Hybrid Universal Generating Function for the Reliability Assessment of Multi-State Systems under Aleatory and Epistemic Uncertainties

Abstract : In this work, we extend the traditional universal generating function (UGF) approach for multi-state system (MSS) reliability assessment to account for both aleatory and epistemic uncertainties. Firstly, a theoretical extension, named hybrid UGF (HUGF), is made to introduce the use of random fuzzy variables (RFVs) in the approach; secondly, the composition operator of HUGF is defined by considering simultaneously the probabilistic convolution and the fuzzy extension principle; finally, an efficient algorithm is designed to extract probability boxes (p-boxes) from the system HUGF, which allow quantifying different levels of imprecision in system reliability estimation. The HUGF approach is demonstrated on a numerical example.
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Yan-Fu Li, Y. Ding, Enrico Zio. Hybrid Universal Generating Function for the Reliability Assessment of Multi-State Systems under Aleatory and Epistemic Uncertainties. ESREL 2013, Sep 2013, Amsterdam, Netherlands. pp.1-8. ⟨hal-00911991⟩

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