LISNIANSKI A , FRENKEL I , DING Y . Multi-state system reliability analysis and optimization for engineers and industrial managers [M ] . London,UK : Springer , 2010 .

史跃东 , 徐一帆 , 金家善 . 装备复杂系统多状态可靠性分析与评估技术 [M ] . 北京 : 科学出版社 , 2017 .

SHI Y D , XU Y F , JIN J S . Multistate reliability analysis and evaluation technology for complex equipment systems [M ] . Beijing : Science Press , 2017 . (in Chinese)

BIRNBAUM Z W . On the importance of different components in a multicomponent system [J ] . Multivariate Analysis II , 1969 ,1: 581 - 592 .

MIZIULA P , NAVARRO J . Birnbaum importance measure for reliability systems with dependent components [J ] . IEEE Transactions on Reliability , 2019 , 68 : 39 - 50 .

DO P , B’ERENGUER C . Conditional reliability-based importance measures [J ] . Reliability Engineering and System Safety , 2020 , 193 : 106633 .

SI S B , LIU M L , JIANG Z Y , et al. System reliability allocation and optimization based on generalized Birnbaum importance measure [J ] . IEEE Transactions on Reliability , 2019 , 68 : 831 - 843 .

MESHKAT R S , MAHMOUDI E . Joint reliability and weighted importance measures of a k-out-of-n system with random weights for components [J ] . Journal of Computational and Applied Mathematics , 2017 , 326 : 273 - 283 .

何爱民 , 赵先 , 崔利荣 , 等 . 线形可重叠的m-consecutive-k-out-of-n:F系统可靠性和单元重要度研究 [J ] . 兵工学报 , 2009 , 30 ( 增刊 ): 135 - 138 .

HE A M , ZHAO X , CUI L R , et al. A study on reliability and component importance of linear overlapping m-consecutive-k-out-of-n: F system [J ] . Acta Armamentarii , 2009 , 30(S) : 135 - 138 . (in Chinese)

吕弘 , 袁海文 , 张莉 , 等 . 基于模式重要度的航空电源系统可靠性估计 [J ] . 航空学报 , 2010 , 31 ( 3 ): 609 - 613 .

LÜ H , YUAN H W , ZHANG L , et al. Aircraft electrical power system reliability estimation based on pattern importance [J ] . Acta Aeronautica et Astronautica Sinica , 2010 , 31 ( 3 ): 609 - 613 . (in Chinese)

白光晗 , 张弛 , 兑红炎 , 等 . 无人机集群任务可靠性建模及重要度分析 [J ] . 机械工程学报 , 2022 , 58 ( 10 ): 361 - 373 . DOI: 10.3901/JME.2022.10.361 http://doi.org/10.3901/JME.2022.10.361 面对复杂、高对抗的战场环境,传统以平台为中心的静态可靠性评估难以满足无人机集群执行多样化任务的可靠性分析需求。由于无人机集群本身具有一定的冗余性,对其可靠性的研究重点已转变为以任务为中心的可靠性。及时、准确评估无人机集群任务可靠性,并分析集群的薄弱环节,对于任务规划、决策制定和提高任务成功率具有重要意义。根据集群的编队队形和任务,建立基于一维线性连续n中取k系统和二维连续(m, n)中取(r, s)系统的无人机集群任务可靠性模型,并得出当集群中不同位置的某架或某些无人机失效时对集群任务可靠性变化以及性能的影响。然后分别建立无人机集群在一维、二维空间的Birnbaum重要度和综合重要度分析模型,确定集群中的薄弱环节和关键无人机。最后基于不同编队形式的无人机集群任务可靠性算例,分析无人机失效对集群任务可靠性以及性能的影响,验证了提出方法的正确性和有效性。

BAI G H , ZHANG C , DUI H Y , et al. Mission reliability modeling and importance analysis of UAV swarm [J ] . Journal of Mechanical Engineering , 2022 , 58 ( 10 ): 361 - 373 . (in Chinese) DOI: 10.3901/JME.2022.10.361 http://doi.org/10.3901/JME.2022.10.361 Traditional platform-centric static reliability assessment cannot meet the reliability analysis requirements of UAV swarms for diversified tasks under complex and confrontational battlefield. Due to the redundancy of UAV swarms, the research focus on its reliability has changed to mission-centric reliability, which is of great significance for mission planning, decision-making and improving mission success rate. According to the formation and task of the swarm, a mission reliability model of the UAV swarm based on the one-dimensional linear continuous <i>k</i>-out-of-<i>n</i> system and the two-dimensional linear continuous (<i>r, s</i>)-out-of- (<i>m, n</i>) system is developed. The influence on the mission reliability change and performance of the swarm was obtained when one or several UAVs fail. Next, the Birnbaum importance and Integrated importance measure of UAV swarms in one-dimensional and two-dimensional spaces are proposed respectively. The impact of changes in the reliability of UAVs in different locations on the performance of the swarm is analyzed. Then weak links and key UAV in the swarm are determined. Finally, based on the case study of UAV swarm in different formations, the impact of UAVs failure on swarm mission reliability and performance is analyzed and the correctness and effectiveness of the proposed method are verified.

MOHAM L R , DAOUD A K . A new integrated strategy for optimizing the maintenance cost of complex systems using reliability importance measures [J ] . Journal of Production Research , 2024 , 62 ( 11 ): 4143 - 4164 .

王成 , 许建新 , 张振明 , 等 . 基于成本效益重要度的复杂系统可靠性保障策略 [J ] . 西北工业大学学报 , 2020 , 38 ( 6 ): 1316 - 1321 .

WANG C , XU J X , ZHANG Z M , et al. Reliability guarantee strategy for complex system based on cost-benefit importance [J ] . Journal of Northwestern Polytechnical University , 2020 , 38 ( 6 ): 1316 - 1321 . (in Chinese)

LIU M L , WANG D , ZHAO J B , et al. Importance measure construction and solving algorithm oriented to the cost-constrained reliability optimization model [J ] . Reliability Engineering and System Safety , 2022 , 222 : 108406 .

LIU M L , WANG D , SI S B . Mixed reliability importance-based solving algorithm design for the cost-constrained reliability optimization model [J ] . Reliability Engineering and System Safety , 2023 , 237 : 109363 .

史跃东 , 徐一帆 , 金家善 . 基于逻辑报酬矩阵的多状态系统可靠性评估 [J ] . 系统工程理论与实践 , 2019 , 39 ( 5 ): 1315 - 1325 .

SHI Y D , XU Y F , JIN J S . Reliability assessment for multi-state system based on logic reward matrix [J ] . Systems Engineering-Theory & Practice , 2019 , 39 ( 5 ): 1315 - 1325 . (in Chinese)

史跃东 , 金家善 , 徐一帆 . 半马尔可夫跃迁历程下装备复杂系统多状态可靠性分析与评估 [J ] . 系统工程与电子技术 , 2019 , 41 ( 2 ): 445 - 453 .

SHI Y D , JIN J S , XU Y F . Study on multi-state reliability analysis and assessment for complex technical system under semi-Markov processes [J ] . Systems Engineering and Electronics , 2019 , 41 ( 2 ): 445 - 453 . (in Chinese)

史跃东 , 金家善 , 柴凯 . 大型复杂系统可靠性快速评估算法 [J ] . 系统工程与电子技术 , 2022 , 44 ( 10 ): 3282 - 3290 . DOI: 10.12305/j.issn.1001-506X.2022.10.35 http://doi.org/10.12305/j.issn.1001-506X.2022.10.35 开展装备系统可靠性评估工作, 对于发挥装备固有性能、提升装备使用效能、降低装备管控风险, 具有重要工程应用价值。针对大型装备复杂系统, 通过构建面向不同耦合结构的极限序列核和极限可靠度逼近函数, 探索了一类计算资源要求低, 计算便捷, 且逼近精度满足工程需要的多状态可靠性建模、分析与快速评估方法。案例研究表明: 算法突破了装备复杂系统大维度可靠性解算技术瓶颈, 提升了可靠性评估效率, 且评估与风险预报效果好; 算法丰富了装备复杂系统多状态可靠性建模、分析与评估体系, 可为可靠性工程的设计、使用与管理人员, 提供前沿理论储备和工程技术借鉴。

SHI Y D , JIN J S , CHAI K . Multi-state reliability fast evaluation for large-scale complex system [J ] . Systems Engineering and Electronics , 2022 , 44 ( 10 ): 3282 - 3290 . (in Chinese)

陈童 , 胡斌 , 狄鹏 . 舰船发电系统多状态可靠性马尔可夫报酬模型 [J ] . 兵工学报 , 2023 , 44 ( 10 ): 3177 - 3186 . DOI: 10.12382/bgxb.2022.0558 http://doi.org/10.12382/bgxb.2022.0558 针对舰船发电系统的多状态特征,考虑舰船计划维修间隔期对系统可靠性参数的影响,利用马尔可夫报酬模型构建冷储备结构的发电系统状态转移矩阵、报酬矩阵、报酬函数和系统需求满足函数,通过对报酬矩阵元素的合理赋值,获得系统区间可用度、平均可工作时间、平均停机时间、平均故障次数、计划维修间隔期内系统可靠度等参数,并通过算例验证模型正确性和适用性,分析系统计划维修间隔时间、单机组平均修复时间等指标对系统可靠性参数的影响,为研究舰船发电系统可靠性设计提供建模工具,为合理安排舰船装备维修结构提供技术支持。研究结果验证了马尔可夫报酬模型在复杂多状态系统可靠性建模和计算方面的便捷性和灵活性。

CHEN T , HU B , DI P . Multi-state system reliability analysis for ship power generation system based on Markov reward model [J ] . Acta Armamentaii , 2023 , 44 ( 10 ): 3177 - 3186 . (in Chinese)

XU Y F , SHI Y D , XIONG Z H , et al. Multi-state reliability assessment for shipboard hybrid turbine-diesel generation system with redundancy and aging effects [J ] . Quality and Reliability Engineering International , 2023 , 39 ( 3 ): 1001 - 1023 .

SIBEL Y , OZGE E G . Reliability analysis of repairable multistate phased mission systems with Markov approach based on states [J ] . Engineering Computations , 2023 , 40 ( 5 ): 1041 - 1062 .

YIN J , YE Z S , CUI L R . Reliability and optimal replacement policy of a multistate system under Markov renewal shock model [J ] . IEEE Transactions on Reliability , 2024 , 73 : 1 - 12 .

HUANG C H , HUANG D H , LIN Y K . A novel approach to predict network reliability for multistate networks by a deep neural network [J ] . Quality Technology & Quantitative Management , 2022 , 19 ( 3 ): 362 - 378 .

PAWEL M K . An efficient algorithm for the reliability evaluation of multistate flow networks under budget constraints [J ] . IISE Transactions , 2023 , 55 ( 11 ): 1091 - 1102 .

YANG L C , WANG C X , LING C Y , et al. Reliability evaluation of an imprecise multistate system with mixed uncertainty [J ] . IEEE Transactions on Reliability , 2024 , 73 : 478 - 491 .

CHANKO V M . On birnbaum type joint importance measures for multistate reliability systems [J ] . Communications in Statistics Theory and Methods , 2023 , 52 ( 9 ): 2799 - 2818 .

田宏 , 陈宝智 , 五穹 , 等 . 多态系统可靠性及元素的不确定性重要度 [J ] . 东北大学学报(自然科学版) , 2000 , 21 ( 6 ): 634 - 638 .

TIAN H , CHEN B Z , WU Q , et al. Multistate system reliability and uncertain importance of its component [J ] . Journal of Northeastern and University(Natural Science) , 2000 , 21 ( 6 ): 634 - 638 . (in Chinese)

LEVITIN G . The universal generating function in reliability analysis and optimization [M ] . London , UK:Springer , 2005 .