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An Application of Copulas to Accident Precursor Analysis

Author

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  • Woojune Yi

    (System and Communication Research Laboratory, Korea Electric Power Research Institute, Taejeon, Korea)

  • Vicki M. Bier

    (Department of Industrial Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706)

Abstract

Data on accident precursors can help in estimating accident frequencies, since they provide a rich source of information on intersystem dependencies. However, Bayesian analysis of accident precursors requires the ability to construct joint prior distributions reflecting such dependencies. For example, the failure probabilities of a particular safety system under normal and accident conditions, respectively, will generally not be identical (because of the effects of the accident), but will almost certainly be correlated (since both failure probabilities reflect the performance of the same components, with the same inherent levels of reliability). In this paper, we explore the use of copulas (a method of representing joint distribution functions with particular marginals) to construct the needed prior distributions, and then use these distributions in a Bayesian analysis of hypothetical precursor data. This demonstrates the usefulness of copulas in practice. The same approach can also be used in a wide variety of other contexts where joint distributions with particular marginals are desired.

Suggested Citation

  • Woojune Yi & Vicki M. Bier, 1998. "An Application of Copulas to Accident Precursor Analysis," Management Science, INFORMS, vol. 44(12-Part-2), pages 257-270, December.
    • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:12-part-2:p:s257-s270
    DOI: 10.1287/mnsc.44.12.S257
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    References listed on IDEAS

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    1. Mohamed N. Jouini & Robert T. Clemen, 1996. "Copula Models for Aggregating Expert Opinions," Operations Research, INFORMS, vol. 44(3), pages 444-457, June.
    2. Bier, Vicki M. & Yi, Woojune, 1995. "A Bayesian method for analyzing dependencies in precursor data," International Journal of Forecasting, Elsevier, vol. 11(1), pages 25-41, March.
    3. Tat-Chi Chow & Robert M. Oliver & G. Anthony Vignaux, 1990. "A Bayesian Escalation Model to Predict Nuclear Accidents and Risk," Operations Research, INFORMS, vol. 38(2), pages 265-277, April.
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    Cited by:

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    3. van Dorp, J. Rene, 2005. "Statistical dependence through common risk factors: With applications in uncertainty analysis," European Journal of Operational Research, Elsevier, vol. 161(1), pages 240-255, February.
    4. Hernández-Bastida, A. & Fernández-Sánchez, M.P. & Gómez-Déniz, E., 2009. "The net Bayes premium with dependence between the risk profiles," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 247-254, October.
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    6. Nima Khakzad & Sina Khakzad & Faisal Khan, 2014. "Probabilistic risk assessment of major accidents: application to offshore blowouts in the Gulf of Mexico," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 74(3), pages 1759-1771, December.
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    9. Agustín Hernández-Bastida & M. Fernández-Sánchez, 2012. "A Sarmanov family with beta and gamma marginal distributions: an application to the Bayes premium in a collective risk model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(4), pages 391-409, November.
    10. Khakzad, Nima & Khan, Faisal & Paltrinieri, Nicola, 2014. "On the application of near accident data to risk analysis of major accidents," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 116-125.
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    12. Robert T. Clemen & Terence Reilly, 1999. "Correlations and Copulas for Decision and Risk Analysis," Management Science, INFORMS, vol. 45(2), pages 208-224, February.
    13. Donald L. Keefer & Craig W. Kirkwood & James L. Corner, 2004. "Perspective on Decision Analysis Applications, 1990–2001," Decision Analysis, INFORMS, vol. 1(1), pages 4-22, March.
    14. J. Eric Bickel & James E. Smith, 2006. "Optimal Sequential Exploration: A Binary Learning Model," Decision Analysis, INFORMS, vol. 3(1), pages 16-32, March.
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    17. Ali E. Abbas & David V. Budescu & Yuhong (Rola) Gu, 2010. "Assessing Joint Distributions with Isoprobability Contours," Management Science, INFORMS, vol. 56(6), pages 997-1011, June.

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