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Multi-scale reliability analysis and updating of complex systems by use of linear programming

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  • Der Kiureghian, Armen
  • Song, Junho

Abstract

Complex systems are characterized by large numbers of components, cut sets or link sets, or by statistical dependence between the component states. These measures of complexity render the computation of system reliability a challenging task. In this paper, a decomposition approach is described, which, together with a linear programming formulation, allows determination of bounds on the reliability of complex systems with manageable computational effort. The approach also facilitates multi-scale modeling and analysis of a system, whereby varying degrees of detail can be considered in the decomposed system. The paper also describes a method for computing bounds on conditional probabilities by use of linear programming, which can be used to update the system reliability for any given event. Applications to a power network demonstrate the methodology.

Suggested Citation

  • Der Kiureghian, Armen & Song, Junho, 2008. "Multi-scale reliability analysis and updating of complex systems by use of linear programming," Reliability Engineering and System Safety, Elsevier, vol. 93(2), pages 288-297.
    • Handle: RePEc:eee:reensy:v:93:y:2008:i:2:p:288-297
    DOI: 10.1016/j.ress.2006.10.022
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    References listed on IDEAS

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    1. Brigitte Jaumard & Pierre Hansen & Marcus Poggi de Aragão, 1991. "Column Generation Methods for Probabilistic Logic," INFORMS Journal on Computing, INFORMS, vol. 3(2), pages 135-148, May.
    2. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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    Cited by:

    1. Tong, Yanjie & Tien, Iris, 2019. "Analytical probability propagation method for reliability analysis of general complex networks," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 21-30.
    2. Ebrahimi, Nader & Shehadeh, Mahmoud, 2015. "Assessing the reliability of components with micro- and nano-structures when they are part a multi-scale system," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 13-20.
    3. Bichon, Barron J. & McFarland, John M. & Mahadevan, Sankaran, 2011. "Efficient surrogate models for reliability analysis of systems with multiple failure modes," Reliability Engineering and System Safety, Elsevier, vol. 96(10), pages 1386-1395.
    4. Zohre Alipour & Mohammad Ali Saniee Monfared & Enrico Zio, 2014. "Comparing topological and reliability-based vulnerability analysis of Iran power transmission network," Journal of Risk and Reliability, , vol. 228(2), pages 139-151, April.
    5. Kang, Won-Hee & Kliese, Alyce, 2014. "A rapid reliability estimation method for directed acyclic lifeline networks with statistically dependent components," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 81-91.
    6. Byun, Ji-Eun & de Oliveira, Welington & Royset, Johannes O., 2023. "S-BORM: Reliability-based optimization of general systems using buffered optimization and reliability method," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    7. Kang, Won-Hee & Song, Junho & Gardoni, Paolo, 2008. "Matrix-based system reliability method and applications to bridge networks," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1584-1593.
    8. Kim, Dong-Seok & Ok, Seung-Yong & Song, Junho & Koh, Hyun-Moo, 2013. "System reliability analysis using dominant failure modes identified by selective searching technique," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 316-331.
    9. Wang, Zhiheng & Hawi, Philippe & Masri, Sami & Aitharaju, Venkat & Ghanem, Roger, 2023. "Stochastic multiscale modeling for quantifying statistical and model errors with application to composite materials," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    10. Rodríguez, Joanna & Lillo, Rosa E. & Ramírez-Cobo, Pepa, 2015. "Failure modeling of an electrical N-component framework by the non-stationary Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 126-133.
    11. Tien, Iris & Der Kiureghian, Armen, 2016. "Algorithms for Bayesian network modeling and reliability assessment of infrastructure systems," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 134-147.
    12. Bensi, Michelle & Kiureghian, Armen Der & Straub, Daniel, 2013. "Efficient Bayesian network modeling of systems," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 200-213.
    13. Stern, R.E. & Song, J. & Work, D.B., 2017. "Accelerated Monte Carlo system reliability analysis through machine-learning-based surrogate models of network connectivity," Reliability Engineering and System Safety, Elsevier, vol. 164(C), pages 1-9.

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