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On the use of uncertainty importance measures in reliability and risk analysis

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  • Aven, T.
  • Nøkland, T.E.

Abstract

This paper discusses the use of uncertainty importance measures in reliability and risk analysis. Such measures are used to rank the importance of components (activities) of complex systems. The measures reflect to what degree the uncertainties on the component level influence the uncertainties on the system level. An example of such a measure is the change in the variance of the reliability of the system when ignoring the uncertainties in the component reliability. The measures are traditionally based on a Bayesian perspective as knowledge-based (subjective) probabilities express the epistemic uncertainties about the reliability and risk parameters introduced. In this paper we carry out a rethinking of the rationale for such measures. What information do they provide compared to the traditional importance measures such as the improvement potential and the Birnbaum measure? To discuss these issues we distinguish between two situations: (A) the key quantities of interest are observable quantities such as the occurrence of a system failure and the number of failures and (B) the key quantities of interest are fictional parameters constructed to reflect the aleatory uncertainties. A new type of combined sets of measures are introduced based on an integration of a traditional measure and a related uncertainty importance measure. A simple reliability example is used to illustrate the analysis and findings.

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  • 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.
    • Handle: RePEc:eee:reensy:v:95:y:2010:i:2:p:127-133
    DOI: 10.1016/j.ress.2009.09.002
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    References listed on IDEAS

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    1. 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.
    2. Helton, J.C. & Johnson, J.D. & Sallaberry, C.J. & Storlie, C.B., 2006. "Survey of sampling-based methods for uncertainty and sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1175-1209.
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    Cited by:

    1. Huang, Xianzhen & Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2019. "A heuristic survival signature based approach for reliability-redundancy allocation," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 511-517.
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    3. Roger Flage & Terje Aven & Piero Baraldi & Enrico Zio, 2012. "An imprecision importance measure for uncertainty representations interpreted as lower and upper probabilities, with special emphasis on possibility theory," Journal of Risk and Reliability, , vol. 226(6), pages 656-665, December.
    4. Xu, Ming & Chen, Tao & Yang, Xianhui, 2012. "The effect of parameter uncertainty on achieved safety integrity of safety system," Reliability Engineering and System Safety, Elsevier, vol. 99(C), pages 15-23.
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    6. Tatsuya Sakurahara & Seyed Reihani & Ernie Kee & Zahra Mohaghegh, 2020. "Global importance measure methodology for integrated probabilistic risk assessment," Journal of Risk and Reliability, , vol. 234(2), pages 377-396, April.
    7. Bodda, Saran Srikanth & Gupta, Abhinav & Dinh, Nam, 2020. "Enhancement of risk informed validation framework for external hazard scenario," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    8. Martorell, S. & Martón, I. & Villamizar, M. & Sánchez, A.I. & Carlos, S., 2014. "Evaluation of risk impact of changes to Completion Times addressing model and parameter uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 190-201.
    9. Zdeněk Kala, 2022. "Quantification of Model Uncertainty Based on Variance and Entropy of Bernoulli Distribution," Mathematics, MDPI, vol. 10(21), pages 1-19, October.
    10. Hao, Wenrui & Lu, Zhenzhou & Tian, Longfei, 2012. "Importance measure of correlated normal variables and its sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 99(C), pages 151-160.
    11. Michele Compare & Michele Bellora & Enrico Zio, 2017. "Aggregation of importance measures for decision making in reliability engineering," Post-Print hal-01652234, HAL.
    12. Martorell, S. & Villamizar, M. & Martón, I. & Villanueva, J.F. & Carlos, S. & Sánchez, A.I., 2014. "Evaluation of risk impact of changes to surveillance requirements addressing model and parameter uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 153-165.
    13. Hao, Wenrui & Lu, Zhenzhou & Wei, Pengfei, 2013. "Uncertainty importance measure for models with correlated normal variables," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 48-58.
    14. Amundrud, Øystein & Aven, Terje, 2015. "On how to understand and acknowledge risk," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 42-47.
    15. Øystein Amundrud & Terje Aven & Roger Flage, 2017. "How the definition of security risk can be made compatible with safety definitions," Journal of Risk and Reliability, , vol. 231(3), pages 286-294, June.
    16. Xianzhen Huang & Frank PA Coolen, 2018. "Reliability sensitivity analysis of coherent systems based on survival signature," Journal of Risk and Reliability, , vol. 232(6), pages 627-634, December.
    17. Pesenti, Silvana M. & Millossovich, Pietro & Tsanakas, Andreas, 2019. "Reverse sensitivity testing: What does it take to break the model?," European Journal of Operational Research, Elsevier, vol. 274(2), pages 654-670.
    18. Zdeněk Kala, 2021. "New Importance Measures Based on Failure Probability in Global Sensitivity Analysis of Reliability," Mathematics, MDPI, vol. 9(19), pages 1-20, September.

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