  This paper presents a novel numerical method for the hybrid reliability
analysis by using the uncertainty theory. Aleatory uncertainty and epistemic
uncertainty are considered simultaneously in this method. Epistemic uncertainty
is characterized by the uncertainty theory, and the effect of epistemic
uncertainty is quantified by the sub-additive uncertain measure. Then, under
the framework of the chance theory which can be interpreted as the combination
of the probability theory and the uncertainty theory, a general uncertainty
quantification model is established to deal with the hybrid reliability
analysis problem, then the corresponding reliability metric is defined. After
that, to improve the feasibility of the proposed model, by utilizing the polar
coordinate transformation based dimension reduction method, a numerical
analysis method for the hybrid reliability model are provided. At last, several
application cases are presented to prove the effectiveness of the proposed
method for the reliability analysis under hybrid uncertainty. The comparisons
between the results of the proposed method and the Monte Carlo simulation also
illustrate the merit of this method.
