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Probability and Possibility‐Based Representations of Uncertainty in Fault Tree Analysis

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  • Roger Flage
  • Piero Baraldi
  • Enrico Zio
  • Terje Aven

Abstract

Expert knowledge is an important source of input to risk analysis. In practice, experts might be reluctant to characterize their knowledge and the related (epistemic) uncertainty using precise probabilities. The theory of possibility allows for imprecision in probability assignments. The associated possibilistic representation of epistemic uncertainty can be combined with, and transformed into, a probabilistic representation; in this article, we show this with reference to a simple fault tree analysis. We apply an integrated (hybrid) probabilistic‐possibilistic computational framework for the joint propagation of the epistemic uncertainty on the values of the (limiting relative frequency) probabilities of the basic events of the fault tree, and we use possibility‐probability (probability‐possibility) transformations for propagating the epistemic uncertainty within purely probabilistic and possibilistic settings. The results of the different approaches (hybrid, probabilistic, and possibilistic) are compared with respect to the representation of uncertainty about the top event (limiting relative frequency) probability. Both the rationale underpinning the approaches and the computational efforts they require are critically examined. We conclude that the approaches relevant in a given setting depend on the purpose of the risk analysis, and that further research is required to make the possibilistic approaches operational in a risk analysis context.

Suggested Citation

  • Roger Flage & Piero Baraldi & Enrico Zio & Terje Aven, 2013. "Probability and Possibility‐Based Representations of Uncertainty in Fault Tree Analysis," Risk Analysis, John Wiley & Sons, vol. 33(1), pages 121-133, January.
  • Handle: RePEc:wly:riskan:v:33:y:2013:i:1:p:121-133
    DOI: 10.1111/j.1539-6924.2012.01873.x
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    References listed on IDEAS

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    1. Stephen D. Unwin, 1986. "A Fuzzy Set Theoretic Foundation for Vagueness in Uncertainty Analysis," Risk Analysis, John Wiley & Sons, vol. 6(1), pages 27-34, March.
    2. Durga Rao Karanki & Hari Shankar Kushwaha & Ajit Kumar Verma & Srividya Ajit, 2009. "Uncertainty Analysis Based on Probability Bounds (P‐Box) Approach in Probabilistic Safety Assessment," Risk Analysis, John Wiley & Sons, vol. 29(5), pages 662-675, May.
    3. Piero Baraldi & Enrico Zio, 2008. "A Combined Monte Carlo and Possibilistic Approach to Uncertainty Propagation in Event Tree Analysis," Risk Analysis, John Wiley & Sons, vol. 28(5), pages 1309-1326, October.
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    Cited by:

    1. Isadora Antoniano‐Villalobos & Emanuele Borgonovo & Sumeda Siriwardena, 2018. "Which Parameters Are Important? Differential Importance Under Uncertainty," Risk Analysis, John Wiley & Sons, vol. 38(11), pages 2459-2477, November.
    2. Hu, Lunhu & Kang, Rui & Pan, Xing & Zuo, Dujun, 2020. "Risk assessment of uncertain random system—Level-1 and level-2 joint propagation of uncertainty and probability in fault tree analysis," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    3. Nicola Pedroni & Enrico Zio & Alberto Pasanisi & Mathieu Couplet, 2017. "A critical discussion and practical recommendations on some issues relevant to the non-probabilistic treatment of uncertainty in engineering risk assessment," Post-Print hal-01652230, HAL.
    4. Ibsen Chivatá Cárdenas & Saad S.H. Al‐Jibouri & Johannes I.M. Halman & Frits A. van Tol, 2014. "Modeling Risk‐Related Knowledge in Tunneling Projects," Risk Analysis, John Wiley & Sons, vol. 34(2), pages 323-339, February.
    5. Nicola Pedroni & Enrico Zio & Alberto Pasanisi & Mathieu Couplet, 2017. "A Critical Discussion and Practical Recommendations on Some Issues Relevant to the Nonprobabilistic Treatment of Uncertainty in Engineering Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 37(7), pages 1315-1340, July.

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