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Accounting for components interactions in the differential importance measure

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  • Zio, Enrico
  • Podofillini, Luca

Abstract

A limitation of the importance measures (IMs) currently used in reliability and risk analyses is that they rank only individual components or basic events whereas they are not directly applicable to combinations or groups of components or basic events. To partially overcome this limitation, recently, the differential importance measure (DIM), has been introduced for use in risk-informed decision making. The DIM is a first-order sensitivity measure that ranks the parameters of the risk model according to the fraction of total change in the risk that is due to a small change in the parameters’ values, taken one at a time. However, it does not account for the effects of interactions among components. In this paper, a second-order extension of the DIM, named DIMII, is proposed for accounting of the interactions of pairs of components when evaluating the change in system performance due to changes of the reliability parameters of the components. A numerical application is presented in which the informative contents of DIM and DIMII are compared. The results confirm that in certain cases when second-order interactions among components are accounted for, the importance ranking of the components may differ from that produced by a first-order sensitivity measure.

Suggested Citation

  • Zio, Enrico & Podofillini, Luca, 2006. "Accounting for components interactions in the differential importance measure," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1163-1174.
    • Handle: RePEc:eee:reensy:v:91:y:2006:i:10:p:1163-1174
    DOI: 10.1016/j.ress.2005.11.044
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    Citations

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    Cited by:

    1. Wu, Shaomin & Chen, Yi & Wu, Qingtai & Wang, Zhonglai, 2016. "Linking component importance to optimisation of preventive maintenance policy," Reliability Engineering and System Safety, Elsevier, vol. 146(C), pages 26-32.
    2. Xiaoyan Zhu & Way Kuo, 2014. "Importance measures in reliability and mathematical programming," Annals of Operations Research, Springer, vol. 212(1), pages 241-267, January.
    3. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    4. Mirko Ginocchi & Ferdinanda Ponci & Antonello Monti, 2021. "Sensitivity Analysis and Power Systems: Can We Bridge the Gap? A Review and a Guide to Getting Started," Energies, MDPI, vol. 14(24), pages 1-59, December.
    5. Gao, Xueli & Cui, Lirong & Li, Jinlin, 2007. "Analysis for joint importance of components in a coherent system," European Journal of Operational Research, Elsevier, vol. 182(1), pages 282-299, October.
    6. Emanuele Borgonovo & Alessandra Cillo, 2017. "Deciding with Thresholds: Importance Measures and Value of Information," Risk Analysis, John Wiley & Sons, vol. 37(10), pages 1828-1848, October.
    7. Borgonovo, E., 2010. "The reliability importance of components and prime implicants in coherent and non-coherent systems including total-order interactions," European Journal of Operational Research, Elsevier, vol. 204(3), pages 485-495, August.
    8. Aven, T. & Nøkland, T.E., 2010. "On the use of uncertainty importance measures in reliability and risk analysis," Reliability Engineering and System Safety, Elsevier, vol. 95(2), pages 127-133.
    9. E. Borgonovo & C. L. Smith, 2011. "A Study of Interactions in the Risk Assessment of Complex Engineering Systems: An Application to Space PSA," Operations Research, INFORMS, vol. 59(6), pages 1461-1476, December.
    10. L Podofillini & E Zio, 2008. "Events group risk importance by genetic algorithms," Journal of Risk and Reliability, , vol. 222(3), pages 337-346, September.
    11. Do Van, Phuc & Barros, Anne & Bérenguer, Christophe, 2010. "From differential to difference importance measures for Markov reliability models," European Journal of Operational Research, Elsevier, vol. 204(3), pages 513-521, August.
    12. Zhai, Qingqing & Yang, Jun & Zhao, Yu, 2014. "Space-partition method for the variance-based sensitivity analysis: Optimal partition scheme and comparative study," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 66-82.
    13. Li, Jian & Dueñas-Osorio, Leonardo & Chen, Changkun & Shi, Congling, 2017. "AC power flow importance measures considering multi-element failures," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 89-97.
    14. Dui, Hongyan & Tian, Tianzi & Zhao, Jiangbin & Wu, Shaomin, 2022. "Comparing with the joint importance under consideration of consecutive-k-out-of-n system structure changes," Reliability Engineering and System Safety, Elsevier, vol. 219(C).

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