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Quantification of margins and uncertainties: Conceptual and computational basis

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  • Helton, Jon C.

Abstract

In 2001, the National Nuclear Security Administration of the U.S. Department of Energy in conjunction with the national security laboratories (i.e., Los Alamos National Laboratory, Lawrence Livermore National Laboratory and Sandia National Laboratories) initiated development of a process designated Quantification of Margins and Uncertainties (QMU) for the use of risk assessment methodologies in the certification of the reliability and safety of the nation's nuclear weapons stockpile. This presentation discusses and illustrates the conceptual and computational basis of QMU in analyses that use computational models to predict the behavior of complex systems. The following topics are considered: (i) the role of aleatory and epistemic uncertainty in QMU, (ii) the representation of uncertainty with probability, (iii) the probabilistic representation of uncertainty in QMU analyses involving only epistemic uncertainty, and (iv) the probabilistic representation of uncertainty in QMU analyses involving aleatory and epistemic uncertainty.

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  • Helton, Jon C., 2011. "Quantification of margins and uncertainties: Conceptual and computational basis," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 976-1013.
    • Handle: RePEc:eee:reensy:v:96:y:2011:i:9:p:976-1013
    DOI: 10.1016/j.ress.2011.03.017
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    8. Helton, J.C. & Johnson, J.D. & Sallaberry, C.J. & Storlie, C.B., 2006. "Survey of sampling-based methods for uncertainty and sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1175-1209.
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    Cited by:

    1. Benoumechiara Nazih & Bousquet Nicolas & Michel Bertrand & Saint-Pierre Philippe, 2020. "Detecting and modeling critical dependence structures between random inputs of computer models," Dependence Modeling, De Gruyter, vol. 8(1), pages 263-297, January.
    2. Iaccarino, Gianluca & Sharp, David & Glimm, James, 2013. "Quantification of margins and uncertainties using multiple gates and conditional probabilities," Reliability Engineering and System Safety, Elsevier, vol. 114(C), pages 99-113.
    3. Di Maio, Francesco & Bandini, Alessandro & Zio, Enrico & Alberola, Sofia Carlos & Sanchez-Saez, Francisco & Martorell, Sebastián, 2016. "Bootstrapped-ensemble-based Sensitivity Analysis of a trace thermal-hydraulic model based on a limited number of PWR large break loca simulations," Reliability Engineering and System Safety, Elsevier, vol. 153(C), pages 122-134.
    4. Hund, Lauren & Schroeder, Benjamin & Rumsey, Kellin & Huerta, Gabriel, 2018. "Distinguishing between model- and data-driven inferences for high reliability statistical predictions," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 201-210.
    5. Helton, Jon C. & Pilch, Martin & Sallaberry, Cédric J., 2014. "Probability of loss of assured safety in systems with multiple time-dependent failure modes: Representations with aleatory and epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 171-200.
    6. Strigini, Lorenzo & Wright, David, 2014. "Bounds on survival probability given mean probability of failure per demand; and the paradoxical advantages of uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 128(C), pages 66-83.
    7. Helton, Jon C. & Brooks, Dusty M. & Sallaberry, Cédric J., 2020. "Property values associated with the failure of individual links in a system with multiple weak and strong links," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    8. Helton, Jon C. & Brooks, Dusty M. & Sallaberry, Cédric J., 2022. "Probability of Loss of Assured Safety in Systems with Multiple Time-Dependent Failure Modes: Incorporation of Delayed Link Failure in the Presence of Aleatory Uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    9. Helton, Jon C. & Johnson, Jay D., 2011. "Quantification of margins and uncertainties: Alternative representations of epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1034-1052.
    10. Roger Flage & Terje Aven & Enrico Zio & Piero Baraldi, 2014. "Concerns, Challenges, and Directions of Development for the Issue of Representing Uncertainty in Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 34(7), pages 1196-1207, July.
    11. Benoumechiara Nazih & Bousquet Nicolas & Michel Bertrand & Saint-Pierre Philippe, 2020. "Detecting and modeling critical dependence structures between random inputs of computer models," Dependence Modeling, De Gruyter, vol. 8(1), pages 263-297, January.
    12. Shah, Harsheel & Hosder, Serhat & Winter, Tyler, 2015. "Quantification of margins and mixed uncertainties using evidence theory and stochastic expansions," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 59-72.
    13. Riley, Matthew E., 2015. "Evidence-based quantification of uncertainties induced via simulation-based modeling," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 79-86.
    14. Di Maio, Francesco & Rai, Ajit & Zio, Enrico, 2016. "A dynamic probabilistic safety margin characterization approach in support of Integrated Deterministic and Probabilistic Safety Analysis," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 9-18.
    15. Cao, Jiaokun & Du, Farong & Ding, Shuiting, 2013. "Global sensitivity analysis for dynamic systems with stochastic input processes," Reliability Engineering and System Safety, Elsevier, vol. 118(C), pages 106-117.
    16. Certa, Antonella & Hopps, Fabrizio & Inghilleri, Roberta & La Fata, Concetta Manuela, 2017. "A Dempster-Shafer Theory-based approach to the Failure Mode, Effects and Criticality Analysis (FMECA) under epistemic uncertainty: application to the propulsion system of a fishing vessel," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 69-79.
    17. Alban, Andres & Darji, Hardik A. & Imamura, Atsuki & Nakayama, Marvin K., 2017. "Efficient Monte Carlo methods for estimating failure probabilities," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 376-394.
    18. Mathieu Balesdent & Jérôme Morio & Loïc Brevault, 2016. "Rare Event Probability Estimation in the Presence of Epistemic Uncertainty on Input Probability Distribution Parameters," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 197-216, March.
    19. 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).
    20. Sankararaman, S. & Mahadevan, S., 2013. "Separating the contributions of variability and parameter uncertainty in probability distributions," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 187-199.
    21. Teferra, Kirubel & Shields, Michael D. & Hapij, Adam & Daddazio, Raymond P., 2014. "Mapping model validation metrics to subject matter expert scores for model adequacy assessment," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 9-19.
    22. Francesco, Di Maio & Matteo, Fumagalli & Carlo, Guerini & Federico, Perotti & Enrico, Zio, 2021. "Time-dependent reliability analysis of the reactor building of a nuclear power plant for accounting of its aging and degradation," Reliability Engineering and System Safety, Elsevier, vol. 205(C).

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