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1

MO, Yu-Chang. "Mission Reliability Analysis of Generalized Phased Mission Systems." Journal of Software 18, no. 4 (2007): 1068. http://dx.doi.org/10.1360/jos181068.

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2

Jia, Xisheng, Wenbin Cao, and Qiwei Hu. "Selective maintenance optimization for random phased-mission systems subject to random common cause failures." Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 233, no. 3 (August 13, 2018): 379–400. http://dx.doi.org/10.1177/1748006x18791724.

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In both industrial and military fields, there is such a kind of complicated system termed as phased-mission system, which executes missions composed of several different phases in sequence. The structure, failure behavior, and working conditions of such a system may change from phase to phase. The duration of each phase of such a system involved is random and follows a probability distribution, and the system may suffer some events resulting in simultaneous failures of different elements with different probabilities. In order to guarantee such a system completes the phased-mission successfully, a selective maintenance model for random phased-mission systems subject to random common cause failures is proposed to optimally identify a subset of maintenance activities to be performed on some elements of the system. Thereinto, a novel analytic model is developed to estimate the probability of the maintained random phased-mission system successfully completing the phased-mission, and we compare it with a well-known Monte Carlo Simulation approach. Finally, the proposed selective maintenance model has been successfully applied to an artillery weapon system. Comparative analysis is carried out to compare the proposed model with the traditional ones, including selective maintenance models for deterministic phased-mission systems and deterministic single-phase mission systems. The results show that ignoring some mission properties (e.g. randomness and multiple phases) in selective maintenance optimization will lead to (1) incorrect system and mission modeling, (2) incorrect computation of the probability of the random phased-mission system successfully completing a mission, and/or (3) nonoptimal selective maintenance options.
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3

Dai, Yuanshun, Gregory Levitin, and Liudong Xing. "Structure Optimization of Nonrepairable Phased Mission Systems." IEEE Transactions on Systems, Man, and Cybernetics: Systems 44, no. 1 (January 2014): 121–29. http://dx.doi.org/10.1109/tsmc.2013.2256127.

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4

Mo, Yuchang, Jinping Liao, Liudong Xing, and Xuli Liu. "Efficient Mincuts Identification for Phased-Mission Systems." IEEE Access 8 (2020): 223652–60. http://dx.doi.org/10.1109/access.2020.3045283.

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5

Park, Kyung S., and Young K. Yoo. "Reliability apportionment for phased-mission oriented systems." Reliability Engineering & System Safety 27, no. 3 (January 1990): 357–64. http://dx.doi.org/10.1016/0951-8320(90)90006-9.

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6

Zhao, Jiangbin, Zhiqiang Cai, Weitao Si, and Shuai Zhang. "Mission success evaluation of repairable phased-mission systems with spare parts." Computers & Industrial Engineering 132 (June 2019): 248–59. http://dx.doi.org/10.1016/j.cie.2019.04.038.

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7

Hu, Qiguo, and Jinyin He. "Path Sets Combination Method for Reliability Analysis of Phased-Mission Systems Based on Cumulative Exposure Model." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 36, no. 5 (October 2018): 995–1003. http://dx.doi.org/10.1051/jnwpu/20183650995.

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The modeling of phased-mission systems is difficult and the solving process is complex because of the relevance of the phase tasks and the sharing of components existing in different phases or between phases. To solve the problem, based on the cumulative exposure model, the path sets combination method of phased-mission systems is proposed. Aiming at the problem of the cross-stage correlation of components and its different failure rate in each phase, the cumulative exposure model considering the historical damage of components is used to solve by obtaining the cumulative damage distribution of each component in each phase. Firstly, a phased-mission systems reliability model is build by mapping phased-mission system fault trees into a Bayesian network. By traversing the Bayesian network, the minimal path sets of each phase are obtained. Secondly, the disjoint formulas introduced by variable elimination method are used to do the disjoint operation of the minimal path sets of each phase and the conditional probability relations of the common components are used to reduce the minimal path sets scale. Finally, the minimum disjoint path sets of each phase are combined and summed according to the component conditional probability relation. The path sets combination method of phased-mission systems avoids the large conditional probability table, large storage and large computation problems caused by the excessive discrete states in the traditional Bayesian method and the problem that the PMS-BDD method has strict requirements for variable ordering and is difficult to solve the system reliability with multiple failure distribution types of components. In the end, a phased-mission systems reliability modeling and solving is carried out for a geosynchronous orbit satellite, and compared with the PMS-BDD method, which verifies the correctness of the method.
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8

Mura, I., and A. Bondavalli. "Hierarchical modeling and evaluation of phased-mission systems." IEEE Transactions on Reliability 48, no. 4 (1999): 360–68. http://dx.doi.org/10.1109/24.814518.

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9

Wang, Yujie, Liudong Xing, Gregory Levitin, and Ning Huang. "Probabilistic competing failure analysis in phased-mission systems." Reliability Engineering & System Safety 176 (August 2018): 37–51. http://dx.doi.org/10.1016/j.ress.2018.03.031.

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10

Wang, Chaonan, Liudong Xing, and Gregory Levitin. "Probabilistic common cause failures in phased-mission systems." Reliability Engineering & System Safety 144 (December 2015): 53–60. http://dx.doi.org/10.1016/j.ress.2015.07.004.

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11

Feyzioğlu, Orhan, İ. Kuban Altınel, and Süleyman Özekici. "Optimum component test plans for phased-mission systems." European Journal of Operational Research 185, no. 1 (February 2008): 255–65. http://dx.doi.org/10.1016/j.ejor.2007.01.053.

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12

ALAM, MANSOOR, and UBAID M. AL-SAGGAF. "Reliability modelling and evaluation of phased mission systems." International Journal of Systems Science 17, no. 12 (December 1986): 1699–707. http://dx.doi.org/10.1080/00207728608926918.

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13

Zhao, Jiangbin, Shubin Si, Zhiqiang Cai, Peng Guo, and Wenjin Zhu. "Mission success probability optimization for phased-mission systems with repairable component modules." Reliability Engineering & System Safety 195 (March 2020): 106750. http://dx.doi.org/10.1016/j.ress.2019.106750.

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14

Yang, Haojie, Yifan Xu, and Jianwei Lv. "An Accelerated Simulation Approach for Multistate System Mission Reliability and Success Probability under Complex Mission." Mathematical Problems in Engineering 2020 (July 26, 2020): 1–18. http://dx.doi.org/10.1155/2020/8686717.

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The mission reliability and success probability estimation of multistate systems under complex mission conditions are studied. The reliability and success probability of multistate phased mission systems (MS-PMS) is difficult to use analytic modeling and solving. An estimation approach for mission reliability and success probability based on Monte Carlo simulation is established. By introducing accelerated sampling methods such as forced transition and failure biasing, the sampling efficiency of small-probability events is improved while ensuring unbiasedness. The ship’s propulsion and power systems are used as applications, and the effectiveness of the method is verified by a numerical example. Under complex missions, such as missions with different mission time and their combinations, and phased-missions, the proposed method is superior in small-probability event sampling than the crude simulation method. The calculation example also studies the influence of mission factors or system reliability and maintainability factors on system availability and mission success probability, and analyzes the relationship between different mission types and system availability and success probability.
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15

LIU, Dong, Chun-Yuan ZHANG, Wei-Yan XING, and Rui LI. "Bayesian Networks Based Reliability Analysis of Phased-Mission Systems." Chinese Journal of Computers 31, no. 10 (October 16, 2009): 1814–25. http://dx.doi.org/10.3724/sp.j.1016.2008.01814.

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16

Li, Fuqiu, Zhenqing Wang, Xiaopeng Li, and Wei Zhang. "A Reliability Synthesis Method for Complicated Phased Mission Systems." IEEE Access 8 (2020): 193681–85. http://dx.doi.org/10.1109/access.2020.3028303.

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17

Shrestha, A., and L. Xing. "Improved modular reliability analyses of hybrid phased mission systems." Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 222, no. 4 (December 2008): 507–20. http://dx.doi.org/10.1243/1748006xjrr197.

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18

Zhu, Peican, Jie Han, Leibo Liu, and Fabrizio Lombardi. "Reliability Evaluation of Phased-Mission Systems Using Stochastic Computation." IEEE Transactions on Reliability 65, no. 3 (September 2016): 1612–23. http://dx.doi.org/10.1109/tr.2016.2570565.

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19

Li, Xiang-Yu, Yan-Feng Li, Hong-Zhong Huang, and Enrico Zio. "Reliability assessment of phased-mission systems under random shocks." Reliability Engineering & System Safety 180 (December 2018): 352–61. http://dx.doi.org/10.1016/j.ress.2018.08.002.

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20

Mo, Yu-chang, Daniel Siewiorek, and Xiao-zong Yang. "Mission reliability analysis of fault-tolerant multiple-phased systems." Reliability Engineering & System Safety 93, no. 7 (July 2008): 1036–46. http://dx.doi.org/10.1016/j.ress.2007.05.001.

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21

Ma, Y., and K. S. Trivedi. "An algorithm for reliability analysis of phased-mission systems." Reliability Engineering & System Safety 66, no. 2 (November 1999): 157–70. http://dx.doi.org/10.1016/s0951-8320(99)00033-2.

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22

Levitin, Gregory, Liudong Xing, and Yanping Xiang. "Series phased-mission systems with heterogeneous warm standby components." Computers & Industrial Engineering 145 (July 2020): 106552. http://dx.doi.org/10.1016/j.cie.2020.106552.

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23

Levitin, Gregory, Liudong Xing, Suprasad V. Amari, and Yuanshun Dai. "Optimal elements separation in non-repairable phased-mission systems." International Journal of General Systems 43, no. 8 (May 2, 2014): 864–79. http://dx.doi.org/10.1080/03081079.2014.913286.

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24

He, Hua-Feng, Juan Li, Qing-Hua Zhang, and Guoxi Sun. "A Data-Driven Reliability Estimation Approach for Phased-Mission Systems." Mathematical Problems in Engineering 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/283740.

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We attempt to address the issues associated with reliability estimation for phased-mission systems (PMS) and present a novel data-driven approach to achieve reliability estimation for PMS using the condition monitoring information and degradation data of such system under dynamic operating scenario. In this sense, this paper differs from the existing methods only considering the static scenario without using the real-time information, which aims to estimate the reliability for a population but not for an individual. In the presented approach, to establish a linkage between the historical data and real-time information of the individual PMS, we adopt a stochastic filtering model to model the phase duration and obtain the updated estimation of the mission time by Bayesian law at each phase. At the meanwhile, the lifetime of PMS is estimated from degradation data, which are modeled by an adaptive Brownian motion. As such, the mission reliability can be real time obtained through the estimated distribution of the mission time in conjunction with the estimated lifetime distribution. We demonstrate the usefulness of the developed approach via a numerical example.
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25

Somani, Arun K. "Simplified Phased-Mission System Analysis for Systems with Independent Component Repairs." International Journal of Reliability, Quality and Safety Engineering 04, no. 02 (June 1997): 167–89. http://dx.doi.org/10.1142/s0218539397000126.

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Accurate analysis of the reliability of a system requires that all major variations in the system's operation are accounted for. Most reliability analyses assume that the system's configuration, success criteria, and components' behavior remain the same during an entire mission. However, system requirements and behavior vary over the time. Moreover, individual components may be repaired (if failed) such that repairs do not conflict with the operation of the system. Thus repairs are independent of the system state. Thus, multiple phases are natural. For repairable systems, Markov analysis techniques are used but they suffer from state space explosion. This limits the size of system that can be analyzed and it is expensive in computation. We present a new computationally efficient technique for the analysis of phased-mission systems where the operational states of a system can be described by combinations of component states (such as fault trees or assertions). We avoid the state space explosion. The phase algebra is used to account for the effects of variable configurations, repairs, and success criteria from phase to phase. Our technique yields exact (as opposed to approximate) results. We demonstrate our technique by means of several examples and present numerical results to show the effects of phases and repairs on the system reliability/availability.
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26

Levitin, Gregory, Liudong Xing, Suprasad Amari, and Yuanshun Dai. "Reliability of Nonrepairable Phased-Mission Systems With Common Cause Failures." Systems, Man, and Cybernetics: Systems, IEEE Transactions on 43, no. 4 (June 2013): 967–78. http://dx.doi.org/10.1109/tsmca.2012.2220761.

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Phased-mission systems (PMSs) are systems supporting missions characterized by multiple, consecutive, and nonoverlapping phases of operation. Examples of PMSs abound in many practical applications such as aerospace, nuclear power, and airborne weapon systems. Reliability analysis of a PMS must consider statistical dependence of component states across different phases, as well as dynamics in system structure functions and component behavior. In this paper, we propose a recursive method for exact reliability evaluation of a binary-state or multistate PMS consisting of nonidentical, binary, and nonrepairable elements. The system elements can fail individually or due to common-cause failures (CCFs) caused by some external factors. The proposed method is based on the branch-and-bound principle, and can be fully automated. The method is applicable to PMSs with nonoverlapping or overlapping sets of elements that can fail as a result of CCFs. The method is illustrated using both analytical and numerical examples.
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27

Levitin, Gregory, Liudong Xing, Suprasad V. Amari, and Yuanshun Dai. "Reliability of non-repairable phased-mission systems with propagated failures." Reliability Engineering & System Safety 119 (November 2013): 218–28. http://dx.doi.org/10.1016/j.ress.2013.06.005.

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28

Lu, Ji-Min, and Xiao-Yue Wu. "Reliability evaluation of generalized phased-mission systems with repairable components." Reliability Engineering & System Safety 121 (January 2014): 136–45. http://dx.doi.org/10.1016/j.ress.2013.08.005.

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29

Zhou, Hang, Xiangyu Li, and Hongzhong Huang. "Approximate method for reliability assessment of complex phased mission systems." Journal of Shanghai Jiaotong University (Science) 22, no. 2 (March 31, 2017): 247–51. http://dx.doi.org/10.1007/s12204-017-1828-2.

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30

Dui, Hongyan, Huiting Xu, and Yun-An Zhang. "Reliability Analysis and Redundancy Optimization of a Command Post Phased-Mission System." Mathematics 10, no. 22 (November 9, 2022): 4180. http://dx.doi.org/10.3390/math10224180.

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This paper divides the execution process of the command post system into four stages: information acquisition, information processing, decision control and response execution. It combines multilayer complex networks with a phased-mission system. Most studies have only evaluated the reliability of phased-mission systems. This paper evaluates and optimizes the reliability of a phased-mission system. In order to improve the mission success rate and maximize the reliability of a command post system, this paper provides a multitasking node criticality index, and the index is used to identify the key nodes in the command post’s four-stage network Then, the hot backup system of the node is selected to determine the redundant structure of the key node. Under the constraints of the operation and maintenance costs of key nodes, with the goal of maximizing the reliability of the information processing network layer, the multitask redundancy optimization model of each stage is established. Finally, the reliability of the missions before and after redundancy optimization is compared, using the case analysis of the four-layer network to verify the effectiveness of the proposed model.
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31

Ma, Chenyang, Shuai Zhang, Mi Zhou, Shubin Si, and Zhiqiang Cai. "Reliability Evaluation and Optimization for Phased Mission Systems with Cascading Effects." IOP Conference Series: Materials Science and Engineering 1043, no. 2 (January 1, 2021): 022045. http://dx.doi.org/10.1088/1757-899x/1043/2/022045.

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32

Gong, Yuhuan, and Yuchang Mo. "Qualitative Analysis of Commercial Services in MEC as Phased-Mission Systems." Security and Communication Networks 2020 (October 10, 2020): 1–11. http://dx.doi.org/10.1155/2020/8823952.

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Currently, mobile edge computing (MEC) is one of the most popular techniques used to respond to real-time services from a wide range of mobile terminals. Compared with single-phase systems, commercial services in MEC can be modeled as phased-mission systems (PMS) and are much more complex, because of the dependencies across the phases. Over the past decade, researchers have proposed a set of new algorithms based on BDD for fault tree analysis of a wide range of PMS with various mission requirements and failure behaviors. The analysis to be performed on a fault tree can be either qualitative or quantitative. For the quantitative fault tree analysis of PMS by means of BDD, much work has been conducted. However, for the qualitative fault tree analysis of PMS by means of BDD, no much related work can be found. In this paper, we have presented some efficient methods to calculate the MCS encoding by a PMS BDD. Firstly, three kinds of redundancy relations-inclusive relation, internal-implication relation, and external-implication relation-within the cut set are identified, which prevent the cut set from being minimal cut set. Then, three BDD operations, IncRed, InImpRed, and ExImpRed, are developed, respectively, for the elimination of these redundancy relations. Using some proper combinations of these operations, MCS can be calculated correctly. As an illustration, some experimental results on a benchmark MEC system are given.
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33

Somani, A. K., J. A. Ritcey, and S. H. L. Au. "Computationally-efficient phased-mission reliability analysis for systems with variable configurations." IEEE Transactions on Reliability 41, no. 4 (1992): 504–11. http://dx.doi.org/10.1109/24.249576.

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34

Xinyu Zang, Nairong Sun, and K. S. Trivedi. "A BDD-based algorithm for reliability analysis of phased-mission systems." IEEE Transactions on Reliability 48, no. 1 (March 1999): 50–60. http://dx.doi.org/10.1109/24.765927.

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35

Huang, Xianzhen, Frank P. A. Coolen, Tahani Coolen-Maturi, and Yimin Zhang. "A New Study on Reliability Importance Analysis of Phased Mission Systems." IEEE Transactions on Reliability 69, no. 2 (June 2020): 522–32. http://dx.doi.org/10.1109/tr.2019.2923695.

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36

Yu, Huan, Jun Yang, and Yu Zhao. "Reliability of nonrepairable phased-mission systems with common bus performance sharing." Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 232, no. 6 (March 9, 2018): 647–60. http://dx.doi.org/10.1177/1748006x18757074.

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This article considers the reliability analysis of phased-mission systems with common bus performance sharing. The whole system consists of client nodes, service elements, and a common bus redistribution system and it undertakes a multi-phase mission. In each phase, the service elements must satisfy the demands of the prespecified client nodes set. The service elements can share their surplus performance with other client nodes through the common bus. In any phase, the system fails if the demands of the prespecified client nodes set are not satisfied. In other words, the entire system succeeds if the demands of the prespecified client nodes set are satisfied in all phases. The reliability of the proposed model is analyzed by the backward recursive algorithm. The optimal allocation problem is solved by the genetic algorithm. Two examples are presented to demonstrate the proposed reliability evaluation method and optimal allocation algorithm.
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37

Alam, Mansoor, and Ubaid M. Al-Saggaf. "Quantitative Reliability Evaluation of Repairable Phased-Mission Systems Using Markov Approach." IEEE Transactions on Reliability 35, no. 5 (1986): 498–503. http://dx.doi.org/10.1109/tr.1986.4335529.

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38

Tang, Z., and J. B. Dugan. "BDD-Based Reliability Analysis of Phased-Mission Systems With Multimode Failures." IEEE Transactions on Reliability 55, no. 2 (June 2006): 350–60. http://dx.doi.org/10.1109/tr.2006.874941.

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39

Zhai, Qingqing, Liudong Xing, Rui Peng, and Jun Yang. "Aggregated combinatorial reliability model for non-repairable parallel phased-mission systems." Reliability Engineering & System Safety 176 (August 2018): 242–50. http://dx.doi.org/10.1016/j.ress.2018.04.017.

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40

Gong, Yu-Huan, Yu-Chang Mo, Yu Liu, and Yi Ding. "Analyzing phased-mission industrial network systems with multiple ordered performance levels." Journal of Industrial and Production Engineering 36, no. 3 (April 3, 2019): 125–33. http://dx.doi.org/10.1080/21681015.2019.1644543.

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41

Zhang, Yang, and Darren Prescott. "Using reliability analysis to support decision making in phased mission systems." Quality and Reliability Engineering International 33, no. 8 (June 13, 2017): 2105–19. http://dx.doi.org/10.1002/qre.2170.

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42

Steurer, Mikael, Andrey Morozov, Klaus Janschek, and Klaus-Peter Neitzke. "Model-Based Dependability Assessment of Phased-Mission Unmanned Aerial Vehicles." IFAC-PapersOnLine 53, no. 2 (2020): 8915–22. http://dx.doi.org/10.1016/j.ifacol.2020.12.1416.

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43

Shrestha, Akhilesh, Liudong Xing, and Yuanshun Dai. "Reliability Analysis of Multistate Phased-Mission Systems With Unordered and Ordered States." IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 41, no. 4 (July 2011): 625–36. http://dx.doi.org/10.1109/tsmca.2010.2089513.

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44

Yuchang Mo. "New Insights Into the BDD-Based Reliability Analysis of Phased-Mission Systems." IEEE Transactions on Reliability 58, no. 4 (December 2009): 667–78. http://dx.doi.org/10.1109/tr.2009.2026804.

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45

Wang, Chaonan, Liudong Xing, Rui Peng, and Zhusheng Pan. "Competing failure analysis in phased-mission systems with multiple functional dependence groups." Reliability Engineering & System Safety 164 (August 2017): 24–33. http://dx.doi.org/10.1016/j.ress.2017.02.006.

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46

Levitin, Gregory, Maxim Finkelstein, and Yuanshun Dai. "Redundancy optimization for series-parallel phased mission systems exposed to random shocks." Reliability Engineering & System Safety 167 (November 2017): 554–60. http://dx.doi.org/10.1016/j.ress.2017.07.006.

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47

Huang, Xianzhen, Louis J. M. Aslett, and Frank P. A. Coolen. "Reliability analysis of general phased mission systems with a new survival signature." Reliability Engineering & System Safety 189 (September 2019): 416–22. http://dx.doi.org/10.1016/j.ress.2019.04.019.

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48

Peng, Rui, Qingqing Zhai, Liudong Xing, and Jun Yang. "Reliability of demand-based phased-mission systems subject to fault level coverage." Reliability Engineering & System Safety 121 (January 2014): 18–25. http://dx.doi.org/10.1016/j.ress.2013.07.013.

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49

Wang, Chaonan, Liudong Xing, and Bo Tang. "Multivalued decision diagram-based common cause failure analysis in phased-mission systems." Computers & Industrial Engineering 146 (August 2020): 106622. http://dx.doi.org/10.1016/j.cie.2020.106622.

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50

ZHANG, Shuai, Shudong SUN, Shubin Si, and Peng Wang. "A decision diagram based reliability evaluation method for multiple phased-mission systems." Eksploatacja i Niezawodnosc - Maintenance and Reliability 19, no. 3 (June 12, 2017): 485–92. http://dx.doi.org/10.17531/ein.2017.3.20.

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