IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v195y2020ics0951832018303843.html
   My bibliography  Save this article

Margins associated with loss of assured safety for systems with multiple weak links and strong links

Author

Listed:
  • Helton, Jon C.
  • Brooks, Dusty M.
  • Sallaberry, Cédric J.

Abstract

Representations for margins associated with loss of assured safety (LOAS) for weak link (WL)/strong link (SL) systems involving multiple time-dependent failure modes are developed. The following topics are described: (i) defining properties for WLs and SLs, (ii) background on cumulative distribution functions (CDFs) for link failure time, link property value at link failure, and time at which LOAS occurs, (iii) CDFs for failure time margins defined by (time at which SL system fails) − (time at which WL system fails), (iv) CDFs for SL system property values at LOAS, (v) CDFs for WL/SL property value margins defined by (property value at which SL system fails) − (property value at which WL system fails), and (vi) CDFs for SL property value margins defined by (property value of failing SL at time of SL system failure) − (property value of this SL at time of WL system failure). Included in this presentation is a demonstration of a verification strategy based on defining and approximating the indicated margin results with (i) procedures based on formal integral representations and associated quadrature approximations and (ii) procedures based on algorithms for sampling-based approximations.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:reensy:v:195:y:2020:i:c:s0951832018303843
    DOI: 10.1016/j.ress.2019.106548
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832018303843
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2019.106548?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wei, Pengfei & Lu, Zhenzhou & Song, Jingwen, 2015. "Variable importance analysis: A comprehensive review," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 399-432.
    2. 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.
    3. Eldred, M.S. & Swiler, L.P. & Tang, G., 2011. "Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1092-1113.
    4. 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).
    5. Storlie, Curtis B. & Helton, Jon C., 2008. "Multiple predictor smoothing methods for sensitivity analysis: Description of techniques," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 28-54.
    6. 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.
    7. Helton, Jon C. & Hansen, Clifford W. & Sallaberry, Cédric J., 2012. "Uncertainty and sensitivity analysis in performance assessment for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 44-63.
    8. Anderson-Cook, Christine M. & Crowder, Stephen & Huzurbazar, Aparna V. & Lorio, John & Ringland, James & Wilson, Alyson G., 2011. "Quantifying reliability uncertainty from catastrophic and margin defects: A proof of concept," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1063-1075.
    9. Urbina, Angel & Mahadevan, Sankaran & Paez, Thomas L., 2011. "Quantification of margins and uncertainties of complex systems in the presence of aleatoric and epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1114-1125.
    10. 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.
    11. Garthwaite, Paul H. & Kadane, Joseph B. & O'Hagan, Anthony, 2005. "Statistical Methods for Eliciting Probability Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 680-701, June.
    12. Storlie, Curtis B. & Helton, Jon C., 2008. "Multiple predictor smoothing methods for sensitivity analysis: Example results," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 55-77.
    13. 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.
    14. Helton, J.C. & Johnson, J.D. & Oberkampf, W.L., 2009. "Effect of delayed link failure on probability of loss of assured safety in temperature-dependent systems with multiple weak and strong links," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 294-310.
    15. Hemez, François M. & Atamturktur, Sezer, 2011. "The dangers of sparse sampling for the quantification of margin and uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1220-1231.
    16. Helton, J.C. & Hansen, C.W. & Sallaberry, C.J., 2014. "Expected dose for the nominal scenario class in the 2008 performance assessment for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada," Reliability Engineering and System Safety, Elsevier, vol. 122(C), pages 267-271.
    17. 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.
    18. Helton, Jon C. & Johnson, Jay D. & Sallaberry, Cédric J., 2011. "Quantification of margins and uncertainties: Example analyses from reactor safety and radioactive waste disposal involving the separation of aleatory and epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1014-1033.
    19. Helton, J.C. & Johnson, J.D. & Oberkampf, W.L., 2007. "Verification test problems for the calculation of probability of loss of assured safety in temperature-dependent systems with multiple weak and strong links," Reliability Engineering and System Safety, Elsevier, vol. 92(10), pages 1374-1387.
    20. 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.
    21. Storlie, Curtis B. & Swiler, Laura P. & Helton, Jon C. & Sallaberry, Cedric J., 2009. "Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1735-1763.
    22. Robert J. Budnitz & George Apostolakis & David M. Boore & Lloyd S. Cluff & Kevin J. Coppersmith & C. Allin Cornell & Peter A. Morris, 1998. "Use of Technical Expert Panels: Applications to Probabilistic Seismic Hazard Analysis," Risk Analysis, John Wiley & Sons, vol. 18(4), pages 463-469, August.
    23. Pilch, Martin & Trucano, Timothy G. & Helton, Jon C., 2011. "Ideas underlying the Quantification of Margins and Uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 965-975.
    24. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    25. Sentz, Kari & Ferson, Scott, 2011. "Probabilistic bounding analysis in the Quantification of Margins and Uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1126-1136.
    26. 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.
    27. Wallstrom, Timothy C., 2011. "Quantification of margins and uncertainties: A probabilistic framework," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1053-1062.
    28. Wilson, Alyson G. & Anderson-Cook, Christine M. & Huzurbazar, Aparna V., 2011. "A case study for quantifying system reliability and uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1076-1084.
    29. Helton, J.C. & Hansen, C.W. & Sallaberry, C.J., 2014. "Conceptual structure and computational organization of the 2008 performance assessment for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada," Reliability Engineering and System Safety, Elsevier, vol. 122(C), pages 223-248.
    30. Helton, J.C. & Johnson, J.D. & Oberkampf, W.L., 2007. "Verification of the calculation of probability of loss of assured safety in temperature-dependent systems with multiple weak and strong links," Reliability Engineering and System Safety, Elsevier, vol. 92(10), pages 1363-1373.
    31. 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.
    32. Iaccarino, Gianluca & Pecnik, Rene & Glimm, James & Sharp, David, 2011. "A QMU approach for characterizing the operability limits of air-breathing hypersonic vehicles," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1150-1160.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. 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.
    3. 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).
    4. 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.
    5. Chabridon, Vincent & Balesdent, Mathieu & Bourinet, Jean-Marc & Morio, Jérôme & Gayton, Nicolas, 2018. "Reliability-based sensitivity estimators of rare event probability in the presence of distribution parameter uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 164-178.
    6. 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.
    7. 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.
    8. Wei, Pengfei & Lu, Zhenzhou & Song, Jingwen, 2015. "Variable importance analysis: A comprehensive review," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 399-432.
    9. 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.
    10. 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.
    11. Hou, Tianfeng & Nuyens, Dirk & Roels, Staf & Janssen, Hans, 2019. "Quasi-Monte Carlo based uncertainty analysis: Sampling efficiency and error estimation in engineering applications," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    12. Tang, Zhang-Chun & Zuo, Ming J. & Xiao, Ningcong, 2016. "An efficient method for evaluating the effect of input parameters on the integrity of safety systems," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 111-123.
    13. 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.
    14. Elmar Plischke & Emanuele Borgonovo, 2020. "Fighting the Curse of Sparsity: Probabilistic Sensitivity Measures From Cumulative Distribution Functions," Risk Analysis, John Wiley & Sons, vol. 40(12), pages 2639-2660, December.
    15. Helton, Jon C. & Johnson, Jay D. & Sallaberry, Cédric J., 2011. "Quantification of margins and uncertainties: Example analyses from reactor safety and radioactive waste disposal involving the separation of aleatory and epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1014-1033.
    16. McFarland, John & DeCarlo, Erin, 2020. "A Monte Carlo framework for probabilistic analysis and variance decomposition with distribution parameter uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    17. Hansen, C.W. & Behie, G.A. & Bier, A. & Brooks, K.M. & Chen, Y. & Helton, J.C. & Hommel, S.P. & Lee, K.P. & Lester, B. & Mattie, P.D. & Mehta, S. & Miller, S.P. & Sallaberry, C.J. & Sevougian, S.D. & , 2014. "Uncertainty and sensitivity analysis for the nominal scenario class in the 2008 performance assessment for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada," Reliability Engineering and System Safety, Elsevier, vol. 122(C), pages 272-296.
    18. Helton, Jon C. & Hansen, Clifford W. & Sallaberry, Cédric J., 2012. "Uncertainty and sensitivity analysis in performance assessment for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 44-63.
    19. Hu, Zhen & Mahadevan, Sankaran, 2019. "Probability models for data-Driven global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 40-57.
    20. Blatman, Géraud & Sudret, Bruno, 2010. "Efficient computation of global sensitivity indices using sparse polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 95(11), pages 1216-1229.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:195:y:2020:i:c:s0951832018303843. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.