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Importance measures based on system performance loss for multi-state phased-mission systems

Author

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  • Zhang, Chao
  • Qiao, Jingming
  • Wang, Shaoping
  • Chen, Rentong
  • Dui, Hongyan
  • Zhang, Yuwei
  • Bao, Yunpeng
  • Zhou, Yulong

Abstract

It is essential to identify weaknesses in a complex phased-mission system (PMS) in the early design or maintenance stage using importance measures to ensure high reliability and performance. However, most systems have multiple states, and sufficient analyses of importance measures for multi-state phased-mission systems (MS-PMSs) are lacking. This paper proposes novel importance measures for MS-PMSs that consider component and phase criticalities. The Markov model is used to describe the degradation of multi-state components. The failure rates are obtained from a recurrence model that considers the cumulative damage effect due to phase changes. A multi-state multi-valued decision diagram (MMDD) is used to describe the system structure in different phases and establish the system reliability model. Two importance measures that consider the system's performance loss during a phase mission are proposed: the phase-weighted Griffith importance measure (PWGIM) and the phase-weighted integrated importance measure (PWIIM). The two importance measures consider phase criticality and reflect the comprehensive impact of component state changes on MS-PMS performance. A case study of an unmanned aerial reconnaissance system (UARS) is conducted to demonstrate the effectiveness of the importance measures. The results indicate that the proposed importance measures are reliable and effective during the design or maintenance stages of MS-PMSs.

Suggested Citation

  • Zhang, Chao & Qiao, Jingming & Wang, Shaoping & Chen, Rentong & Dui, Hongyan & Zhang, Yuwei & Bao, Yunpeng & Zhou, Yulong, 2025. "Importance measures based on system performance loss for multi-state phased-mission systems," Reliability Engineering and System Safety, Elsevier, vol. 256(C).
    • Handle: RePEc:eee:reensy:v:256:y:2025:i:c:s0951832024008470
    DOI: 10.1016/j.ress.2024.110776
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    1. Li, Xiang-Yu & Xiong, Xiaoyan & Guo, Junyu & Huang, Hong-Zhong & Li, Xiaopeng, 2022. "Reliability assessment of non-repairable multi-state phased mission systems with backup missions," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    2. Feng, Qiang & Liu, Meng & Dui, Hongyan & Ren, Yi & Sun, Bo & Yang, Dezhen & Wang, Zili, 2022. "Importance measure-based phased mission reliability and UAV number optimization for swarm," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    3. Mohamed-Larbi Rebaiaia & Daoud Ait-Kadi, 2024. "A new integrated strategy for optimising the maintenance cost of complex systems using reliability importance measures," International Journal of Production Research, Taylor & Francis Journals, vol. 62(11), pages 4143-4164, June.
    4. Vaurio, J.K., 2011. "Importance measures for multi-phase missions," Reliability Engineering and System Safety, Elsevier, vol. 96(1), pages 230-235.
    5. Chen, Liwei & Cheng, Chunchun & Dui, Hongyan & Xing, Liudong, 2022. "Maintenance cost-based importance analysis under different maintenance strategies," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    6. Cai, Baoping & Zhang, Yanping & Wang, Haifeng & Liu, Yonghong & Ji, Renjie & Gao, Chuntan & Kong, Xiangdi & Liu, Jing, 2021. "Resilience evaluation methodology of engineering systems with dynamic-Bayesian-network-based degradation and maintenance," Reliability Engineering and System Safety, Elsevier, vol. 209(C).
    7. Haojie Yang & Yifan Xu & Jianwei Lv, 2020. "An Accelerated Simulation Approach for Multistate System Mission Reliability and Success Probability under Complex Mission," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-18, July.
    8. Levitin, Gregory & Jia, Heping & Ding, Yi & Song, Yonghua & Dai, Yuanshun, 2017. "Reliability of multi-state systems with free access to repairable standby elements," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 192-197.
    9. Li, Jingkui & Lu, Yuze & Liu, Xiaona & Jiang, Xiuhong, 2023. "Reliability analysis of cold-standby phased-mission system based on GO-FLOW methodology and the universal generating function," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    10. Dui, Hongyan & Wei, Xuan & Xing, Liudong, 2023. "A new multi-criteria importance measure and its applications to risk reduction and safety enhancement," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    11. Tang, Maochun & Xiahou, Tangfan & Liu, Yu, 2023. "Mission performance analysis of phased-mission systems with cross-phase competing failures," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    12. Yu, Haiyue & Wu, Xinyang & Wu, Xiaoyue, 2020. "An extended object-oriented petri net model for mission reliability evaluation of phased-mission system with time redundancy," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    13. Levitin, Gregory & Finkelstein, Maxim & Xiang, Yanping, 2021. "Optimal mission abort policies for repairable multistate systems performing multi-attempt mission," Reliability Engineering and System Safety, Elsevier, vol. 209(C).
    14. Peng, Rui & Wu, Di & Xiao, Hui & Xing, Liudong & Gao, Kaiye, 2019. "Redundancy versus protection for a non-reparable phased-mission system subject to external impacts," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    15. Dui, Hongyan & Si, Shubin & Yam, Richard C.M., 2018. "Importance measures for optimal structure in linear consecutive-k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 339-350.
    16. Andrews, J.D., 2008. "Birnbaum and criticality measures of component contribution to the failure of phased missions," Reliability Engineering and System Safety, Elsevier, vol. 93(12), pages 1861-1866.
    17. Ramirez-Marquez, Jose E. & Rocco, Claudio M. & Gebre, Bethel A. & Coit, David W. & Tortorella, Michael, 2006. "New insights on multi-state component criticality and importance," Reliability Engineering and System Safety, Elsevier, vol. 91(8), pages 894-904.
    18. Li, Y.F. & Peng, R., 2014. "Availability modeling and optimization of dynamic multi-state series–parallel systems with random reconfiguration," Reliability Engineering and System Safety, Elsevier, vol. 127(C), pages 47-57.
    19. Si, Shubin & Levitin, Gregory & Dui, Hongyan & Sun, Shudong, 2013. "Component state-based integrated importance measure for multi-state systems," Reliability Engineering and System Safety, Elsevier, vol. 116(C), pages 75-83.
    20. Li, Xiang-Yu & Li, Xiaopeng & Feng, Jianxiang & Li, Congming & Xiong, Xiaoyan & Huang, Hong-Zhong, 2023. "Reliability analysis and optimization of multi-phased spaceflight with backup missions and mixed redundancy strategy," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    21. Chen, Rentong & Zhang, Chao & Wang, Shaoping & Zio, Enrico & Dui, Hongyan & Zhang, Yadong, 2023. "Importance measures for critical components in complex system based on Copula Hierarchical Bayesian Network," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    22. Matsuoka, Takeshi, 2023. "Reliability analysis of a BWR plant system at startup stage  - analysis by the GO-FLOW methodology with consideration of loop structures and phased mission problem -," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    23. Dui, Hongyan & Lu, Yaohui & Wu, Shaomin, 2024. "Competing risks-based resilience approach for multi-state systems under multiple shocks," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    24. Lu, Yaohui & Wang, Shaoping & Zhang, Chao & Chen, Rentong & Dui, Hongyan & Mu, Rui, 2024. "Adaptive maintenance window-based opportunistic maintenance optimization considering operational reliability and cost," Reliability Engineering and System Safety, Elsevier, vol. 250(C).
    25. Wang, Zengkai & Zeng, Shengkui & Guo, Jianbin & Che, Haiyang, 2021. "A Bayesian network for reliability assessment of man-machine phased-mission system considering the phase dependencies of human cognitive error," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    26. Rentong Chen & Chao Zhang & Shaoping Wang & Enrico Zio & Hongyan Dui & Yadong Zhang, 2023. "Importance measures for critical components in complex system based on Copula Hierarchical Bayesian Network," Post-Print hal-04103914, HAL.
    27. Li, Xiang-Yu & Li, Yan-Feng & Huang, Hong-Zhong & Zio, Enrico, 2018. "Reliability assessment of phased-mission systems under random shocks," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 352-361.
    28. Wu, Xin-yang & Wu, Xiao-yue & Balakrishnan, Narayanaswamy, 2018. "Reliability allocation model and algorithm for phased mission systems with uncertain component parameters based on importance measure," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 266-276.
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