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A Stable Approach Based on Asymptotic Space Integration for Moment‐Independent Uncertainty Importance Measure

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  • Xin Xu
  • Zhenzhou Lu
  • Xiaopeng Luo

Abstract

The error estimate of Borgonovo's moment‐independent index δi is considered, and it shows that the possible computational complexity of δi is mainly due to the probability density function (PDF) estimate because the PDF estimate is an ill‐posed problem and its convergence rate is quite slow. So it reminds us to compute Borgonovo's index using other methods. To avoid the PDF estimate, δi, which is based on the PDF, is first approximatively represented by the cumulative distribution function (CDF). The CDF estimate is well posed and its convergence rate is always faster than that of the PDF estimate. From the representation, a stable approach is proposed to compute δi with an adaptive procedure. Since the small probability multidimensional integral needs to be computed in this procedure, a computational strategy named asymptotic space integration is introduced to reduce a high‐dimensional integral to a one‐dimensional integral. Then we can compute the small probability multidimensional integral by adaptive numerical integration in one dimension with an improved convergence rate. From the comparison of numerical error analysis of some examples, it can be shown that the proposed method is an effective approach to uncertainty importance measure computation.

Suggested Citation

  • Xin Xu & Zhenzhou Lu & Xiaopeng Luo, 2014. "A Stable Approach Based on Asymptotic Space Integration for Moment‐Independent Uncertainty Importance Measure," Risk Analysis, John Wiley & Sons, vol. 34(2), pages 235-251, February.
    • Handle: RePEc:wly:riskan:v:34:y:2014:i:2:p:235-251
    DOI: 10.1111/risa.12087
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    References listed on IDEAS

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    1. Borgonovo, E., 2007. "A new uncertainty importance measure," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 771-784.
    2. Emanuele Borgonovo & William Castaings & Stefano Tarantola, 2011. "Moment Independent Importance Measures: New Results and Analytical Test Cases," Risk Analysis, John Wiley & Sons, vol. 31(3), pages 404-428, March.
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    7. Emanuele Borgonovo, 2006. "Measuring Uncertainty Importance: Investigation and Comparison of Alternative Approaches," Risk Analysis, John Wiley & Sons, vol. 26(5), pages 1349-1361, October.
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    Cited by:

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