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A Matrix‐Based Approach to Uncertainty and Sensitivity Analysis for Fault Trees

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  • Ronald L. Iman

Abstract

System unavailabilities for large complex systems such as nuclear power plants are often evaluated through use of fault tree analysis. The system unavailability is obtained from a Boolean representation of a system fault tree. Even after truncation of higher order terms these expressions can be quite large, involving thousands of terms. A general matrix notation is proposed for the representation of Boolean expressions which facilitates uncertainty and sensitivity analysis calculations.

Suggested Citation

  • Ronald L. Iman, 1987. "A Matrix‐Based Approach to Uncertainty and Sensitivity Analysis for Fault Trees," Risk Analysis, John Wiley & Sons, vol. 7(1), pages 21-33, March.
    • Handle: RePEc:wly:riskan:v:7:y:1987:i:1:p:21-33
    DOI: 10.1111/j.1539-6924.1987.tb00966.x
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    References listed on IDEAS

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    1. Stanley Kaplan, 1982. "Matrix Theory Formalism for Event Tree Analysis: Application to Nuclear‐Risk Analysis," Risk Analysis, John Wiley & Sons, vol. 2(1), pages 9-18, March.
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    Cited by:

    1. Pengfei Wei & Zhenzhou Lu & Jingwen Song, 2014. "Uncertainty Importance Analysis Using Parametric Moment Ratio Functions," Risk Analysis, John Wiley & Sons, vol. 34(2), pages 223-234, February.
    2. Emanuele Borgonovo, 2006. "Measuring Uncertainty Importance: Investigation and Comparison of Alternative Approaches," Risk Analysis, John Wiley & Sons, vol. 26(5), pages 1349-1361, October.
    3. Ronald L. Iman & Mark E. Johnson & Charles C. Watson, 2005. "Uncertainty Analysis for Computer Model Projections of Hurricane Losses," Risk Analysis, John Wiley & Sons, vol. 25(5), pages 1299-1312, October.
    4. 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.
    5. 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.
    6. Xiaoyan Zhu & Way Kuo, 2014. "Importance measures in reliability and mathematical programming," Annals of Operations Research, Springer, vol. 212(1), pages 241-267, January.
    7. Guijie Li & Zhenzhou Lu & Longfei Tian & Jia Xu, 2013. "The importance measure on the non-probabilistic reliability index of uncertain structures," Journal of Risk and Reliability, , vol. 227(6), pages 651-661, December.
    8. Ronald L. Iman & Jon C. Helton, 1988. "An Investigation of Uncertainty and Sensitivity Analysis Techniques for Computer Models," Risk Analysis, John Wiley & Sons, vol. 8(1), pages 71-90, March.
    9. 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.
    10. Ronald L. Iman & Stephen C. Hora, 1990. "A Robust Measure of Uncertainty Importance for Use in Fault Tree System Analysis," Risk Analysis, John Wiley & Sons, vol. 10(3), pages 401-406, September.
    11. Xin Xu & Zhenzhou Lu & Xiaopeng Luo, 2014. "A Stable Approach Based on Asymptotic Space Integration for Moment‐Independent Uncertainty Importance Measure," Risk Analysis, John Wiley & Sons, vol. 34(2), pages 235-251, February.
    12. Derennes, Pierre & Morio, Jérôme & Simatos, Florian, 2019. "A nonparametric importance sampling estimator for moment independent importance measures," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 3-16.
    13. Timothy A. Wheeler & Kishore Gawande & Stephen Bespalko, 1997. "Development of Risk‐Based Ranking Measures of Effectiveness for the United States Coast Guard's Vessel Inspection Program," Risk Analysis, John Wiley & Sons, vol. 17(3), pages 333-340, June.
    14. Ronald L. Iman & Jon C. Helton, 1991. "The Repeatability of Uncertainty and Sensitivity Analyses for Complex Probabilistic Risk Assessments," Risk Analysis, John Wiley & Sons, vol. 11(4), pages 591-606, December.
    15. Tong, Ming-Na & Zhao, Yan-Gang & Lu, Zhao-Hui, 2021. "Normal transformation for correlated random variables based on L-moments and its application in reliability engineering," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    16. Pengfei Wei & Zhenzhou Lu & Jingwen Song, 2014. "Moment‐Independent Sensitivity Analysis Using Copula," Risk Analysis, John Wiley & Sons, vol. 34(2), pages 210-222, February.

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