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Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links

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  • Helton, J.C.
  • Johnson, J.D.
  • Oberkampf, W.L.

Abstract

Relationships to determine the probability that a weak link (WL)/strong link (SL) safety system will fail to function as intended in a fire environment are investigated. In the systems under study, failure of the WL system before failure of the SL system is intended to render the overall system inoperational and thus prevent the possible occurrence of accidents with potentially serious consequences. Formal developments of the probability that the WL system fails to deactivate the overall system before failure of the SL system (i.e. the probability of loss of assured safety, PLOAS) are presented for several WL/SL configurations: (i) one WL, one SL; (ii) multiple WLs, multiple SLs with failure of any SL before any WL constituting failure of the safety system; (iii) multiple WLs, multiple SLs with failure of all SLs before any WL constituting failure of the safety system; and (iv) multiple WLs, multiple SLs and multiple sublinks in each SL with failure of any sublink constituting failure of the associated SL and failure of all SLs before failure of any WL constituting failure of the safety system. The indicated probabilities derive from time-dependent temperatures in the WL/SL system and variability (i.e. aleatory uncertainty) in the temperatures at which the individual components of this system fail and are formally defined as multidimensional integrals. Numerical procedures based on quadrature (i.e. trapezoidal rule, Simpson's rule) and also on Monte Carlo techniques (i.e. simple random sampling, importance sampling) are described and illustrated for the evaluation of these integrals.

Suggested Citation

  • Helton, J.C. & Johnson, J.D. & Oberkampf, W.L., 2006. "Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links," Reliability Engineering and System Safety, Elsevier, vol. 91(3), pages 320-348.
    • Handle: RePEc:eee:reensy:v:91:y:2006:i:3:p:320-348
    DOI: 10.1016/j.ress.2005.01.011
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    References listed on IDEAS

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    1. Perwez Shahabuddin, 1994. "Importance Sampling for the Simulation of Highly Reliable Markovian Systems," Management Science, INFORMS, vol. 40(3), pages 333-352, March.
    2. Peter W. Glynn & Donald L. Iglehart, 1989. "Importance Sampling for Stochastic Simulations," Management Science, INFORMS, vol. 35(11), pages 1367-1392, November.
    3. Evans, Michael & Swartz, Timothy, 2000. "Approximating Integrals via Monte Carlo and Deterministic Methods," OUP Catalogue, Oxford University Press, number 9780198502784.
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    Citations

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    Cited by:

    1. 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.
    2. 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).
    3. Pi, Shiqiang & Xiao, Longyuan, 2020. "Investigation of temperature-dependent high consequence system with weak and strong links based on probability of loss of assured safety," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    4. 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.
    5. 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.
    6. 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.
    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. Pi, Shiqiang & Liu, Ying & Chen, Haiyan & Deng, Yan & Xiao, Longyuan, 2021. "Probability of loss of assured safety in systems with weak and strong links subject to dependent failures and random shocks," Reliability Engineering and System Safety, Elsevier, vol. 209(C).
    9. 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.
    10. Helton, J.C. & Johnson, J.D. & Oberkampf, W.L. & Sallaberry, C.J., 2006. "Sensitivity analysis in conjunction with evidence theory representations of epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1414-1434.

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