This paper presents an approach for estimating the fuzzy failure probability associated with reliability problems where uncertainty is characterized through random variables whose distribution parameters are described as fuzzy variables. The main contribution of this work is addressing such problem with the First-Order Reliability Method, with some minor modifications. The epistemic uncertainty is addressed by resorting to an augmented reliability problem. In this way, a single reliability analysis suffices for estimating the membership function associated with the fuzzy failure probability. Numerical results suggest that the proposed approach is most useful for providing an estimate of the membership function associated with the failure probability with reduced numerical costs.

本文提出了一种估计与可靠性问题相关的模糊失效概率的方法，其中不确定性通过随机变量来表征，随机变量的分布参数被描述为模糊变量。这项工作的主要贡献是使用一阶可靠性方法解决此类问题，并进行一些小的修改。认知不确定性是通过求助于增强可靠性问题来解决的。这样，单个可靠性分析足以估计与模糊故障概率相关的隶属函数。数值结果表明，所提出的方法对于提供与故障概率相关的隶属函数的估计最有用，同时降低了数值成本。