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Importance measures in reliability and mathematical programming

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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.

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Notes

  1. A consecutive-k-out-of-n (Con/k/n) system is an ordered sequence of n components that are connected either linearly (Lin/Con/k/n) or circularly (Cir/Con/k/n). A Con/k/n:F (G) system fails (functions) if and only if at least k consecutive components fail (function).

  2. A (minimal) cut is a (minimal) set of components whose failure causes the system to fail; a (minimal) path is a (minimal) set of components whose functioning ensures the functioning of the system.

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Acknowledgements

This work is supported in part by a National Science Foundation Project # CMMI-0825908.

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  1. Department of Industrial and Information Engineering, University of Tennessee, Knoxville, TN, 37996, USA

    Xiaoyan Zhu

  2. City University of Hong Kong, Kowloon, Hong Kong, China

    Way Kuo

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Zhu, X., Kuo, W. Importance measures in reliability and mathematical programming. Ann Oper Res 212, 241–267 (2014). https://doi.org/10.1007/s10479-012-1127-0

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