Abstract Fuzzy probability offers a framework for taking into account the effects of both aleatoric and epistemic uncertainty on the performance of a system, quantifying its level of safety, for example, in terms of a fuzzy failure probability. However, the practical application of fuzzy probability is often challenging due to increased numerical efforts arising from the need to propagate both types of uncertainties. Hence, this contribution proposes an approach for approximate calculation of fuzzy failure probabilities for a class of problems that involve moderately nonlinear performance functions, where uncertain input parameters of a model are characterized as random variables while their associated distribution parameters (for example, mean and standard deviation) are described as fuzzy variables. The proposed approach is cast as a post-processing step of a standard (yet advanced) reliability analysis. The key issue for performing an approximate calculation of the fuzzy failure probabilities is extracting probability sensitivity information from the reliability analysis stage as well as the introduction of intervening variables that capture – to some extent – the nonlinear relation between distribution parameters and the failure probability. A series of relatively simple illustrative examples demonstrate the capabilities of the proposed approach, highlighting its numerical advantages, as it comprises a single standard reliability analysis plus some additional system analyses.

中文翻译：

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应用干预变量的模糊故障概率估计

摘要 模糊概率提供了一个框架，用于考虑任意和认知不确定性对系统性能的影响，量化其安全水平，例如，根据模糊故障概率。然而，模糊概率的实际应用通常具有挑战性，因为需要传播两种类型的不确定性而增加了数值计算。因此，这个贡献提出了一种近似计算模糊失效概率的方法，用于一类涉及适度非线性性能函数的问题，其中模型的不确定输入参数被表征为随机变量，而它们的相关分布参数（例如，均值和标准偏差）被描述为模糊变量。所提出的方法被视为标准（但高级）可靠性分析的后处理步骤。执行模糊失效概率近似计算的关键问题是从可靠性分析阶段提取概率敏感性信息以及引入干预变量，这些变量在某种程度上捕获分布参数和失效概率之间的非线性关系。一系列相对简单的说明性示例展示了所提出方法的能力，突出了其数值优势，因为它包括单个标准可靠性分析和一些额外的系统分析。执行模糊失效概率近似计算的关键问题是从可靠性分析阶段提取概率敏感性信息以及引入干预变量，这些变量在某种程度上捕获分布参数和失效概率之间的非线性关系。一系列相对简单的说明性示例展示了所提出方法的能力，突出了其数值优势，因为它包括单个标准可靠性分析和一些额外的系统分析。执行模糊失效概率近似计算的关键问题是从可靠性分析阶段提取概率敏感性信息以及引入干预变量，这些变量在某种程度上捕获分布参数和失效概率之间的非线性关系。一系列相对简单的说明性示例展示了所提出方法的能力，突出了其数值优势，因为它包括单个标准可靠性分析和一些额外的系统分析。