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Competing Failure Risk Analysis Using Evidence Theory

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  • Jon C. Helton
  • William L. Oberkampf
  • Jay D. Johnson

Abstract

Safety systems are important components of high‐consequence systems that are intended to prevent the unintended operation of the system and thus the potentially significant negative consequences that could result from such an operation. This presentation investigates and illustrates formal procedures for assessing the uncertainty in the probability that a safety system will fail to operate as intended in an accident environment. Probability theory and evidence theory are introduced as possible mathematical structures for the representation of the epistemic uncertainty associated with the performance of safety systems, and a representation of this type is illustrated with a hypothetical safety system involving one weak link and one strong link that is exposed to a high temperature fire environment. Topics considered include (1) the nature of diffuse uncertainty information involving a system and its environment, (2) the conversion of diffuse uncertainty information into the mathematical structures associated with probability theory and evidence theory, and (3) the propagation of these uncertainty structures through a model for a safety system to obtain representations in the context of probability theory and evidence theory of the uncertainty in the probability that the safety system will fail to operate as intended. The results suggest that evidence theory provides a potentially valuable representational tool for the display of the implications of significant epistemic uncertainty in inputs to complex analyses.

Suggested Citation

  • Jon C. Helton & William L. Oberkampf & Jay D. Johnson, 2005. "Competing Failure Risk Analysis Using Evidence Theory," Risk Analysis, John Wiley & Sons, vol. 25(4), pages 973-995, August.
    • Handle: RePEc:wly:riskan:v:25:y:2005:i:4:p:973-995
    DOI: 10.1111/j.1539-6924.2005.00644.x
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    1. F. Owen Hoffman & Jana S. Hammonds, 1994. "Propagation of Uncertainty in Risk Assessments: The Need to Distinguish Between Uncertainty Due to Lack of Knowledge and Uncertainty Due to Variability," Risk Analysis, John Wiley & Sons, vol. 14(5), pages 707-712, October.
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    3. Kohlas, Jurg, 1989. "Modeling uncertainty with belief functions in numerical models," European Journal of Operational Research, Elsevier, vol. 40(3), pages 377-388, June.
    4. Jon C. Helton, 1994. "Treatment of Uncertainty in Performance Assessments for Complex Systems," Risk Analysis, John Wiley & Sons, vol. 14(4), pages 483-511, August.
    5. Gert de Cooman & Peter Walley, 2002. "A possibilistic hierarchical model for behaviour under uncertainty," Theory and Decision, Springer, vol. 52(4), pages 327-374, June.
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    Cited by:

    1. 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.
    2. Helton, Jon C. & Brooks, Dusty M. & Sallaberry, Cédric J., 2020. "Margins associated with loss of assured safety for systems with multiple weak links and strong links," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    3. 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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