^{1,3,a}, Pei-Pei Li

^{1,b}and Yan-Gnag Zhao

^{2,3,c}

^{1}School of Civil Engineering, Central South University, Changsha, China

^{a}luzhaohui@csu.edu.cn

^{b}lipeipei@csu.edu.cn

^{2}Department of Architecture, Kanagawa University, Kanagawa-ku, Yokohama, Japan

^{3}Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing, China

^{c}Zhao@kanagawa-u.ac.jp

We investigate the evaluation of the failure probability considering the uncertainties of the distribution parameters of random variables. When these uncertainties are considered, the failure probability becomes a random variable that is referred to as the conditional failure probability. In the present paper, a point-estimate method based on univariate-dimension reduction integration is used to approximate the mean of the conditional failure probability. The simplicity, accuracy and efficiency of the proposed methodology for evaluating the failure probability considering the uncertainties of distribution parameters are numerically examined, where MCS is utilized for comparison. It is found that neglecting parameter uncertainties will lead to the failure probability being underestimated. Since the developed method can be realized only if the first few central moments of the basic random variables are known, it can be utilized even when the probability distributions of the basic random variables are unknown.