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A comparative study of probability estimation methods for reliability analysis

Structural and Multidisciplinary Optimization volume 45, pages 33–52 (2012)Cite this article

Abstract

In this paper we investigate the performance of probability estimation methods for reliability analysis. The probability estimation methods typically construct the probability density function (PDF) of a system response using estimated statistical moments, and then perform reliability analysis based on the approximate PDF. In recent years, a number of probability estimation methods have been proposed, such as the Pearson system, saddlepoint approximation, Maximum Entropy Principle (MEP), and Johnson system. However, no general guideline to suggest a most appropriate probability estimation method has yet been proposed. In this study, we carry out a comparative study of the four probability estimation methods so as to derive the general guidelines. Several comparison metrics are proposed to quantify the accuracy in the PDF approximation, cumulative density function (CDF) approximation and tail probability estimations (or reliability analysis). This comparative study gives an insightful guidance for selecting the most appropriate probability estimation method for reliability analysis. The four probability estimation methods are extensively tested with one mathematical and two engineering examples, each of which considers eight different combinations of the system response characteristics in terms of response boundness, skewness, and kurtosis.

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Acknowledgments

Research is partially supported by the NSF GOALI 07294, the STAS contract (TCN-05122) sponsored by the U.S. Army TARDEC, by the New Faculty Development Program by Seoul National University, and by the SNU-IAMD.

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Authors and Affiliations

  1. Department of Industrial and Manufacturing Systems Engineering, University of Michigan, Dearborn, MI, 48168, USA

    Zhimin Xi

  2. Department of Mechanical Engineering, University of Maryland, College Park, MD, 20742, USA

    Chao Hu

  3. School of Mechanical and Aerospace Engineering, Seoul National University, Seoul, South Korea

    Byeng D. Youn

Authors
  1. Zhimin Xi
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  2. Chao Hu
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  3. Byeng D. Youn
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Corresponding author

Correspondence to Byeng D. Youn.

Appendix

Appendix

Table 12 Random input properties of three examples in case 1
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Table 13 Random input properties of three examples in case 2
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Table 14 Random input properties of three examples in case 5
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Table 15 Random input properties of three examples in case 6
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Table 16 Random input properties of three examples in case 7
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Table 17 Random input properties of three examples in case 8
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Xi, Z., Hu, C. & Youn, B.D. A comparative study of probability estimation methods for reliability analysis. Struct Multidisc Optim 45, 33–52 (2012). https://doi.org/10.1007/s00158-011-0656-5

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  • DOI: https://doi.org/10.1007/s00158-011-0656-5

Keywords

  • Reliability analysis
  • Pearson system
  • Saddlepoint approximation
  • MEP
  • Johnson system