Journal article
Random Fuzzy Extension of the Universal Generating Function Approach for the Reliability Assessment of Multi-State Systems Under Aleatory and Epistemic Uncertainties
Many engineering systems can perform their intended tasks with various levels of performance, which are modeled as multi-state systems (MSS) for system availability and reliability assessment problems. Uncertainty is an unavoidable factor in MSS modeling, and it must be effectively handled. In this work, we extend the traditional universal generating function (UGF) approach for multi-state system (MSS) availability and reliability assessment to account for both aleatory and epistemic uncertainties.
First, a theoretical extension, named hybrid UGF (HUGF), is made to introduce the use of random fuzzy variables (RFVs) in the approach. Second, 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 availability and reliability estimation.
The HUGF approach is demonstrated with a numerical example, and applied to study a distributed generation system, with a comparison to the widely used Monte Carlo simulation method.
Language: | English |
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Publisher: | IEEE |
Year: | 2014 |
Pages: | 13-25 |
ISSN: | 15581721 and 00189529 |
Types: | Journal article |
DOI: | 10.1109/TR.2014.2299031 |
<formula formulatype="inline"><tex Notation="TeX">$p$</tex></formula>-box Availability Generators HUGF approach Joints MSS availability Monte Carlo methods Monte Carlo simulation method Multi-state system Random variables Uncertainty aleatory uncertainties aleatory uncertainty availability assessment composition operator convolution distributed generation system epistemic uncertainties epistemic uncertainty fuzzy set theory hybrid UGF multistate systems p-boxes probabilistic convolution probability boxes random fuzzy extension random fuzzy variable reliability assessment problems reliability theory universal generating function universal generating function approach