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Global Sensitivity Analysis of Fuzzy Distribution Parameter on Failure Probability and Its Single‐Loop Estimation

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  • Lei Cheng
  • Zhenzhou Lu
  • Luyi Li

Abstract

An extending Borgonovo’s global sensitivity analysis is proposed to measure the influence of fuzzy distribution parameters on fuzzy failure probability by averaging the shift between the membership functions (MFs) of unconditional and conditional failure probability. The presented global sensitivity indices can reasonably reflect the influence of fuzzy‐valued distribution parameters on the character of the failure probability, whereas solving the MFs of unconditional and conditional failure probability is time‐consuming due to the involved multiple‐loop sampling and optimization operators. To overcome the large computational cost, a single‐loop simulation (SLS) is introduced to estimate the global sensitivity indices. By establishing a sampling probability density, only a set of samples of input variables are essential to evaluate the MFs of unconditional and conditional failure probability in the presented SLS method. Significance of the global sensitivity indices can be verified and demonstrated through several numerical and engineering examples.

Suggested Citation

  • Lei Cheng & Zhenzhou Lu & Luyi Li, 2014. "Global Sensitivity Analysis of Fuzzy Distribution Parameter on Failure Probability and Its Single‐Loop Estimation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:490718
    DOI: 10.1155/2014/490718
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    References listed on IDEAS

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    2. Barry Anderson & Emanuele Borgonovo & Marzio Galeotti & Roberto Roson, 2014. "Uncertainty in Climate Change Modeling: Can Global Sensitivity Analysis Be of Help?," Risk Analysis, John Wiley & Sons, vol. 34(2), pages 271-293, February.
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    4. Manel Baucells & Emanuele Borgonovo, 2013. "Invariant Probabilistic Sensitivity Analysis," Management Science, INFORMS, vol. 59(11), pages 2536-2549, November.
    5. 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.
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