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Reliability analysis of series systems with multiple failure modes under epistemic and aleatory uncertainties

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  • N-C Xiao
  • H-Z Huang
  • Z Wang
  • Y Li
  • Y Liu

Abstract

Uncertainty exists widely in engineering practice. An engineering system may have multiple failure criteria. In the current paper, system reliability analysis with multiple failure modes under both epistemic and aleatory uncertainties is presented. Epistemic uncertainty is modelled using p-boxes, while aleatory uncertainty is modelled using probability distributions. A first-order reliability method is developed and non-linear performance functions are linearized by the sampling method instead of the commonly used Taylor’s expansion at the most probable point. Furthermore, multiple failure modes in a system are often correlated because they depend on the same uncertain variables. In order to consider these correlated failure modes, the methods proposed by Feng and Frank are extended in this paper in order to calculate the joint probability of failure for two arbitrary failure modes under both aleatory and epistemic uncertainties. The Pearson correlation coefficient of two arbitrary failure modes is determined by the sampling method. Since two types of uncertainty exist in the system, the probability of system failure is an interval rather than a point value. The probability of failure of the system can be obtained by the combination of the extension ‘narrow’ bound method and the interval arithmetic. A numerical example is presented to demonstrate the applicability of the proposed method.

Suggested Citation

  • N-C Xiao & H-Z Huang & Z Wang & Y Li & Y Liu, 2012. "Reliability analysis of series systems with multiple failure modes under epistemic and aleatory uncertainties," Journal of Risk and Reliability, , vol. 226(3), pages 295-304, June.
  • Handle: RePEc:sae:risrel:v:226:y:2012:i:3:p:295-304
    DOI: 10.1177/1748006X11421266
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    References listed on IDEAS

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    1. J.M. Aughenbaugh & J.W. Herrmann, 2009. "Information management for estimating system reliability using imprecise probabilities and precise Bayesian updating," International Journal of Reliability and Safety, Inderscience Enterprises Ltd, vol. 3(1/2/3), pages 35-56.
    2. Phani R. Adduri & Ravi C. Penmetsa, 2007. "Fast Fourier transform based system reliability analysis," International Journal of Reliability and Safety, Inderscience Enterprises Ltd, vol. 1(3), pages 239-259.
    3. Sankararaman, Shankar & Mahadevan, Sankaran, 2011. "Likelihood-based representation of epistemic uncertainty due to sparse point data and/or interval data," Reliability Engineering and System Safety, Elsevier, vol. 96(7), pages 814-824.
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    Cited by:

    1. Mi, Jinhua & Li, Yan-Feng & Yang, Yuan-Jian & Peng, Weiwen & Huang, Hong-Zhong, 2016. "Reliability assessment of complex electromechanical systems under epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 1-15.
    2. Ning-Cong Xiao & Yan-Feng Li & Le Yu & Zhonglai Wang & Hong-Zhong Huang, 2014. "Saddlepoint approximation-based reliability analysis method for structural systems with parameter uncertainties," Journal of Risk and Reliability, , vol. 228(5), pages 529-540, October.
    3. Chengning Zhou & Ning-Cong Xiao & Ming J Zuo & Xiaoxu Huang, 2020. "AK-PDF: An active learning method combining kriging and probability density function for efficient reliability analysis," Journal of Risk and Reliability, , vol. 234(3), pages 536-549, June.
    4. Ying-Kui Gu & Chao-Jun Fan & Ling-Qiang Liang & Jun Zhang, 2022. "Reliability calculation method based on the Copula function for mechanical systems with dependent failure," Annals of Operations Research, Springer, vol. 311(1), pages 99-116, April.

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