of Pressure Vessels and Piping,2006,83(4): 312-320.
[12]K. D. Rao, H. S. Kushwaha, A. K. Verma, et al. Simulation based reliability evaluation of AC power supply system of Indian Nuclear Power Plant. International Journal of Quality and Reliability Management,2007,24(6):628-642.
[13]R. Karki, P. Hu, R. Billinton. A simplified wind power generation model for reliability evaluation. IEEE Transactions on Energy Conversion,2006,21(2):533-540.
[14]R. Billinton, Y. Gao. Adequacy assessment of composite power generation and transmission systems with wind energy. International Journal of Reliability and Safety,2008,2(1-2): 79-98.
[15]D. Elmakias. New computational methods in power system reliability. London:Springer, 2008.
[16]A. Lisnianski, G. Levitin. Multi-state system reliability assessment, optimization, application. Singapore:World Scientific,2003.
[17]G. Levitin, L. Meizin. Structure optimization for continuous production systems with buffers under reliability constraints. International Journal of Production Economics,2001,70(1): 77-87.
[18]S. T. Bae, G. S. Cho, H. S. Hwang. Multi-state availability model for manufacturing system considering system cost. International Journal of Information Systems for Logistics and Management,2007,2(2):93-98.
[19]G. Levitin. Linear multi-state sliding-window systems. IEEE Transactions on Reliability, 2003,52(2):263-269.
[20]A. M. A. Youssel, A. Mohib, H. A. EMaraghy. Availability assessment of multi-state manufacturing systems using universal generating function. RP Annals-Manufacturing Technology,2006,55(1):445-448.
[21]P. D. Van, A. Barros, C. Berenguer. Importance measure on finite time horizon and application to Markovian multi-state production systems. Journal of Risk and Reliability, 2008,222(3):449-461.
[22]M. Nourelfath, M. Fitouhi, M. Machani. An integrated model for production and preventive maintenance planning in multi-state systems. IEEE Transactions on Reliability,2010,59(3): 496-506.
[23]高鹏,谢里阳.基于改进发生函数方法的多状态系统可靠性分析.航空学报,2010,31(5)：934-939.
[24]周金宇,谢里阳,王学敏.多状态系统共因失效分析及可靠性模型.机械工程学报,2005,41(6)：60-70.
[25]钱文学,尹晓伟,谢里阳.多状态机械系统可靠性的离散化建模方法.东北大学学报(自然科学版),2008,29(11)：1609-1632.
[26]周金宇,谢里阳.多状态系统共因失效机理与定量分析.机械工程学报,2008,44(10)：77-82.
[27]尹晓伟,钱文学,谢里阳.基于贝叶斯网络的多状态系统可靠性建模与评估.机械工程学报,2009,45(2)：206-212.
[28]S. V. Amari, L. Xing, A. Shrestha, et al. Performability analysis of multi-state computing systems using multivalued decision diagrams. IEEE Transactions on Computers,2010, 59(10):1419-1433.
[29]S. Patra, R. B. Misra. Reliability evaluation of flow networks considering multi-state modelling of network elements. Microelectronics and Reliability,1993,33(14):2161-2164.
[30]Y. K. Lin. System capacity for a two-commodity multi-state flow network with unreliable nodes and capacity weight. Computers and Operations Research,2007,34(10):3043-3054.
[31]W. C. Yeh. An evaluation of the multi-state node networks reliability using the traditional binary-state networks reliability algorithm. Reliability Engineering and System Safety,2003, 81(1):1-7.
[32]W. C. Yeh. A simple minimal path method for estimating the weighted multi-commodity multi-state unreliable networks reliability. Reliability Engineering and System Safety,2008, 93(1):125-136.
[33]W. C. Yeh, X. He. A new universal generating function method for estimating the novel multiresource multi-state information network reliability. IEEE Transactions on Reliability, 2010,59(3):528-538.
[34]W. C. Yeh, Y. C. Lin, Y. Y. Chuang, et al. A particle swarm optimization approach based on Monte Carlo simulation for solving the complex network reliability problem. IEEE Transactions on Reliability,2010,59(1):212-221.
[35]J. E. Ramirez-Marquez, D. Coit. A Monte-Carlo simulation approach for approximating multi-state two-terminal reliability. Reliability Engineering and System Safety,2005,87(2): 253-264.
[36]J. E. Ramirez-Marquez, D. Coit, M. Tortorella. A generalized multi-state based path vector approach for multi-state two-terminal reliability. IIE Transactions,2006,38(6):477-488.
[37]J. L. Cook, J. E. Ramirez-Marquez. Reliability of capacitated mobile ad hoc networks. Journal of Risk and Reliability,2007,221(4):307-318.
[38]J. L. Cook, J. E. Ramirez-Marquez. Reliability analysis of cluster-based ad-hoc network. Reliability Engineering and System Safety,2008,93(10):1512-1522.
[39]H. Fan, X. Sun. A multi-state reliability evaluation model for P2P networks. Reliability Engineering and System Safety,2010,95(4):402-411.
[40]Y. K. Lin, C. T. Yeh. Optimal resource assignment to maximize multi-state network reliability for a computer network. Computers and Operations Research,2010,37(12):2229-2238.
[41]郭夙昌.网格服务可靠性建模及任务调度优化研究：[博士学位论文].成都：电子科技大学,2010.
[42]M. Xie, K. L. Poh, Y. S. Dai. Computing system reliability:models and analysis. London: Springer,2004.
[43]G. Levitin, Y. S. Dai. Service reliability and performance in grid system with star topology. Reliability Engineering and System Safety,2007,92(1):40-46.
[44]G. Levitin, Y. S. Dai. Optimal service task partition and distribution in grid system with star topology. Reliability Engineering and System Safety,2008,93(1):152-159.
[45]Y. S. Dai, G. Levitin, K. S. Trivedi. Performance and reliability of tree-structured grid services considering data dependence and failure correlation. IEEE Transcations on Computers,2007,56(7):925-936.
[46]Y. S. Dai, X. L. Wang. Optimal resource allocation on grid systems for maximizing service reliability using a genetic algorithm. Reliability Engineering and System Safety,2006,91(9): 1071-1082.
[47]G. Levitin. Optimal allocation of multi-state elements in linear consecutively connected systems with vulnerable nodes. European Journal of Operational Research,2003,150(2): 406-419.
[48]G. Levitin. Optimal allocation of multi-state elements in a linear consecutively-connected system. IEEE Transactions on Reliability,2003,52(2):192-199.
[49]G. Levitin. The universal generating function in reliability analysis and optimization. London: Springer,2005.
[50]G. Levitin. Reliability of acyclic multi-state networks with constant transmission characteristics of lines. Reliability Engineering and System Safety,2002,78(3):297-305.
[51]G. Levitin. Optimal allocation of multi-state retransmitters in acyclic transmission networks. Reliability Engineering and System Safety,2002,75(1):73-82.
[52]G. Levitin. Reliability evaluation for acyclic transmission networks of multi-state elements with delays. IEEE Transactions on Reliability,2003,52(2):231-237.
[53]J. S. Huang, M. J. Zuo, Z. D. Fang. Multi-state consecutive-k-out-of-n systems, ⅡE Transcations,2003,35(6):527-534.
[54]H. Yamanoto, M. J. Zuo, T. Akiba, et al. Recursive formulas for the reliability of multi-state consecutive-k-out-of-n:G systems. IEEE Transactions on Reliability,2006,55(1):98-104.
[55]W. C. Yen. Multi-state-node acyclic network reliability evaluation. Reliability Engineering and System Safety,2002,78(2):123-129.
[56]W. C. Yeh. A convolution universal generating function method for evaluating the symbolic one-to-all-target-subset reliability functions of acyclic multi-state information networks. IEEE Transactions on Reliability,2009,58(3):476-484.
[57]A. Habib, R. O. Al-Seedy, T. Radwan. Reliability evaluation of multi-state consecutive k-out-of-r-from-n:G system. Applied Mathematical Modelling,2007,31(11):2412-2423.
[58]Y. Ding, M. J. Zuo, Z. Tian, et al. The hierarchical weighted multi-state k-out-of-n system model and its application for infrastructure management. IEEE Transactions on Reliability, 2010,59(3):593-603.
[59]H. T. AI-Battaineh. Infrastructure intermediate-level modeling and optimization of budget allocation:[Ph.D. Dissertation]. Alberta, Canada:University of Alberta,2007.
[60]E. Zio, M. Marella, L. Podofillini. Importance measures-based prioritization for improving the performance of multi-state systems:application to the railway industry. Reliability Engineering and System Safety,2007,92(10):1303-1314.
[61]G. Levitin. Optimal defense strategy against intentional attacks. IEEE Transactions on Reliability,2007,56(1):148-157.
[62]G. Levitin, K. Hausken. Protection vs. redundancy in homogeneous parallel systems. Reliability Engineering and System Safety,2008,93(10):1444-1451.
[63]G. Levitin, K. Hausken. False targets vs. redundancy in homogeneous parallel systems. Reliability Engineering and System Safety,2009,94(2):588-595.
[64]G. Levitin, K. Hausken. Parallel systems under two sequential attacks. Reliability Engineering and System Safety,2009,94(3):763-772.
[65]G. Levitin, K. Hausken. Redundancy vs. protection in defending parallel systems against unintentional and intentional impacts. IEEE Transactions on Reliability,2009,58(4): 679-690.
[66]K. Hausken, G. Levitin. Defense of homogeneous parallel multi-state systems subject to two sequential attacks. Journal of Risk and Reliability,2010,224(3):171-183.
[67]J. E. Ramirez-Marquez, C. Rocco, G. Levitin. Optimal protection of general source-sink networks via evolutionary techniques. Reliability Engineering and System Safety,2009, 94(10):1676-1684.
[68]J. Murchland. Fundamental concepts and relations for reliability analysis of multi-state systems reliability and fault tree analysis. Theoretical and Applied Aspects of System Reliability,1975,581-618.
[69]E. EI-Neveihi, F. Proschan, J. Setharaman. Multi-state coherent system. Journal of Applied Probability,1978,15:675-688
[70]R. Barlow, A. S. Wu. Coherent systems with multi-state elements. Journal Mathematics of Operations Research,1978,3:275-281.
[71]S. Ross. Multivalued state element systems. Annals of Probability,1979,7:379-383.
[72]E. Zio. Reliability engineering:old problems and new challenges. Reliability Engineering and System Safety,2009,94(2):125-141.
[73]J. Xue. On multi-state system analysis. IEEE Transactions on Reliability,1985,34(4): 329-337.
[74]A. Shrestha, L. Xing, D. Coit. An efficient multi-state multi-valued decision diagram-based approach for multi-state system sensitivity analysis. IEEE Transactions on Reliability,2010, 59(3):581-592.
[75]A. Bobbio, A. Premoli, O. Saracco. Multi-state homogeneous Markov models in reliability analysis. Microelectronics and Reliability,1980,20(6):875-880.
[76]Y. W. Liu, K. C. Kapur. Reliability measures for dynamic multi-state nonrepairable systems and their applications to system performance evaluation. IIE Transactions,2006,38(6): 511-520.
[77]W. J. Li, H. Pham. Reliability modeling of multi-state degraded systems with multi-competing failures and random shocks. IEEE Transactions on Reliability,2005,54(2) 297-303.
[78]I. A. Ushakov. Universal generating function. Soviet Journal of Computer and System Sciences,1986,24(5):118-29.
[79]E. Zio, L. Podofillini, G. Levitin. Estimation of the importance measures of multi-state elements by Monte Carlo simulation. Reliability Engineering and System Safety,2004,86(3): 191-204.
[80]E. Zio, M. Marella, L. Podofillini. A Monte Carlo simulation approach to the availability assessment of multi-state systems with operational dependencies. Reliability Engineering and System Safety,2007,92(7):871-882.
[81]M. Nourelfath, Y. Dutuit. A combined approach to solve the redundancy optimization problem for multi-state systems under repair policies. Reliability Engineering and System Safety,2004,86(3):205-213.
[82]T. Aven. Reliability evaluation of multi-state systems with multi-state components. IEEE Transactions on Reliability,1985,34(5):473-479.
[83]A. Shrestha, L. Xing. A logarithmic binary decision diagram-based method for multi-state system analysis. IEEE Transactions on Reliability,2008,57(4):595-606.
[84]L. Xing, Y. S. Dai. A new decision-diagram-based method for efficient analysis on multi-state systems. IEEE Transactions on Dependable and Secure Computing,2009,6(3):161-174.
[85]J. S. Huang, M. J. Zuo, Y. H. Wu. Generalized multi-state k-out-of-n:G systems. IEEE Transactions on Reliability,2000,49(1):105-111.
[86]Z. G. Tian, M. J. Zuo, R. C. M. Yam. Multi-state k-out-of-n systems and their performance evaluation. IIE Transactions,2009,41(1):32-44.
[87]Z. G. Tian, R. C. M. Yam, M. J. Zuo, et al. Reliability bounds for multi-state k-out-of-n systems. IEEE Transactions on Reliability,2008,57(1):53-58.
[88]W. Li, M. J. Zuo. Reliability evaluation of multi-state weighted k-out-of-n systems. Reliability Engineering and System Safety,2008,93(1):160-167.
[89]S. V. Amari, M. J. Zuo, G. Dill. A fast and robust reliability evaluation algorithm for generalized multi-state k-out-of-n systems. IEEE Transactions on Reliability,2009,58(1): 88-97.
[90]Y. Ding, A. Lisnianski. Fuzzy universal generating functions for multi-state system reliability assessment. Fuzzy Sets and Systems,2008,159(3):307-24.
[91]Y. Ding, M. J. Zuo, A. Lisnianski, et al. Fuzzy multi-state systems:general definitions, and performance assessment. IEEE Transactions on Reliability,2008,57(4):589-594.
[92]B. Natvig, A. Streller. The steady-state behavior of multi-state monotone systems. Journal of Applied Probability,1984,21:826-835.
[93]M. Lanus, Y. Liang, K. S. Trivedi. Hierarchical composition and aggregation of state-based availability and performability models. IEEE Transactions on Reliability,2003,52(1):44-52.
[94]A. Lisnianski. Extended block diagram method for a multi-state system reliability assessment. Reliability Engineering and System Safety,2007,92(12):1601-1607.
[95]E. Zio. Computational methods for reliability and risk analysis. Singapore:World Scientific, 2009.
[96]J. E. Ramirez-Marquez, C. M. Rocco, B. A. Gebre, et al. New insights on multi-state component criticality and importance. Reliability Engineering and System Safety,2006, 91(8):894-904.
[97]E. Zio, L. Podofillini. Monte Carlo simulation analysis of the effects of different system performance levels on the importance of multi-state components. Reliability Engineering and System Safety,2003,82(1):63-73.
[98]G. Levitin. A universal generating function approach for the analysis of multi-state systems with dependent elements. Reliability Engineering and System Safety,2004,84(3):285-292.
[99]G. Levitin, L. Xing. Reliability and performance of multi-state systems with propagated failures having selective effect. Reliability Engineering and System Safety,2010,95(6): 655-661.
[100]W. Li. Reliability evaluation and optimal design of multi-state weighted systems:[Ph.D. Dissertation]. Alberta, Canada:University of Alberta,2008
[101]Z. Tian. Multi-state system reliability analysis and optimization:[Ph.D. Dissertation]. Alberta, Canada:University of Alberta,2007.
[102]Z. G. Tian, G. Levitin, M. J. Zuo. A joint reliability-redundancy optimization approach for multi-state series-parallel systems. Reliability Engineering and System Safety,2009,94(10): 1568-1576
[103]W. Li, M. J. Zuo. Optimal design of multi-state weighted k-out-of-n systems based on component design. Reliability Engineering and System Safety,2008,93(11):1673-1681
[104]G. Levitin, S. V. Amari. Optimal load distribution in series-parallel systems. Reliability Engineering and System Safety,2009,94(2):254-260.
[105]J. E. Ramirez-Marquez, C. M. Rocco. Evolutionary optimization technique for multi-state two-terminal reliability allocation in multi-objective problems. IIE Transcations,2010,42(8): 539-552.
[106]H. Yu, C. Chu, E. Chatelet, et al. Reliability optimization of a redundant system with failure dependencies. Reliability Engineering and System Safety,2005,92(12):1627-1634.
[107]C. Y. Li, X. Chen, X. S. Yi, et al. Heterogeneous redundancy optimization for multi-state series-parallel systems subject to common cause failures. Reliability Engineering and System Safety,2010,95(3):202-207.
[108]G. Levitin, A. Lisnianski, H. Ben-Haim, et al. Redundancy optimization for series-parallel multi-state systems. IEEE Transactions on Reliability,1998,47(2):165-172.
[109]J. E. Ramirez-Marquez, D. W. Coit. A heuristic for solving the redundancy allocation problem for multi-state series-parallel systems. Reliability Engineering and System Safety, 2004,83(3):341-349.
[110]N. Nahas, T. M. Dao. Harmony search algorithm:application to the redundancy optimization problem. Engineering Optimization,2010,42(9):845-861
[111]G. Levitin. Intelligence in reliability engineering, new metaheuristics, neural and fuzzy techniques in reliability. London:Springer,2007.
[112]R. Meziane, Y. Massim, A. Zeblah, et al. Reliability optimization using ant colony algorithm under performance and cost constraints. Electric Power Systems Research,2005,76(1-3): 1-8.
[113]V. K. Sharma, M. Agarwal, K. Sen. Optimal structure in heterogeneous multi-state series-parallel reliability systems. Economic Quality Control,2010,25(1):127-150.
[114]M. Ouzineb, M. Nourelfath, M. Gendreau. Tabu search for the redundancy allocation problem of homogenous series-parallel multi-state systems. Reliability Engineering and System Safety,2008,93(8):1257-1272.
[115]T. I. Kuo, S. H. Chen, J. E. Chiu. Tabu Search in the redundancy allocation optimization for multi-state series-parallel systems. Journal of the Chinese Institute of Industrial Engineers, 2007,24(3):210-218.
[116]Z. Tian, M. J. Zuo. Redundancy allocation for multi-state systems using physical programming and genetic algorithms. Reliability Engineering and System Safety,2006,91(9): 1049-1056.
[117]Z. Tian, M. J. Zuo, H. Z. Huang. Reliability-redundancy allocation for multi-state series-parallel systems. IEEE Transactions on Reliability,2008,57(2):303-310.
[118]H. A. Taboada, J. F. Espiritu, D. W. Coit. MOMS-GA:A multi-objective multi-state genetic algorithm for system reliability optimization design problem. IEEE Transactions on Reliability,2008,57(1):182-191.
[119]G. Levitin, A. Lisnianski. Joint redundancy and maintenance optimization for multi-state series-parallel systems. Reliability Engineering and System Safety,1999,64(1):33-42.
[120]G. Levitin, A. Lisnianski. Optimization of imperfect preventive maintenance for multi-state systems. Reliability Engineering and System Safety,2000,67(2):193-203.
[121]N. Nahas, A. Khatab, D. Ait-Kadi, et al. Extended great deluge algorithm for the imperfect preventive maintenance optimization of multi-state systems. Reliability Engineering and System Safety,2008,93(11):1658-1672.
[122]Y. L. Zhang, R. C. M. Yam, M. J. Zuo. Optimal replacement policy for a multi-state repairable system. Journal of the Operational Research Society,2002,53(3):336-341.
[123]Y. L. Zhang, R. C. M. Yam, M. J. Zuo. A bivariate optimal replacement policy for a multi-state repairable system. Reliability Engineering and System Safety,2007,92(4): 535-542.
[124]Y. L. Zhang, G. J. Wang. An optimal replacement policy for a multi-state degenerative simple system. Applied Mathematical Modelling,2010,34(12):4138-4150.
[125]L. Yeh. Monotone process maintenance model for a multi-state system. Journal of Applied Probability,2005,42(1):1-14.
[126]M. Nourelfath, D. Ait-Kadi. Optimization of series-parallel multi-state systems under maintenance policies. Reliability Engineering and System Safety,2007,92(12):1620-1626.
[127]C. M. Tan, N. Raghavan. A framework to practical predictive maintenance modeling for multi-state systems. Reliability Engineering and System Safety,2008,93(8):1138-1150.
[128]J. Wu, T. S. A. Ng, M. Xie, et al. Analysis of maintenance policies for finite life-cycle multi-state systems. Computers and Industrial Engineering,2010,59(4):638-646.
[129]I. W. Soro, M. Nourelfath, D. Ait-Kadi. Performance evaluation of multi-state degraded systems with minimal repairs and imperfect preventive maintenance. Reliability Engineering and System Safety,2010,95(2):65-69.
[130]C. C. Huang, J. Yuan. A two-stage preventive maintenance policy for a multi-state deterioration system. Reliability Engineering and System Safety,2010,95(11):1255-1260.
[131]A. Lisnianski, I. Frenkel, L. Khvatskin, et al. Maintenance contract assessment for aging systems. Quality and Reliability Engineering International,2008,24(5):519-531.
[132]Y. Ding, A. Lisnianski, I. Frenkel, et al. Optimal corrective maintenance contract planning for aging multi-state system. Applied Stochastic Models in Business and Industry,2009,25(5): 612-631.
[133]M. J. Kim, V. Makis. Optimal maintenance policy for a multi-state deteriorating system with two types of failures under general repair. Computers and Industrial Engineering,2009,57(1): 298-303.
[134]M. J. Zuo, B. Liu, D. N. P. Murthy. Replacement-repair policy for multi-state deteriorating products under warranty. European Journal of Operational Research,2000,123(3):519-530.
[135]W. Kuo, M. J. Zuo. Optimal reliability modeling:principles and applications. New York: John Wiley & Sons,2003.
[136]Y. Ding, M. J. Zuo, A. Lisnianski, et al. A framework for reliability approximation of multi-state weighted k-out-of-n systems. IEEE Transactions on Reliability,2010,59(2): 297-308.
[137]A. Lisnianski. Estimation of boundary points for continuum-state system reliability measures. Reliability Engineering and System Safety,2001,74(1):81-88.
[138]W. C. Yeh. A simple universal generating function method for estimating the reliability of general multi-state node networks. IIE Transactions,2009,41(1):3-11.
[139]K. Trivedi. Probability and statistics with reliability, queuing and computer science application. New York:John Wiley & Sons,2002.
[140]Z. An, H. Z. Huang, Y. Liu. A discrete stress-strength interference model based on universal generating function. Reliability Engineering and System Safety,2008,93(10):1485-1490.
[141]H. Z. Huang, Z. An. A discrete stress-strength interference model with stress dependent strength. IEEE Transactions on Reliability,2009,58(1):118-122.
[142]Z. W. An, H. Z. Huang, Z. L. Wang, et al. Discrete stress-strength interference model of reliability analysis under multi-operating conditions. Chinese Journal of Mechanical Engineering,2010,23(3):398-402.
[143]J. Y. Zhou, L. Y. Xie. Generating function approach to reliability analysis of structural systems. Science in China Series E-Technological Sciences,2009,52(10):2849-2858
[144]H. Pham, H. Z. Wang. Imperfect maintenance. European Journal of Operational Research, 1996,94(3):425-438.
[145]T. Nakagawa. Optimum policies when preventive maintenance is imperfect. IEEE Transactions on Reliability,1979,28(4):331-332.
[146]H. W. Block, W. S. Borges, T. H. Savits. Age dependent minimal repair. Journal of Applied Probability,1985,22(2):370-385.
[147]V. Makis, A. K. S. Jardine. Optimal replacement policy for a general model with imperfect repair. Journal of the Operational Research Society,1992,42(2):111-120.
[148]M. Kijima, H. Morimura, Y. Suzuki. Periodical replacement problem without assuming minimal repair. European Journal of Operational Research,1988,37(2):194-203.
[149]M. Kijima. Some results for repairable systems with general repair. Journal of Applied Probability,1989,26(1):89-102.
[150]L. Doyen,O. Gaudoin. Classes of imperfect repair models based on reduction of failure intensity or virtual age. Reliability Engineering and System Safety,2004,84(1):45-56
[151]M. A. K. Malik. Reliable preventive maintenance scheduling. AⅡE Transactions,1979,11(3): 221-228.
[152]D. Lin, M. J. Zuo, R. C. M. Yam. General sequential imperfect preventive maintenance models. International Journal of Reliability, Quality and Safety Engineering,2000,7(3): 253-266.
[153]Y. Lam. A note on the optimal replacement problem. Advances in Applied Probability,1988, 20(2):479-482.
[154]H. Z. Wang, H. Pham. A quasi renewal process and its application in the imperfect maintenance. International Journal of Systems Science,1996,27(10):1055-1062.
[155]H. Z. Wang, H. Pham. Reliability and optimal maintenance. London:Springer,2006.
[156]S. Wu, M. J. Zuo. Linear and nonlinear preventive maintenance models. IEEE Transactions Reliability,2010,59(1):242-249.
[157]M. Bartholomew-Biggs, M. J. Zuo, X. H. Li. Modelling and optimizing sequential imperfect preventive maintenance. Reliability Engineering and System Safety,2009,94(1):53-62.
[158]Y. Liu, H. Z. Huang, X. Zhang. Data-driven approach for imperfect maintenance model selection. Proceedings of Annual Reliability and Maintainability Symposium,2011RM0200, 2011.
[159]H. C. Wu. Fuzzy reliability estimation using Bayesian approach. Computers and Industrial Engineering,2004,46(3):467-493.
[160]H. Z. Huang, M. J. Zuo, Z. Q. Sun. Bayesian reliability analysis for fuzzy lifetime data. Fuzzy Sets and Systems,2006,157(12):1674-1686.
[161]Y. Liu, Y. Li, H. Z. Huang, et al. Optimal preventive maintenance policy under fuzzy Bayesian reliability assessment environments. HE Transactions,2010,42(10):734-745.
[162]A. K. Verma, A. Srividya, R. P. Gaonkar. Fuzzy dynamic reliability evaluation of a deteriorating system under imperfect repair. International Journal of Reliability, Quality and Safety Engineering,2004,11(4):387-398.
[163]H. I. Huang, C. H. Lin, J. C. Ke. Two-unit repairable systems with common-cause shock failures and fuzzy parameters:parametric programming approach. International Journal of Systems Science,2008,39(5):449-459.
[164]L. A. Zadeh. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems,1978, 1(1):3-28.
[165]L. A. Zadeh. Fuzzy sets. Information and Control,1965,8(3):338-353.
[166]A. Saltelli, M. Ratto, T. Andres, et al. Global sensitivity analysis:the primer. New York:John Wiley & Sons,2008
[167]D. Allaire, K. Willcox. Surrogate modeling for uncertainty assessment with application to aviation environmental system models. AIAA Journal,2010,48(8):1791-1803.
[168]B. Krzykacz. Samos:a computer program for the derivation of empirical sensitivity measures of results from large computer models. Technical Report GRS-A-1700, Garching, Germany, 1990.
[169]J. D. Cawlfield, M. C. Wu. Probabilistic sensitivity analysis for one-dimensional reactive transport in porous media. Water Resources Research,1993,29(3):661-672.
[170]A. Saltelli, S. Tarantola, K. P. S. Chan. A quantitative model-independent method for global sensitivity analysis of model output. Technometrics,1999,41(1):39-56.
[171]C. Xu, G. Z. Gertner. A general first-order global sensitivity analysis method. Reliability Engineering and System Safety,2008,93(7):1060-1071
[172]T. A. Mara. Extension of the RBD-FAST method to the computation of global sensitivity indices. Reliability Engineering and System Safety,2009,94(8):1274-1281
[173]I. M. Sobol. Sensitivity analysis for nonlinear mathematical models. Mathematical Modeling and Computational Experiment,1993,1:407-414.
[174]I. M. Sobol. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation,2001,55(1-3):271-280.
[175]H. Liu, W. Chen, A. Sudjianto. Relative entropy based method for probabilistic sensitivity analysis in engineering design. ASME Journal of Mechanical Design,2006,128(3):326-336.
[176]K. Chan, A. Saltelli, S. Tarantola. Sensitivity analysis of model output:variance-based methods make the difference. Proceedings of the 1997 Winter Simulation Conference, 261-268,1997.
[177]J. C. Helton. Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal. Reliability Engineering and System Safety,1993, 42(2-3):327-367.
[178]C. I. Reedijk. Sensitivity analysis of model output:performance of various local and global sensitivity measures on reliability problems:[M.S. Dissertation]. Delft, Nederland:Delft University of Technology,2000.
[179]W. Chen, R. Jin, A. Sudjianto. Analytical variance-based global sensitivity analysis in simulation-based design under uncertainty. ASME Journal of Mechanical Design,2005, 127(5):875-886.
[180]B. Sudret. Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering and System Safety,93(7):964-979.
[181]H. Z. Wang. A survey of maintenance policies of deteriorating systems. European Journal of Operational Research,2002,139(3):469-489.
[182]C. R. Cassady, E. A. Pohl, W. P. M. Jr. Selective maintenance modeling for industrial system. Journal of Quality in Maintenance Engineering,2001,7(2):104-117.
[183]W. F. Rice, C. R. Cassady, J. A. Nachlas. Optimal maintenance plans under limited maintenance time. Proceedings of the Seventh Industrial Engineering Research Conference, 1998.
[184]C. R. Cassady, W. P. M. Jr, E. A. Pohl. Selective maintenance for support equipment involving multiple maintenance actions. European Journal of Operational Research,2001, 129(2):252-258.
[185]K. Schneider, C. R. Cassady. Fleet performance under selective maintenance. Proceedings of Annual Reliability and Maintainability Symposium,571-576,2004.
[186]R. Rajagopalan, C. R. Cassady. An improved selective maintenance solution approach. Journal of Quality in Maintenance Engineering,2006,12(2):172-185.
[187]T. Lust, O. Roux, F. Riane. Exact and heuristic methods for the selective maintenance problem. European Journal of Operational Research,2009,197(3):1166-1177.
[188]I. M. Iyoob, C. R. Cassady, E. A. Pohl. Establishing maintenance resource levels using selective maintenance. The Engineering Economist,2006,51(2):99-114.
[189]K. Schneider, L. M. Maillart, C. R. Cassady, et al. Selective maintenance decision-making over extended planning horizons. IEEE Transactions Reliability,2009,58(3):462-469.
[190]C. Chen, M. Q. H. Meng, M. J. Zuo. Selective maintenance optimization for multi-state systems. Proceedings of IEEE Canadian Conference on Electrical and Computer Engineering, 1477-1482,1999.
[191]C. H. Lie, Y. H. Chun. An algorithm for preventive maintenance policy. IEEE Transactions Reliability,1986,35(1):71-75.
[192]G. Levitin. Genetic algorithms in reliability engineering. Reliability Engineering and System Safety,2006,91(9):975-976.
[193]H. I. H. Saravanamuttoo, G. F. C. Rogers, H. Cohen, et al. Gas turbine theory (6th Edition). Harlow:Pearson Education,2009.
[194]刘长富,邓明,等.航空发动机结构分析.西安：西北工业大学出版社,2006.
[195]Y. Liu, H. Z. Huang. Comment on "A framework to practical predictive maintenance modeling for multi-state systems" by Tan CM. and Raghavan N. [Reliab Eng Syst Saf 2008;93(8):1138-50]. Reliability Engineering and System Safety,2009,94(3):776-780.
[196]F. Camci. System maintenance scheduling with prognostics information using genetic algorithm. IEEE Transactions Reliability,2009,58(3):539-552.
[197]C. M. Tan, N. Raghavan. Reply to comments on "A framework to practical predictive maintenance modeling for multi-state systems". Reliability Engineering and System Safety, 2009,94(3):781-782.
[198]Y. Liu, K. C. Kapur. Customer's cumulative experience measures for reliability of non-repairable aging multi-state systems. Quality, Technology and Quantitative Management, 2007,4(2):225-234.
[199]Y. Liu, K. C. Kapur. New model and measurement for reliability of multi-state systems. Handbook of performability engineering, London:Springer,2008.
[200]T. Sun, G. C. Zhao, P. B. Luh, et al. Optimization of joint replacement policies for multipart systems by a rollout framework. IEEE Transactions on Automation Science and Engineering, 2008,5(4):609-619.
[201]W. J. Hopp, Y. L. Kuo. Heuristics for multicomponent joint replacement; applications to aircraft engine maintenance. Naval Research Logistics,1998,45(5):435-458.
[202]H. S. Lee, M. M. Srinivasan. Optimal replacement policies for systems with multiple standby components. IEEE Transactions on Reliability,1994,43(3):414-422.
[203]T. W. Archibald, R. Dekker. Modified block-replacement for multiple-component systems IEEE Transactions on Reliability,1996,45(1):75-83.
[204]M. S. Moustafa, E. Y. A. Makasoud, S. Sadek. Optimal major and minimal maintenance policies for deteriorating systems. Reliability Engineering and System Safety,2004,83(3): 363-368.
[205]M. Marseguerra, E. Zio, L. Podofillini. Condition-based maintenance optimization by means of genetic algorithms and Monte Carlo simulation. Reliability Engineering and System Safety, 2002,77(2):151-166
[206]Y. C. Liang, A. E. Smith. An ant colony optimization algorithm for the redundancy allocation problem (RAP). IEEE Transactions on Reliability,2004,53(3):417-423.
[207]M. Samrout, F. Yalaoui, E. Chatelet, et al. New methods to minimize the preventive maintenance cost of series-parallel systems using ant colony optimization. Reliability Engineering and System Safety,2005,89(3):346-354.
[208]N. Nahas, M. Mourelfath. Ant system for reliability optimization of a series system with multiple-choice and budget constraints. Reliability Engineering and System Safety,2005, 87(1):1-12.
[209]J. H. Zhao, Z. Liu, M. T. Dao. Reliability optimization using multiobjective ant colony system approaches. Reliability Engineering and System Safety,2007,92(1):109-120.
[210]V. Maniezzo. Exact and approximate nondeterministic tree-search procedures for the quadratic assignment problem. INFORMS Journal on Computing,1999,11(4):358-369.
[211]G. Levitin, T. Zhang, M. Xie. State probability of a series-parallel repairable system with two-types of failure states. International Journal of Systems Science,2006,37(14-15): 1011-1020.
[212]P. Yu, J. J. Song, C. R. Cassady. Parameter estimation for a repairable system under imperfect maintenance. Proceedings of Annual Reliability and Maintainability Symposium,13D-3, 2009.
[213]W. Kuo, R. Wan. Recent advances in optimal reliability allocation. IEEE Transactions on Systems, Man and Cybernetics, Part A:Systems and Humans,2007,77(2):143-156.
[214]W. Kuo, H. Lin, Z. Xu, et al. Reliability optimization with the Lagrange multiplier and branch-and-bound technique. IEEE Transactions on Reliability,1987,36(5):624-630.
[215]C. S. Sung, Y. K. Cho. Branch-and-bound redundancy optimization for a series system with multiple-choice constraints. IEEE Transactions on Reliability,1999,48(2):108-117.
[216]M. Hikita, Y. Nakagawa, K. Nakashima, et al. Reliability optimization of systems by a surrogate-constraints algorithm. IEEE Transactions on Reliability,1992,41(3):472-480.
[217]C. H. Ha, W. Kuo. Multi-path approach for reliability-redundancy allocation using a scaling method. Journal of Heuristics,2005,11(3):201-217.
[218]D. W. Coit, A. E. Smith. Reliability optimization of series-parallel systems using a genetic algorithm. IEEE Transactions on Reliability,1996,45(2):254-260.
[219]S. Kulturel-Konak, A. E. Smith, D. W. Coit. Efficiently solving the redundancy allocation problem using tabu search. HE Transactions,2003,35(6):515-526.
[220]M. Agarwal, R. Gupta. Homogeneous redundancy optimization in multi-state series-parallel systems:A heuristic approach. IIE Transactions,2007,39(3):277-289.
[221]U. K. D. Kumar, J. E. Ramirez-Marquez, D. Nowicki, et al. Reliability and maintainability allocation to minimize total cost of ownership in a series-parallel system. Journal of Risk and Reliability,2007,221(2):133-140.
[222]K. Y. Cai. Fuzzy reliability theories. Fuzzy Sets and Systems,1991,40(3):510-511.
[223]K. Y. Cai, C. Y. Wen, M. L. Zhang. Fuzzy reliability modeling of gracefully degradable computing systems. Reliability Engineering and System Safety,1991,33(1):141-157.
[224]H. Z. Huang. Reliability analysis method in the presence of fuzziness attached to operation time. Microelectronics and Reliability,1995,35(12):1483-1487.
[225]H. Z. Huang, X. Tong, M. J. Zuo. Posbist fault tree analysis of coherent systems. Reliability Engineering and System Safety,2004,84(2):141-148.
[226]H. C. Wu. Bayesian system reliability assessment under fuzzy environment. Reliability Engineering and System Safety,2004,83(3):277-86.
[227]J. C. Ke, H. I. Huang, C. H. Lin. Fuzzy analysis for steady-state availability:a mathematical programming approach. Engineering Optimization,2006,38(8):909-921.
[228]D. Pandey, S. K. Tyagi. Profust reliability of a gracefully degradable system. Fuzzy Sets and Systems,2007,158(7):794-803.
[229]E. Popova, H. C. Wu. Renewal reward processes with fuzzy rewards and their application to T-age replacement policies. European Journal of Operation Research,1999,117(3):606-617.
[230]S. M. Chen. Fuzzy system reliability analysis using fuzzy number arithmetic operations. Fuzzy Sets and Systems,1994,64(1):31-38.
[231]K. H. Lee. First course on fuzzy theory and applications. London:Springer,2005.
[232]S. Murakami, S. Maeda, S. Imamura. Fuzzy decision analysis on the development of centralized regional energy control system. Proceedings of the IFAC Symposium on Fuzzy Information, Knowledge Representation and Decision Analysis,363-368,1983.
[233]C. H. Cheng. A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets and Systems,1998,95(3):307-317.
[234]T. S. Liou, M. J. J. Wang. Ranking fuzzy numbers with integral value. Fuzzy Sets and Systems,1992,50(3):247-255.
[235]H. M. Kim, D. G. Rideout, P. Y. Papalambros, et al. Analytical target cascading in automotive vehicle design. ASME Journal of Mechanical Design,2003,125(3):481-489.
[236]H. Liu, W. Chen, M. Kakkolaras, et al. Probabilistic analytical target cascading:a moment matching formulation for multilevel optimization under uncertainty. ASME Journal of Mechanical Design,2006,128(4):991-1000.
[237]X. Du, W. Chen. Collaborative reliability analysis under the framework of multidisciplinary systems design. Optimization and Engineering,2005,6(1):63-84.
[238]H. M. Kim, D. K. D. Kumar, W. Chen, et al. Target exploration for disconnected feasible regions in enterprise-driven multilevel product design. AIAA Journal,2006,44(1):67-77
[239]M. Kokkolaras, Z. P. Mourelatos, P. Y. Papalambros. Design optimization of hierarchically decomposed multilevel system under uncertainty. ASME Journal of Mechanical Design,2006, 128(2):503-508.
[240]R. S. Krishnamachari, P. Y. Papalambros. Hierarchical decomposition synthesis in optimal systems design. ASME Journal of Mechanical Design,1997,119(4):448-457.
[241]D. Z. Chen, C. P. Liu. A hierarchical decomposition scheme for the topological synthesis of articulated gear mechanisms. ASME Journal of Mechanical Design 1999,121(2):256-263
[242]D. Li, Y. Y. Haimes. A decomposition method for optimization of large-system reliability. IEEE Transactions on Reliability,1994,41(2):183-189.
[243]X. L. Zhang, H. Z. Huang, Y. Liu. A hierarchical decomposition approach for large system reliability allocation. Eksploatacja i Niezawodnosc-Maintenance and Reliability,2009,43, 32-37.
[244]Z. Wang, K. Tang, X. Yao. A memetic algorithm for multi-level redundancy allocation. IEEE Transactions on Reliability,2010,59(4):754-765.
[245]X. Yin, W. Chen, A. To, et al. Statistical volume element method for predicting microstructure-constitutive property relations. Computer Methods in Applied Mechanics and Engineering,2008,197(43):3516-3529.
[246]X. Yin, S. Lee, W. Chen, et al. Efficient random field uncertainty propagation in design using multiscale analysis. ASME Journal of Mechanical Design,2009,131(2):021006.
[247]W. Chen, X. Yin, S. Lee, et al. A multiscale design methodology for hierarchical systems with random field uncertainty. ASME Journal of Mechanical Design,2010,132(4):041006.
[248]H. Choi, D. L. McDowell, J. K. Allen, et al. An inductive design exploration method for robust multiscale materials design. ASME Journal of Mechanical Design,2008,130(3): 031402
[249]G. B. Olson. Computational design of hierarchically structured materials. Science,1997, 277(5330):1237-1242.
[250]H. M. Kim, N. F. Michelena, P. Y. Papalambros, et al. Target cascading in optimal system design. ASME Journal of Mechanical Design,2003,125(3):474-480.
[251]J. Han, P. Y. Papalambros. A sequential linear programming coordination algorithm for analytical target cascading. ASME Journal of Mechanical Design,2010,132(2):021003.
[252]Y Li, Z. Lu, J. J. Michalek. Diagonal quadratic approximation for parallelization of analytical target cascading. ASME Journal of Mechanical Design,2008,130(5):0514021.
[253]W. Y. Yuna, Y. M. Song, H. G. Kim. Multiple multi-level redundancy allocation in series systems. Reliability Engineering and System Safety,2007,92(3):308-313.
[254]R. Kumar, K. Izui, M. Yoshimura, et al. Optimal multilevel redundancy allocation in series and series-parallel systems. Computers and Industrial Engineering,2009,57(1):169-180.
[255]X. Yin, W. Chen. A hierarchical statistical sensitivity analysis method for complex engineering systems design. ASME Journal of Mechanical Design,2008,130(7):071402.
[256]F. Xiong, X. Yin, W. Chen, et al. Enhanced probabilistic analytical target cascading with application to multi-scale design. Engineering Optimization,2010,42(6):581-592.
[257]A. Saltelli, K. Chan, E. M. Scott. Sensitivity analysis. New York:John Wiley & Sons,2000.
[258]H. Liu, W. Chen, A. Sudjianto. Probabilistic sensitivity analysis methods for design under uncertainty. Proceedings of 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA2004-4589,2004.
[259]C. Xu, G. Z. Gertner. Uncertainty and sensitivity analysis for models with correlated parameters. Reliability Engineering and System Safety,2008,93(10):1563-1573.
[260]C. Xu, G. Z. Gertner. Extending a global sensitivity analysis technique to models with correlated parameters. Computational Statistics and Data Analysis,2007,51(12):5579-5590.
[261]T. Homma, A. Saltelli. Importance measures in global sensitivity analysis of nonlinear models. Reliability Engineering and System Safety,1996,52(1):1-17.
[262]M. D. McKay. Nonparametric variance-based methods of assessing uncertainty importance. Reliability Engineering and System Safety,1997,57(3):267-279.
[263]M. P. R. Haaker, P. J. T. Verheijen. Local and global sensitivity analysis for a reactor design with parameter uncertainty. Chemical Engineering Research and Design,2004,82(5): 591-598.
[264]A. Saltelli, S. Tarantola. On the relative importance of input factors in mathematical models: safety assessment for nuclear waste disposal. Journal of the American Statistical Association, 2002,97(459):702-709.
[265]R. L. Imana, M. E. Johnson, T. A. Schroeder. Assessing hurricane effects. Part 1. Sensitivity analysis. Reliability Engineering and System Safety,2002,78(2):131-145.
[266]R. L. Imana, M. E. Johnson, T. A. Schroeder. Assessing hurricane effects. Part 2. Uncertainty analysis. Reliability Engineering and System Safety,2002,78(2):147-155.
[267]J. Jacques, C. Lavergne, N. Devictor. Sensitivity analysis in present of model uncertainty and correlated inputs. Reliability Engineering and System Safety,2006,91(10):1126-1134.
[268]W. E, B. Engquist, X. Li, et al. The heterogeneous multiscale method:a review. Journal of Communications in Computational Physics,2007,2(3):367-450.
[269]S. Hao, W. K. Liu, B. Moran, et al. Multi-scale constitutive model and computational framework for the design of ultra-high strength, high toughness steels. Computer Methods in Applied Mechanics and Engineering,2004,193(17-20):1865-1908.
[270]R. Jin, W. Chen, T. W. Simpson. Comparative studies of metamodelling techniques under multiple modelling criteria. Structural and Multidisciplinary Optimization,2001,23(1):1-13.
[271]D. C. Cox. An analytical method for uncertainty analysis of nonlinear output function, with application to fault-tree analysis. IEEE Transactions on Reliability,1982, R-31(5):465-468.
[272]T. Jin. Hierarchical variance decomposition of system reliability with duplicated components. IEEE Transactions on Reliability,2008,57(4):564-573.
[2]A. Lisnianski, G. Levitin, H. Ben-Haim, et al. Power system structure optimization subject to reliability constraints. Electric Power Systems Research,1996,39(2):145-152.
[3]G. Levitin, A. Lisnianski, D. Elmakis. Structure optimization of power system with different redundant elements. Electric Power Systems Research,1997,43(1):19-27.
[4]G.. Levitin, A. Lisnianski. Structure optimization of power system with bridge topology. Electric Power Systems Research,1998,45(3):201-208.
[5]R. Billinton, W. Zhang. State extension for adequacy evaluation of composite power systems-application. IEEE Transactions on Power Systems,2002,15(1):427-432.
[6]M. J. Zuo, Z. G. Tian. Performance evaluation of generalized multi-state k-out-of-n systems. IEEE Transactions on Reliability,2006,55(2):319-327.
[7]A. Zeblah. Reliability maximization of power system using ant colony approach. International Journal of Electrical and Power Engineering,2008,2(3):192-201.
[8]Y. Ding, A. Lisnianski, P. Wang, et al. Dynamic reliability assessment for bilateral contract electricity providers in restructured power systems. Electric Power Systems Research,2009, 79(10):1424-1430.
[9]Y. Ding, P. Wang, A. Lisnianski. Optimal reserve management for restructured power generating systems. Reliability Engineering and System Safety,2006,91(7):792-799.
[10]H. A. Taboada, J. F. Espiritu, D. W. Coit. Design allocation of multi-state series-parallel systems for power systems planning:a multiple objective evolutionary approach. Journal of Risk and Reliability,2008,222(3):381-391.
[11]E. Zio, P. Baraldi, E. Patelli. Assessment of the availability of an offshore installation by Monte Carlo simulation. International Journal of Pressure Vessels and Piping,2006,83(4): 312-320.
[12]K. D. Rao, H. S. Kushwaha, A. K. Verma, et al. Simulation based reliability evaluation of AC power supply system of Indian Nuclear Power Plant. International Journal of Quality and Reliability Management,2007,24(6):628-642.
[13]R. Karki, P. Hu, R. Billinton. A simplified wind power generation model for reliability evaluation. IEEE Transactions on Energy Conversion,2006,21(2):533-540.
[14]R. Billinton, Y. Gao. Adequacy assessment of composite power generation and transmission systems with wind energy. International Journal of Reliability and Safety,2008,2(1-2): 79-98.
[15]D. Elmakias. New computational methods in power system reliability. London:Springer, 2008.
[16]A. Lisnianski, G. Levitin. Multi-state system reliability assessment, optimization, application. Singapore:World Scientific,2003.
[17]G. Levitin, L. Meizin. Structure optimization for continuous production systems with buffers under reliability constraints. International Journal of Production Economics,2001,70(1): 77-87.
[18]S. T. Bae, G. S. Cho, H. S. Hwang. Multi-state availability model for manufacturing system considering system cost. International Journal of Information Systems for Logistics and Management,2007,2(2):93-98.
[19]G. Levitin. Linear multi-state sliding-window systems. IEEE Transactions on Reliability, 2003,52(2):263-269.
[20]A. M. A. Youssel, A. Mohib, H. A. EMaraghy. Availability assessment of multi-state manufacturing systems using universal generating function. RP Annals-Manufacturing Technology,2006,55(1):445-448.
[21]P. D. Van, A. Barros, C. Berenguer. Importance measure on finite time horizon and application to Markovian multi-state production systems. Journal of Risk and Reliability, 2008,222(3):449-461.
[22]M. Nourelfath, M. Fitouhi, M. Machani. An integrated model for production and preventive maintenance planning in multi-state systems. IEEE Transactions on Reliability,2010,59(3): 496-506.
[23]高鹏,谢里阳.基于改进发生函数方法的多状态系统可靠性分析.航空学报,2010,31(5)：934-939.
[24]周金宇,谢里阳,王学敏.多状态系统共因失效分析及可靠性模型.机械工程学报,2005,41(6)：60-70.
[25]钱文学,尹晓伟,谢里阳.多状态机械系统可靠性的离散化建模方法.东北大学学报(自然科学版),2008,29(11)：1609-1632.
[26]周金宇,谢里阳.多状态系统共因失效机理与定量分析.机械工程学报,2008,44(10)：77-82.
[27]尹晓伟,钱文学,谢里阳.基于贝叶斯网络的多状态系统可靠性建模与评估.机械工程学报,2009,45(2)：206-212.
[28]S. V. Amari, L. Xing, A. Shrestha, et al. Performability analysis of multi-state computing systems using multivalued decision diagrams. IEEE Transactions on Computers,2010, 59(10):1419-1433.
[29]S. Patra, R. B. Misra. Reliability evaluation of flow networks considering multi-state modelling of network elements. Microelectronics and Reliability,1993,33(14):2161-2164.
[30]Y. K. Lin. System capacity for a two-commodity multi-state flow network with unreliable nodes and capacity weight. Computers and Operations Research,2007,34(10):3043-3054.
[31]W. C. Yeh. An evaluation of the multi-state node networks reliability using the traditional binary-state networks reliability algorithm. Reliability Engineering and System Safety,2003, 81(1):1-7.
[32]W. C. Yeh. A simple minimal path method for estimating the weighted multi-commodity multi-state unreliable networks reliability. Reliability Engineering and System Safety,2008, 93(1):125-136.
[33]W. C. Yeh, X. He. A new universal generating function method for estimating the novel multiresource multi-state information network reliability. IEEE Transactions on Reliability, 2010,59(3):528-538.
[34]W. C. Yeh, Y. C. Lin, Y. Y. Chuang, et al. A particle swarm optimization approach based on Monte Carlo simulation for solving the complex network reliability problem. IEEE Transactions on Reliability,2010,59(1):212-221.
[35]J. E. Ramirez-Marquez, D. Coit. A Monte-Carlo simulation approach for approximating multi-state two-terminal reliability. Reliability Engineering and System Safety,2005,87(2): 253-264.
[36]J. E. Ramirez-Marquez, D. Coit, M. Tortorella. A generalized multi-state based path vector approach for multi-state two-terminal reliability. IIE Transactions,2006,38(6):477-488.
[37]J. L. Cook, J. E. Ramirez-Marquez. Reliability of capacitated mobile ad hoc networks. Journal of Risk and Reliability,2007,221(4):307-318.
[38]J. L. Cook, J. E. Ramirez-Marquez. Reliability analysis of cluster-based ad-hoc network. Reliability Engineering and System Safety,2008,93(10):1512-1522.
[39]H. Fan, X. Sun. A multi-state reliability evaluation model for P2P networks. Reliability Engineering and System Safety,2010,95(4):402-411.
[40]Y. K. Lin, C. T. Yeh. Optimal resource assignment to maximize multi-state network reliability for a computer network. Computers and Operations Research,2010,37(12):2229-2238.
[41]郭夙昌.网格服务可靠性建模及任务调度优化研究：[博士学位论文].成都：电子科技大学,2010.
[42]M. Xie, K. L. Poh, Y. S. Dai. Computing system reliability:models and analysis. London: Springer,2004.
[43]G. Levitin, Y. S. Dai. Service reliability and performance in grid system with star topology. Reliability Engineering and System Safety,2007,92(1):40-46.
[44]G. Levitin, Y. S. Dai. Optimal service task partition and distribution in grid system with star topology. Reliability Engineering and System Safety,2008,93(1):152-159.
[45]Y. S. Dai, G. Levitin, K. S. Trivedi. Performance and reliability of tree-structured grid services considering data dependence and failure correlation. IEEE Transcations on Computers,2007,56(7):925-936.
[46]Y. S. Dai, X. L. Wang. Optimal resource allocation on grid systems for maximizing service reliability using a genetic algorithm. Reliability Engineering and System Safety,2006,91(9): 1071-1082.
[47]G. Levitin. Optimal allocation of multi-state elements in linear consecutively connected systems with vulnerable nodes. European Journal of Operational Research,2003,150(2): 406-419.
[48]G. Levitin. Optimal allocation of multi-state elements in a linear consecutively-connected system. IEEE Transactions on Reliability,2003,52(2):192-199.
[49]G. Levitin. The universal generating function in reliability analysis and optimization. London: Springer,2005.
[50]G. Levitin. Reliability of acyclic multi-state networks with constant transmission characteristics of lines. Reliability Engineering and System Safety,2002,78(3):297-305.
[51]G. Levitin. Optimal allocation of multi-state retransmitters in acyclic transmission networks. Reliability Engineering and System Safety,2002,75(1):73-82.
[52]G. Levitin. Reliability evaluation for acyclic transmission networks of multi-state elements with delays. IEEE Transactions on Reliability,2003,52(2):231-237.
[53]J. S. Huang, M. J. Zuo, Z. D. Fang. Multi-state consecutive-k-out-of-n systems, ⅡE Transcations,2003,35(6):527-534.
[54]H. Yamanoto, M. J. Zuo, T. Akiba, et al. Recursive formulas for the reliability of multi-state consecutive-k-out-of-n:G systems. IEEE Transactions on Reliability,2006,55(1):98-104.
[55]W. C. Yen. Multi-state-node acyclic network reliability evaluation. Reliability Engineering and System Safety,2002,78(2):123-129.
[56]W. C. Yeh. A convolution universal generating function method for evaluating the symbolic one-to-all-target-subset reliability functions of acyclic multi-state information networks. IEEE Transactions on Reliability,2009,58(3):476-484.
[57]A. Habib, R. O. Al-Seedy, T. Radwan. Reliability evaluation of multi-state consecutive k-out-of-r-from-n:G system. Applied Mathematical Modelling,2007,31(11):2412-2423.
[58]Y. Ding, M. J. Zuo, Z. Tian, et al. The hierarchical weighted multi-state k-out-of-n system model and its application for infrastructure management. IEEE Transactions on Reliability, 2010,59(3):593-603.
[59]H. T. AI-Battaineh. Infrastructure intermediate-level modeling and optimization of budget allocation:[Ph.D. Dissertation]. Alberta, Canada:University of Alberta,2007.
[60]E. Zio, M. Marella, L. Podofillini. Importance measures-based prioritization for improving the performance of multi-state systems:application to the railway industry. Reliability Engineering and System Safety,2007,92(10):1303-1314.
[61]G. Levitin. Optimal defense strategy against intentional attacks. IEEE Transactions on Reliability,2007,56(1):148-157.
[62]G. Levitin, K. Hausken. Protection vs. redundancy in homogeneous parallel systems. Reliability Engineering and System Safety,2008,93(10):1444-1451.
[63]G. Levitin, K. Hausken. False targets vs. redundancy in homogeneous parallel systems. Reliability Engineering and System Safety,2009,94(2):588-595.
[64]G. Levitin, K. Hausken. Parallel systems under two sequential attacks. Reliability Engineering and System Safety,2009,94(3):763-772.
[65]G. Levitin, K. Hausken. Redundancy vs. protection in defending parallel systems against unintentional and intentional impacts. IEEE Transactions on Reliability,2009,58(4): 679-690.
[66]K. Hausken, G. Levitin. Defense of homogeneous parallel multi-state systems subject to two sequential attacks. Journal of Risk and Reliability,2010,224(3):171-183.
[67]J. E. Ramirez-Marquez, C. Rocco, G. Levitin. Optimal protection of general source-sink networks via evolutionary techniques. Reliability Engineering and System Safety,2009, 94(10):1676-1684.
[68]J. Murchland. Fundamental concepts and relations for reliability analysis of multi-state systems reliability and fault tree analysis. Theoretical and Applied Aspects of System Reliability,1975,581-618.
[69]E. EI-Neveihi, F. Proschan, J. Setharaman. Multi-state coherent system. Journal of Applied Probability,1978,15:675-688
[70]R. Barlow, A. S. Wu. Coherent systems with multi-state elements. Journal Mathematics of Operations Research,1978,3:275-281.
[71]S. Ross. Multivalued state element systems. Annals of Probability,1979,7:379-383.
[72]E. Zio. Reliability engineering:old problems and new challenges. Reliability Engineering and System Safety,2009,94(2):125-141.
[73]J. Xue. On multi-state system analysis. IEEE Transactions on Reliability,1985,34(4): 329-337.
[74]A. Shrestha, L. Xing, D. Coit. An efficient multi-state multi-valued decision diagram-based approach for multi-state system sensitivity analysis. IEEE Transactions on Reliability,2010, 59(3):581-592.
[75]A. Bobbio, A. Premoli, O. Saracco. Multi-state homogeneous Markov models in reliability analysis. Microelectronics and Reliability,1980,20(6):875-880.
[76]Y. W. Liu, K. C. Kapur. Reliability measures for dynamic multi-state nonrepairable systems and their applications to system performance evaluation. IIE Transactions,2006,38(6): 511-520.
[77]W. J. Li, H. Pham. Reliability modeling of multi-state degraded systems with multi-competing failures and random shocks. IEEE Transactions on Reliability,2005,54(2) 297-303.
[78]I. A. Ushakov. Universal generating function. Soviet Journal of Computer and System Sciences,1986,24(5):118-29.
[79]E. Zio, L. Podofillini, G. Levitin. Estimation of the importance measures of multi-state elements by Monte Carlo simulation. Reliability Engineering and System Safety,2004,86(3): 191-204.
[80]E. Zio, M. Marella, L. Podofillini. A Monte Carlo simulation approach to the availability assessment of multi-state systems with operational dependencies. Reliability Engineering and System Safety,2007,92(7):871-882.
[81]M. Nourelfath, Y. Dutuit. A combined approach to solve the redundancy optimization problem for multi-state systems under repair policies. Reliability Engineering and System Safety,2004,86(3):205-213.
[82]T. Aven. Reliability evaluation of multi-state systems with multi-state components. IEEE Transactions on Reliability,1985,34(5):473-479.
[83]A. Shrestha, L. Xing. A logarithmic binary decision diagram-based method for multi-state system analysis. IEEE Transactions on Reliability,2008,57(4):595-606.
[84]L. Xing, Y. S. Dai. A new decision-diagram-based method for efficient analysis on multi-state systems. IEEE Transactions on Dependable and Secure Computing,2009,6(3):161-174.
[85]J. S. Huang, M. J. Zuo, Y. H. Wu. Generalized multi-state k-out-of-n:G systems. IEEE Transactions on Reliability,2000,49(1):105-111.
[86]Z. G. Tian, M. J. Zuo, R. C. M. Yam. Multi-state k-out-of-n systems and their performance evaluation. IIE Transactions,2009,41(1):32-44.
[87]Z. G. Tian, R. C. M. Yam, M. J. Zuo, et al. Reliability bounds for multi-state k-out-of-n systems. IEEE Transactions on Reliability,2008,57(1):53-58.
[88]W. Li, M. J. Zuo. Reliability evaluation of multi-state weighted k-out-of-n systems. Reliability Engineering and System Safety,2008,93(1):160-167.
[89]S. V. Amari, M. J. Zuo, G. Dill. A fast and robust reliability evaluation algorithm for generalized multi-state k-out-of-n systems. IEEE Transactions on Reliability,2009,58(1): 88-97.
[90]Y. Ding, A. Lisnianski. Fuzzy universal generating functions for multi-state system reliability assessment. Fuzzy Sets and Systems,2008,159(3):307-24.
[91]Y. Ding, M. J. Zuo, A. Lisnianski, et al. Fuzzy multi-state systems:general definitions, and performance assessment. IEEE Transactions on Reliability,2008,57(4):589-594.
[92]B. Natvig, A. Streller. The steady-state behavior of multi-state monotone systems. Journal of Applied Probability,1984,21:826-835.
[93]M. Lanus, Y. Liang, K. S. Trivedi. Hierarchical composition and aggregation of state-based availability and performability models. IEEE Transactions on Reliability,2003,52(1):44-52.
[94]A. Lisnianski. Extended block diagram method for a multi-state system reliability assessment. Reliability Engineering and System Safety,2007,92(12):1601-1607.
[95]E. Zio. Computational methods for reliability and risk analysis. Singapore:World Scientific, 2009.
[96]J. E. Ramirez-Marquez, C. M. Rocco, B. A. Gebre, et al. New insights on multi-state component criticality and importance. Reliability Engineering and System Safety,2006, 91(8):894-904.
[97]E. Zio, L. Podofillini. Monte Carlo simulation analysis of the effects of different system performance levels on the importance of multi-state components. Reliability Engineering and System Safety,2003,82(1):63-73.
[98]G. Levitin. A universal generating function approach for the analysis of multi-state systems with dependent elements. Reliability Engineering and System Safety,2004,84(3):285-292.
[99]G. Levitin, L. Xing. Reliability and performance of multi-state systems with propagated failures having selective effect. Reliability Engineering and System Safety,2010,95(6): 655-661.
[100]W. Li. Reliability evaluation and optimal design of multi-state weighted systems:[Ph.D. Dissertation]. Alberta, Canada:University of Alberta,2008
[101]Z. Tian. Multi-state system reliability analysis and optimization:[Ph.D. Dissertation]. Alberta, Canada:University of Alberta,2007.
[102]Z. G. Tian, G. Levitin, M. J. Zuo. A joint reliability-redundancy optimization approach for multi-state series-parallel systems. Reliability Engineering and System Safety,2009,94(10): 1568-1576
[103]W. Li, M. J. Zuo. Optimal design of multi-state weighted k-out-of-n systems based on component design. Reliability Engineering and System Safety,2008,93(11):1673-1681
[104]G. Levitin, S. V. Amari. Optimal load distribution in series-parallel systems. Reliability Engineering and System Safety,2009,94(2):254-260.
[105]J. E. Ramirez-Marquez, C. M. Rocco. Evolutionary optimization technique for multi-state two-terminal reliability allocation in multi-objective problems. IIE Transcations,2010,42(8): 539-552.
[106]H. Yu, C. Chu, E. Chatelet, et al. Reliability optimization of a redundant system with failure dependencies. Reliability Engineering and System Safety,2005,92(12):1627-1634.
[107]C. Y. Li, X. Chen, X. S. Yi, et al. Heterogeneous redundancy optimization for multi-state series-parallel systems subject to common cause failures. Reliability Engineering and System Safety,2010,95(3):202-207.
[108]G. Levitin, A. Lisnianski, H. Ben-Haim, et al. Redundancy optimization for series-parallel multi-state systems. IEEE Transactions on Reliability,1998,47(2):165-172.
[109]J. E. Ramirez-Marquez, D. W. Coit. A heuristic for solving the redundancy allocation problem for multi-state series-parallel systems. Reliability Engineering and System Safety, 2004,83(3):341-349.
[110]N. Nahas, T. M. Dao. Harmony search algorithm:application to the redundancy optimization problem. Engineering Optimization,2010,42(9):845-861
[111]G. Levitin. Intelligence in reliability engineering, new metaheuristics, neural and fuzzy techniques in reliability. London:Springer,2007.
[112]R. Meziane, Y. Massim, A. Zeblah, et al. Reliability optimization using ant colony algorithm under performance and cost constraints. Electric Power Systems Research,2005,76(1-3): 1-8.
[113]V. K. Sharma, M. Agarwal, K. Sen. Optimal structure in heterogeneous multi-state series-parallel reliability systems. Economic Quality Control,2010,25(1):127-150.
[114]M. Ouzineb, M. Nourelfath, M. Gendreau. Tabu search for the redundancy allocation problem of homogenous series-parallel multi-state systems. Reliability Engineering and System Safety,2008,93(8):1257-1272.
[115]T. I. Kuo, S. H. Chen, J. E. Chiu. Tabu Search in the redundancy allocation optimization for multi-state series-parallel systems. Journal of the Chinese Institute of Industrial Engineers, 2007,24(3):210-218.
[116]Z. Tian, M. J. Zuo. Redundancy allocation for multi-state systems using physical programming and genetic algorithms. Reliability Engineering and System Safety,2006,91(9): 1049-1056.
[117]Z. Tian, M. J. Zuo, H. Z. Huang. Reliability-redundancy allocation for multi-state series-parallel systems. IEEE Transactions on Reliability,2008,57(2):303-310.
[118]H. A. Taboada, J. F. Espiritu, D. W. Coit. MOMS-GA:A multi-objective multi-state genetic algorithm for system reliability optimization design problem. IEEE Transactions on Reliability,2008,57(1):182-191.
[119]G. Levitin, A. Lisnianski. Joint redundancy and maintenance optimization for multi-state series-parallel systems. Reliability Engineering and System Safety,1999,64(1):33-42.
[120]G. Levitin, A. Lisnianski. Optimization of imperfect preventive maintenance for multi-state systems. Reliability Engineering and System Safety,2000,67(2):193-203.
[121]N. Nahas, A. Khatab, D. Ait-Kadi, et al. Extended great deluge algorithm for the imperfect preventive maintenance optimization of multi-state systems. Reliability Engineering and System Safety,2008,93(11):1658-1672.
[122]Y. L. Zhang, R. C. M. Yam, M. J. Zuo. Optimal replacement policy for a multi-state repairable system. Journal of the Operational Research Society,2002,53(3):336-341.
[123]Y. L. Zhang, R. C. M. Yam, M. J. Zuo. A bivariate optimal replacement policy for a multi-state repairable system. Reliability Engineering and System Safety,2007,92(4): 535-542.
[124]Y. L. Zhang, G. J. Wang. An optimal replacement policy for a multi-state degenerative simple system. Applied Mathematical Modelling,2010,34(12):4138-4150.
[125]L. Yeh. Monotone process maintenance model for a multi-state system. Journal of Applied Probability,2005,42(1):1-14.
[126]M. Nourelfath, D. Ait-Kadi. Optimization of series-parallel multi-state systems under maintenance policies. Reliability Engineering and System Safety,2007,92(12):1620-1626.
[127]C. M. Tan, N. Raghavan. A framework to practical predictive maintenance modeling for multi-state systems. Reliability Engineering and System Safety,2008,93(8):1138-1150.
[128]J. Wu, T. S. A. Ng, M. Xie, et al. Analysis of maintenance policies for finite life-cycle multi-state systems. Computers and Industrial Engineering,2010,59(4):638-646.
[129]I. W. Soro, M. Nourelfath, D. Ait-Kadi. Performance evaluation of multi-state degraded systems with minimal repairs and imperfect preventive maintenance. Reliability Engineering and System Safety,2010,95(2):65-69.
[130]C. C. Huang, J. Yuan. A two-stage preventive maintenance policy for a multi-state deterioration system. Reliability Engineering and System Safety,2010,95(11):1255-1260.
[131]A. Lisnianski, I. Frenkel, L. Khvatskin, et al. Maintenance contract assessment for aging systems. Quality and Reliability Engineering International,2008,24(5):519-531.
[132]Y. Ding, A. Lisnianski, I. Frenkel, et al. Optimal corrective maintenance contract planning for aging multi-state system. Applied Stochastic Models in Business and Industry,2009,25(5): 612-631.
[133]M. J. Kim, V. Makis. Optimal maintenance policy for a multi-state deteriorating system with two types of failures under general repair. Computers and Industrial Engineering,2009,57(1): 298-303.
[134]M. J. Zuo, B. Liu, D. N. P. Murthy. Replacement-repair policy for multi-state deteriorating products under warranty. European Journal of Operational Research,2000,123(3):519-530.
[135]W. Kuo, M. J. Zuo. Optimal reliability modeling:principles and applications. New York: John Wiley & Sons,2003.
[136]Y. Ding, M. J. Zuo, A. Lisnianski, et al. A framework for reliability approximation of multi-state weighted k-out-of-n systems. IEEE Transactions on Reliability,2010,59(2): 297-308.
[137]A. Lisnianski. Estimation of boundary points for continuum-state system reliability measures. Reliability Engineering and System Safety,2001,74(1):81-88.
[138]W. C. Yeh. A simple universal generating function method for estimating the reliability of general multi-state node networks. IIE Transactions,2009,41(1):3-11.
[139]K. Trivedi. Probability and statistics with reliability, queuing and computer science application. New York:John Wiley & Sons,2002.
[140]Z. An, H. Z. Huang, Y. Liu. A discrete stress-strength interference model based on universal generating function. Reliability Engineering and System Safety,2008,93(10):1485-1490.
[141]H. Z. Huang, Z. An. A discrete stress-strength interference model with stress dependent strength. IEEE Transactions on Reliability,2009,58(1):118-122.
[142]Z. W. An, H. Z. Huang, Z. L. Wang, et al. Discrete stress-strength interference model of reliability analysis under multi-operating conditions. Chinese Journal of Mechanical Engineering,2010,23(3):398-402.
[143]J. Y. Zhou, L. Y. Xie. Generating function approach to reliability analysis of structural systems. Science in China Series E-Technological Sciences,2009,52(10):2849-2858
[144]H. Pham, H. Z. Wang. Imperfect maintenance. European Journal of Operational Research, 1996,94(3):425-438.
[145]T. Nakagawa. Optimum policies when preventive maintenance is imperfect. IEEE Transactions on Reliability,1979,28(4):331-332.
[146]H. W. Block, W. S. Borges, T. H. Savits. Age dependent minimal repair. Journal of Applied Probability,1985,22(2):370-385.
[147]V. Makis, A. K. S. Jardine. Optimal replacement policy for a general model with imperfect repair. Journal of the Operational Research Society,1992,42(2):111-120.
[148]M. Kijima, H. Morimura, Y. Suzuki. Periodical replacement problem without assuming minimal repair. European Journal of Operational Research,1988,37(2):194-203.
[149]M. Kijima. Some results for repairable systems with general repair. Journal of Applied Probability,1989,26(1):89-102.
[150]L. Doyen,O. Gaudoin. Classes of imperfect repair models based on reduction of failure intensity or virtual age. Reliability Engineering and System Safety,2004,84(1):45-56
[151]M. A. K. Malik. Reliable preventive maintenance scheduling. AⅡE Transactions,1979,11(3): 221-228.
[152]D. Lin, M. J. Zuo, R. C. M. Yam. General sequential imperfect preventive maintenance models. International Journal of Reliability, Quality and Safety Engineering,2000,7(3): 253-266.
[153]Y. Lam. A note on the optimal replacement problem. Advances in Applied Probability,1988, 20(2):479-482.
[154]H. Z. Wang, H. Pham. A quasi renewal process and its application in the imperfect maintenance. International Journal of Systems Science,1996,27(10):1055-1062.
[155]H. Z. Wang, H. Pham. Reliability and optimal maintenance. London:Springer,2006.
[156]S. Wu, M. J. Zuo. Linear and nonlinear preventive maintenance models. IEEE Transactions Reliability,2010,59(1):242-249.
[157]M. Bartholomew-Biggs, M. J. Zuo, X. H. Li. Modelling and optimizing sequential imperfect preventive maintenance. Reliability Engineering and System Safety,2009,94(1):53-62.
[158]Y. Liu, H. Z. Huang, X. Zhang. Data-driven approach for imperfect maintenance model selection. Proceedings of Annual Reliability and Maintainability Symposium,2011RM0200, 2011.
[159]H. C. Wu. Fuzzy reliability estimation using Bayesian approach. Computers and Industrial Engineering,2004,46(3):467-493.
[160]H. Z. Huang, M. J. Zuo, Z. Q. Sun. Bayesian reliability analysis for fuzzy lifetime data. Fuzzy Sets and Systems,2006,157(12):1674-1686.
[161]Y. Liu, Y. Li, H. Z. Huang, et al. Optimal preventive maintenance policy under fuzzy Bayesian reliability assessment environments. HE Transactions,2010,42(10):734-745.
[162]A. K. Verma, A. Srividya, R. P. Gaonkar. Fuzzy dynamic reliability evaluation of a deteriorating system under imperfect repair. International Journal of Reliability, Quality and Safety Engineering,2004,11(4):387-398.
[163]H. I. Huang, C. H. Lin, J. C. Ke. Two-unit repairable systems with common-cause shock failures and fuzzy parameters:parametric programming approach. International Journal of Systems Science,2008,39(5):449-459.
[164]L. A. Zadeh. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems,1978, 1(1):3-28.
[165]L. A. Zadeh. Fuzzy sets. Information and Control,1965,8(3):338-353.
[166]A. Saltelli, M. Ratto, T. Andres, et al. Global sensitivity analysis:the primer. New York:John Wiley & Sons,2008
[167]D. Allaire, K. Willcox. Surrogate modeling for uncertainty assessment with application to aviation environmental system models. AIAA Journal,2010,48(8):1791-1803.
[168]B. Krzykacz. Samos:a computer program for the derivation of empirical sensitivity measures of results from large computer models. Technical Report GRS-A-1700, Garching, Germany, 1990.
[169]J. D. Cawlfield, M. C. Wu. Probabilistic sensitivity analysis for one-dimensional reactive transport in porous media. Water Resources Research,1993,29(3):661-672.
[170]A. Saltelli, S. Tarantola, K. P. S. Chan. A quantitative model-independent method for global sensitivity analysis of model output. Technometrics,1999,41(1):39-56.
[171]C. Xu, G. Z. Gertner. A general first-order global sensitivity analysis method. Reliability Engineering and System Safety,2008,93(7):1060-1071
[172]T. A. Mara. Extension of the RBD-FAST method to the computation of global sensitivity indices. Reliability Engineering and System Safety,2009,94(8):1274-1281
[173]I. M. Sobol. Sensitivity analysis for nonlinear mathematical models. Mathematical Modeling and Computational Experiment,1993,1:407-414.
[174]I. M. Sobol. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation,2001,55(1-3):271-280.
[175]H. Liu, W. Chen, A. Sudjianto. Relative entropy based method for probabilistic sensitivity analysis in engineering design. ASME Journal of Mechanical Design,2006,128(3):326-336.
[176]K. Chan, A. Saltelli, S. Tarantola. Sensitivity analysis of model output:variance-based methods make the difference. Proceedings of the 1997 Winter Simulation Conference, 261-268,1997.
[177]J. C. Helton. Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal. Reliability Engineering and System Safety,1993, 42(2-3):327-367.
[178]C. I. Reedijk. Sensitivity analysis of model output:performance of various local and global sensitivity measures on reliability problems:[M.S. Dissertation]. Delft, Nederland:Delft University of Technology,2000.
[179]W. Chen, R. Jin, A. Sudjianto. Analytical variance-based global sensitivity analysis in simulation-based design under uncertainty. ASME Journal of Mechanical Design,2005, 127(5):875-886.
[180]B. Sudret. Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering and System Safety,93(7):964-979.
[181]H. Z. Wang. A survey of maintenance policies of deteriorating systems. European Journal of Operational Research,2002,139(3):469-489.
[182]C. R. Cassady, E. A. Pohl, W. P. M. Jr. Selective maintenance modeling for industrial system. Journal of Quality in Maintenance Engineering,2001,7(2):104-117.
[183]W. F. Rice, C. R. Cassady, J. A. Nachlas. Optimal maintenance plans under limited maintenance time. Proceedings of the Seventh Industrial Engineering Research Conference, 1998.
[184]C. R. Cassady, W. P. M. Jr, E. A. Pohl. Selective maintenance for support equipment involving multiple maintenance actions. European Journal of Operational Research,2001, 129(2):252-258.
[185]K. Schneider, C. R. Cassady. Fleet performance under selective maintenance. Proceedings of Annual Reliability and Maintainability Symposium,571-576,2004.
[186]R. Rajagopalan, C. R. Cassady. An improved selective maintenance solution approach. Journal of Quality in Maintenance Engineering,2006,12(2):172-185.
[187]T. Lust, O. Roux, F. Riane. Exact and heuristic methods for the selective maintenance problem. European Journal of Operational Research,2009,197(3):1166-1177.
[188]I. M. Iyoob, C. R. Cassady, E. A. Pohl. Establishing maintenance resource levels using selective maintenance. The Engineering Economist,2006,51(2):99-114.
[189]K. Schneider, L. M. Maillart, C. R. Cassady, et al. Selective maintenance decision-making over extended planning horizons. IEEE Transactions Reliability,2009,58(3):462-469.
[190]C. Chen, M. Q. H. Meng, M. J. Zuo. Selective maintenance optimization for multi-state systems. Proceedings of IEEE Canadian Conference on Electrical and Computer Engineering, 1477-1482,1999.
[191]C. H. Lie, Y. H. Chun. An algorithm for preventive maintenance policy. IEEE Transactions Reliability,1986,35(1):71-75.
[192]G. Levitin. Genetic algorithms in reliability engineering. Reliability Engineering and System Safety,2006,91(9):975-976.
[193]H. I. H. Saravanamuttoo, G. F. C. Rogers, H. Cohen, et al. Gas turbine theory (6th Edition). Harlow:Pearson Education,2009.
[194]刘长富,邓明,等.航空发动机结构分析.西安：西北工业大学出版社,2006.
[195]Y. Liu, H. Z. Huang. Comment on "A framework to practical predictive maintenance modeling for multi-state systems" by Tan CM. and Raghavan N. [Reliab Eng Syst Saf 2008;93(8):1138-50]. Reliability Engineering and System Safety,2009,94(3):776-780.
[196]F. Camci. System maintenance scheduling with prognostics information using genetic algorithm. IEEE Transactions Reliability,2009,58(3):539-552.
[197]C. M. Tan, N. Raghavan. Reply to comments on "A framework to practical predictive maintenance modeling for multi-state systems". Reliability Engineering and System Safety, 2009,94(3):781-782.
[198]Y. Liu, K. C. Kapur. Customer's cumulative experience measures for reliability of non-repairable aging multi-state systems. Quality, Technology and Quantitative Management, 2007,4(2):225-234.
[199]Y. Liu, K. C. Kapur. New model and measurement for reliability of multi-state systems. Handbook of performability engineering, London:Springer,2008.
[200]T. Sun, G. C. Zhao, P. B. Luh, et al. Optimization of joint replacement policies for multipart systems by a rollout framework. IEEE Transactions on Automation Science and Engineering, 2008,5(4):609-619.
[201]W. J. Hopp, Y. L. Kuo. Heuristics for multicomponent joint replacement; applications to aircraft engine maintenance. Naval Research Logistics,1998,45(5):435-458.
[202]H. S. Lee, M. M. Srinivasan. Optimal replacement policies for systems with multiple standby components. IEEE Transactions on Reliability,1994,43(3):414-422.
[203]T. W. Archibald, R. Dekker. Modified block-replacement for multiple-component systems IEEE Transactions on Reliability,1996,45(1):75-83.
[204]M. S. Moustafa, E. Y. A. Makasoud, S. Sadek. Optimal major and minimal maintenance policies for deteriorating systems. Reliability Engineering and System Safety,2004,83(3): 363-368.
[205]M. Marseguerra, E. Zio, L. Podofillini. Condition-based maintenance optimization by means of genetic algorithms and Monte Carlo simulation. Reliability Engineering and System Safety, 2002,77(2):151-166
[206]Y. C. Liang, A. E. Smith. An ant colony optimization algorithm for the redundancy allocation problem (RAP). IEEE Transactions on Reliability,2004,53(3):417-423.
[207]M. Samrout, F. Yalaoui, E. Chatelet, et al. New methods to minimize the preventive maintenance cost of series-parallel systems using ant colony optimization. Reliability Engineering and System Safety,2005,89(3):346-354.
[208]N. Nahas, M. Mourelfath. Ant system for reliability optimization of a series system with multiple-choice and budget constraints. Reliability Engineering and System Safety,2005, 87(1):1-12.
[209]J. H. Zhao, Z. Liu, M. T. Dao. Reliability optimization using multiobjective ant colony system approaches. Reliability Engineering and System Safety,2007,92(1):109-120.
[210]V. Maniezzo. Exact and approximate nondeterministic tree-search procedures for the quadratic assignment problem. INFORMS Journal on Computing,1999,11(4):358-369.
[211]G. Levitin, T. Zhang, M. Xie. State probability of a series-parallel repairable system with two-types of failure states. International Journal of Systems Science,2006,37(14-15): 1011-1020.
[212]P. Yu, J. J. Song, C. R. Cassady. Parameter estimation for a repairable system under imperfect maintenance. Proceedings of Annual Reliability and Maintainability Symposium,13D-3, 2009.
[213]W. Kuo, R. Wan. Recent advances in optimal reliability allocation. IEEE Transactions on Systems, Man and Cybernetics, Part A:Systems and Humans,2007,77(2):143-156.
[214]W. Kuo, H. Lin, Z. Xu, et al. Reliability optimization with the Lagrange multiplier and branch-and-bound technique. IEEE Transactions on Reliability,1987,36(5):624-630.
[215]C. S. Sung, Y. K. Cho. Branch-and-bound redundancy optimization for a series system with multiple-choice constraints. IEEE Transactions on Reliability,1999,48(2):108-117.
[216]M. Hikita, Y. Nakagawa, K. Nakashima, et al. Reliability optimization of systems by a surrogate-constraints algorithm. IEEE Transactions on Reliability,1992,41(3):472-480.
[217]C. H. Ha, W. Kuo. Multi-path approach for reliability-redundancy allocation using a scaling method. Journal of Heuristics,2005,11(3):201-217.
[218]D. W. Coit, A. E. Smith. Reliability optimization of series-parallel systems using a genetic algorithm. IEEE Transactions on Reliability,1996,45(2):254-260.
[219]S. Kulturel-Konak, A. E. Smith, D. W. Coit. Efficiently solving the redundancy allocation problem using tabu search. HE Transactions,2003,35(6):515-526.
[220]M. Agarwal, R. Gupta. Homogeneous redundancy optimization in multi-state series-parallel systems:A heuristic approach. IIE Transactions,2007,39(3):277-289.
[221]U. K. D. Kumar, J. E. Ramirez-Marquez, D. Nowicki, et al. Reliability and maintainability allocation to minimize total cost of ownership in a series-parallel system. Journal of Risk and Reliability,2007,221(2):133-140.
[222]K. Y. Cai. Fuzzy reliability theories. Fuzzy Sets and Systems,1991,40(3):510-511.
[223]K. Y. Cai, C. Y. Wen, M. L. Zhang. Fuzzy reliability modeling of gracefully degradable computing systems. Reliability Engineering and System Safety,1991,33(1):141-157.
[224]H. Z. Huang. Reliability analysis method in the presence of fuzziness attached to operation time. Microelectronics and Reliability,1995,35(12):1483-1487.
[225]H. Z. Huang, X. Tong, M. J. Zuo. Posbist fault tree analysis of coherent systems. Reliability Engineering and System Safety,2004,84(2):141-148.
[226]H. C. Wu. Bayesian system reliability assessment under fuzzy environment. Reliability Engineering and System Safety,2004,83(3):277-86.
[227]J. C. Ke, H. I. Huang, C. H. Lin. Fuzzy analysis for steady-state availability:a mathematical programming approach. Engineering Optimization,2006,38(8):909-921.
[228]D. Pandey, S. K. Tyagi. Profust reliability of a gracefully degradable system. Fuzzy Sets and Systems,2007,158(7):794-803.
[229]E. Popova, H. C. Wu. Renewal reward processes with fuzzy rewards and their application to T-age replacement policies. European Journal of Operation Research,1999,117(3):606-617.
[230]S. M. Chen. Fuzzy system reliability analysis using fuzzy number arithmetic operations. Fuzzy Sets and Systems,1994,64(1):31-38.
[231]K. H. Lee. First course on fuzzy theory and applications. London:Springer,2005.
[232]S. Murakami, S. Maeda, S. Imamura. Fuzzy decision analysis on the development of centralized regional energy control system. Proceedings of the IFAC Symposium on Fuzzy Information, Knowledge Representation and Decision Analysis,363-368,1983.
[233]C. H. Cheng. A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets and Systems,1998,95(3):307-317.
[234]T. S. Liou, M. J. J. Wang. Ranking fuzzy numbers with integral value. Fuzzy Sets and Systems,1992,50(3):247-255.
[235]H. M. Kim, D. G. Rideout, P. Y. Papalambros, et al. Analytical target cascading in automotive vehicle design. ASME Journal of Mechanical Design,2003,125(3):481-489.
[236]H. Liu, W. Chen, M. Kakkolaras, et al. Probabilistic analytical target cascading:a moment matching formulation for multilevel optimization under uncertainty. ASME Journal of Mechanical Design,2006,128(4):991-1000.
[237]X. Du, W. Chen. Collaborative reliability analysis under the framework of multidisciplinary systems design. Optimization and Engineering,2005,6(1):63-84.
[238]H. M. Kim, D. K. D. Kumar, W. Chen, et al. Target exploration for disconnected feasible regions in enterprise-driven multilevel product design. AIAA Journal,2006,44(1):67-77
[239]M. Kokkolaras, Z. P. Mourelatos, P. Y. Papalambros. Design optimization of hierarchically decomposed multilevel system under uncertainty. ASME Journal of Mechanical Design,2006, 128(2):503-508.
[240]R. S. Krishnamachari, P. Y. Papalambros. Hierarchical decomposition synthesis in optimal systems design. ASME Journal of Mechanical Design,1997,119(4):448-457.
[241]D. Z. Chen, C. P. Liu. A hierarchical decomposition scheme for the topological synthesis of articulated gear mechanisms. ASME Journal of Mechanical Design 1999,121(2):256-263
[242]D. Li, Y. Y. Haimes. A decomposition method for optimization of large-system reliability. IEEE Transactions on Reliability,1994,41(2):183-189.
[243]X. L. Zhang, H. Z. Huang, Y. Liu. A hierarchical decomposition approach for large system reliability allocation. Eksploatacja i Niezawodnosc-Maintenance and Reliability,2009,43, 32-37.
[244]Z. Wang, K. Tang, X. Yao. A memetic algorithm for multi-level redundancy allocation. IEEE Transactions on Reliability,2010,59(4):754-765.
[245]X. Yin, W. Chen, A. To, et al. Statistical volume element method for predicting microstructure-constitutive property relations. Computer Methods in Applied Mechanics and Engineering,2008,197(43):3516-3529.
[246]X. Yin, S. Lee, W. Chen, et al. Efficient random field uncertainty propagation in design using multiscale analysis. ASME Journal of Mechanical Design,2009,131(2):021006.
[247]W. Chen, X. Yin, S. Lee, et al. A multiscale design methodology for hierarchical systems with random field uncertainty. ASME Journal of Mechanical Design,2010,132(4):041006.
[248]H. Choi, D. L. McDowell, J. K. Allen, et al. An inductive design exploration method for robust multiscale materials design. ASME Journal of Mechanical Design,2008,130(3): 031402
[249]G. B. Olson. Computational design of hierarchically structured materials. Science,1997, 277(5330):1237-1242.
[250]H. M. Kim, N. F. Michelena, P. Y. Papalambros, et al. Target cascading in optimal system design. ASME Journal of Mechanical Design,2003,125(3):474-480.
[251]J. Han, P. Y. Papalambros. A sequential linear programming coordination algorithm for analytical target cascading. ASME Journal of Mechanical Design,2010,132(2):021003.
[252]Y Li, Z. Lu, J. J. Michalek. Diagonal quadratic approximation for parallelization of analytical target cascading. ASME Journal of Mechanical Design,2008,130(5):0514021.
[253]W. Y. Yuna, Y. M. Song, H. G. Kim. Multiple multi-level redundancy allocation in series systems. Reliability Engineering and System Safety,2007,92(3):308-313.
[254]R. Kumar, K. Izui, M. Yoshimura, et al. Optimal multilevel redundancy allocation in series and series-parallel systems. Computers and Industrial Engineering,2009,57(1):169-180.
[255]X. Yin, W. Chen. A hierarchical statistical sensitivity analysis method for complex engineering systems design. ASME Journal of Mechanical Design,2008,130(7):071402.
[256]F. Xiong, X. Yin, W. Chen, et al. Enhanced probabilistic analytical target cascading with application to multi-scale design. Engineering Optimization,2010,42(6):581-592.
[257]A. Saltelli, K. Chan, E. M. Scott. Sensitivity analysis. New York:John Wiley & Sons,2000.
[258]H. Liu, W. Chen, A. Sudjianto. Probabilistic sensitivity analysis methods for design under uncertainty. Proceedings of 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA2004-4589,2004.
[259]C. Xu, G. Z. Gertner. Uncertainty and sensitivity analysis for models with correlated parameters. Reliability Engineering and System Safety,2008,93(10):1563-1573.
[260]C. Xu, G. Z. Gertner. Extending a global sensitivity analysis technique to models with correlated parameters. Computational Statistics and Data Analysis,2007,51(12):5579-5590.
[261]T. Homma, A. Saltelli. Importance measures in global sensitivity analysis of nonlinear models. Reliability Engineering and System Safety,1996,52(1):1-17.
[262]M. D. McKay. Nonparametric variance-based methods of assessing uncertainty importance. Reliability Engineering and System Safety,1997,57(3):267-279.
[263]M. P. R. Haaker, P. J. T. Verheijen. Local and global sensitivity analysis for a reactor design with parameter uncertainty. Chemical Engineering Research and Design,2004,82(5): 591-598.
[264]A. Saltelli, S. Tarantola. On the relative importance of input factors in mathematical models: safety assessment for nuclear waste disposal. Journal of the American Statistical Association, 2002,97(459):702-709.
[265]R. L. Imana, M. E. Johnson, T. A. Schroeder. Assessing hurricane effects. Part 1. Sensitivity analysis. Reliability Engineering and System Safety,2002,78(2):131-145.
[266]R. L. Imana, M. E. Johnson, T. A. Schroeder. Assessing hurricane effects. Part 2. Uncertainty analysis. Reliability Engineering and System Safety,2002,78(2):147-155.
[267]J. Jacques, C. Lavergne, N. Devictor. Sensitivity analysis in present of model uncertainty and correlated inputs. Reliability Engineering and System Safety,2006,91(10):1126-1134.
[268]W. E, B. Engquist, X. Li, et al. The heterogeneous multiscale method:a review. Journal of Communications in Computational Physics,2007,2(3):367-450.
[269]S. Hao, W. K. Liu, B. Moran, et al. Multi-scale constitutive model and computational framework for the design of ultra-high strength, high toughness steels. Computer Methods in Applied Mechanics and Engineering,2004,193(17-20):1865-1908.
[270]R. Jin, W. Chen, T. W. Simpson. Comparative studies of metamodelling techniques under multiple modelling criteria. Structural and Multidisciplinary Optimization,2001,23(1):1-13.
[271]D. C. Cox. An analytical method for uncertainty analysis of nonlinear output function, with application to fault-tree analysis. IEEE Transactions on Reliability,1982, R-31(5):465-468.
[272]T. Jin. Hierarchical variance decomposition of system reliability with duplicated components. IEEE Transactions on Reliability,2008,57(4):564-573.
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