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Variance-based reliability sensitivity analysis and the FORM α-factors

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  • Papaioannou, Iason
  • Straub, Daniel

Abstract

In reliability assessments, it is useful to compute importance measures that provide information on the influence of the input random variables on the probability of failure. Classical importance measures are the α-factors, which are obtained as a by-product of the first-order reliability method (FORM). These factors are the directional cosines of the most probable failure point in an underlying independent standard normal space. Alternatively, one might assess sensitivity by a variance decomposition of the indicator function, i.e., the function that indicates membership of the random variables to the failure domain. This paper discusses the relation of the latter variance-based sensitivity measures to the FORM α-factors and analytically shows that there exist one-to-one relationships between them for linear limit-state functions of normal random variables. We also demonstrate that these relationships enable a good approximation of variance-based sensitivities for general reliability problems. The derived relationships shed light on the behavior of first-order and total-effect indices of the failure event in engineering reliability problems.

Suggested Citation

  • Papaioannou, Iason & Straub, Daniel, 2021. "Variance-based reliability sensitivity analysis and the FORM α-factors," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    • Handle: RePEc:eee:reensy:v:210:y:2021:i:c:s0951832021000612
    DOI: 10.1016/j.ress.2021.107496
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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.
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    4. Ehre, Max & Papaioannou, Iason & Straub, Daniel, 2020. "A framework for global reliability sensitivity analysis in the presence of multi-uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
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    6. Papaioannou, Iason & Geyer, Sebastian & Straub, Daniel, 2019. "Improved cross entropy-based importance sampling with a flexible mixture model," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
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    Cited by:

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    5. Zhang, Feng & Wang, Xinhe & Hou, Xinting & Han, Cheng & Wu, Mingying & Liu, Zhongbing, 2022. "Variance-based global sensitivity analysis of a hybrid thermoelectric generator fuzzy system," Applied Energy, Elsevier, vol. 307(C).

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