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On The Method of Discrete Probability Distributions in Risk and Reliability Calculations–Application to Seismic Risk Assessment

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  • Stanley Kaplan

Abstract

If the point of view is adopted that in calculations of real‐world phenomena we almost invariably have significant uncertainty in the numerical values of our parameters, then, in these calculations, numerical quantities should be replaced by probability distributions and mathematical operations between these quantities should be replaced by analogous operations between probability distributions. Also, practical calculations one way or another always require discretization or truncation. Combining these two thoughts leads to a numerical approach to probabilistic calculations having great simplicity, power, and elegance. The philosophy and technique of this approach is described, some pitfalls are pointed out, and an application to seismic risk assessment is outlined.

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  • Stanley Kaplan, 1981. "On The Method of Discrete Probability Distributions in Risk and Reliability Calculations–Application to Seismic Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 1(3), pages 189-196, September.
    • Handle: RePEc:wly:riskan:v:1:y:1981:i:3:p:189-196
    DOI: 10.1111/j.1539-6924.1981.tb01415.x
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    References listed on IDEAS

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    1. Stanley Kaplan & B. John Garrick, 1981. "On The Quantitative Definition of Risk," Risk Analysis, John Wiley & Sons, vol. 1(1), pages 11-27, March.
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    Cited by:

    1. Edouard Kujawski & Gregory A. Miller, 2007. "Quantitative risk‐based analysis for military counterterrorism systems," Systems Engineering, John Wiley & Sons, vol. 10(4), pages 273-289, December.
    2. Lester B. Lave & Joshua Menkes, 1985. "Managing Risk: A Joint U.S.‐German Perspective," Risk Analysis, John Wiley & Sons, vol. 5(1), pages 17-23, March.
    3. Edouard Kujawski, 2002. "Selection of technical risk responses for efficient contingencies," Systems Engineering, John Wiley & Sons, vol. 5(3), pages 194-212.
    4. Robert E. Kurth & David C. Cox, 1985. "Discrete Probability Distributions for Probabilistic Fracture Mechanics," Risk Analysis, John Wiley & Sons, vol. 5(3), pages 235-240, September.
    5. Stan Kaplan & James C. Lin, 1987. "An Improved Condensation Procedure in Discrete Probability Distribution Calculations," Risk Analysis, John Wiley & Sons, vol. 7(1), pages 15-19, March.
    6. Raymond F. Boykin & Mardyros Kazarians & Raymond A. Freeman, 1986. "Comparative Fire Risk Study of PCB Transformers," Risk Analysis, John Wiley & Sons, vol. 6(4), pages 477-488, December.
    7. Gyun Seob Song & Man Cheol Kim, 2021. "Mathematical Formulation and Analytic Solutions for Uncertainty Analysis in Probabilistic Safety Assessment of Nuclear Power Plants," Energies, MDPI, vol. 14(4), pages 1-15, February.
    8. 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.
    9. Kwag, Shinyoung & Park, Junhee & Choi, In-Kil, 2020. "Development of efficient complete-sampling-based seismic PSA method for nuclear power plant," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    10. M. L. Murray & D. B. Chambers & R. A. Knapp & S. Kaplan, 1987. "Estimation of Long‐Term Risk from Canadian Uranium Mill Tailings," Risk Analysis, John Wiley & Sons, vol. 7(3), pages 287-298, September.
    11. Carolyn D. Heising & Virgilio Lopes de Oliveira, 1995. "A Unified Approach for Calculating Core Melt Frequency Caused by Internal and External Initiating Events," Risk Analysis, John Wiley & Sons, vol. 15(1), pages 41-47, February.

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