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Importance measures in reliability and mathematical programming

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  • Xiaoyan Zhu
  • Way Kuo

Abstract

The importance measures have been a sensitivity analysis for a probabilistic system and are applied in diverse fields along with other design tools. This paper provides a comprehensive view on modeling the importance measures to solve the reliability problems such as component assignment problems, redundancy allocation, system upgrading, and fault diagnosis and maintenance. It also investigates importance measures in broad applications such as networks, mathematical programming, sensitivity and uncertainty analysis, and probabilistic risk analysis and probabilistic safety assessment. The importance-measure based methods are among the most practical decision tools. Copyright Springer Science+Business Media, LLC 2014

Suggested Citation

  • Xiaoyan Zhu & Way Kuo, 2014. "Importance measures in reliability and mathematical programming," Annals of Operations Research, Springer, vol. 212(1), pages 241-267, January.
    • Handle: RePEc:spr:annopr:v:212:y:2014:i:1:p:241-267:10.1007/s10479-012-1127-0
    DOI: 10.1007/s10479-012-1127-0
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    2. Zhu, Xiaoyan & Boushaba, Mahmoud & Coit, David W. & Benyahia, Azzeddine, 2017. "Reliability and importance measures for m-consecutive-k, l-out-of-n system with non-homogeneous Markov-dependent components," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 1-9.
    3. Rushdi, Ali Muhammad Ali & Hassan, Ahmad Kamal, 2015. "Reliability of migration between habitat patches with heterogeneous ecological corridors," Ecological Modelling, Elsevier, vol. 304(C), pages 1-10.
    4. Floreale, Giovanni & Baraldi, Piero & Lu, Xuefei & Rossetti, Paolo & Zio, Enrico, 2024. "Sensitivity analysis by differential importance measure for unsupervised fault diagnostics," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    5. Juan Li & Bin Xin & Panos M. Pardalos & Jie Chen, 2021. "Solving bi-objective uncertain stochastic resource allocation problems by the CVaR-based risk measure and decomposition-based multi-objective evolutionary algorithms," Annals of Operations Research, Springer, vol. 296(1), pages 639-666, January.
    6. Xiaoyan Zhu & Mahmoud Boushaba & Abdelmoumene Boulahia & Xian Zhao, 2019. "A linear m-consecutive-k-out-of-n system with sparse d of non-homogeneous Markov-dependent components," Journal of Risk and Reliability, , vol. 233(3), pages 328-337, June.
    7. Wang, Dan & Si, Shubin & Cai, Zhiqiang & Zhao, Jiangbin, 2021. "Reliability optimization of linear consecutive-k-out-of-n: F systems driven by reconfigurable importance," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    8. Lu, Xuefei & Baraldi, Piero & Zio, Enrico, 2020. "A data-driven framework for identifying important components in complex systems," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    9. Zhu, Xiaoyan & Fu, Yuqiang & Yuan, Tao & Wu, Xinying, 2017. "Birnbaum importance based heuristics for multi-type component assignment problems," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 209-221.
    10. Wang, Yanhui & Bi, Lifeng & Lin, Shuai & Li, Man & Shi, Hao, 2017. "A complex network-based importance measure for mechatronics systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 180-198.

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