Reliability sensitivity analysis is concerned with measuring the influence of a system's uncertain input parameters on its probability of failure. Statistically dependent inputs present a challenge in both computing and interpreting these sensitivity indices; such dependencies require discerning between variable interactions produced by the probabilistic model describing the system inputs and the computational model describing the system itself. To accomplish such a separation of effects in the context of reliability sensitivity analysis we extend on an idea originally proposed by Mara and Tarantola (2012) for model outputs unrelated to rare events. We compute the independent (influence via computational model) and full (influence via both computational and probabilistic model) contributions of all inputs to the variance of the indicator function of the rare event. We compute this full set of variance-based sensitivity indices of the rare event indicator using a single set of failure samples. This is possible by considering $d$ different hierarchically structured isoprobabilistic transformations of this set of failure samples from the original $d$-dimensional space of dependent inputs to standard-normal space. The approach facilitates computing the full set of variance-based reliability sensitivity indices with a single set of failure samples obtained as the byproduct of a single run of a sample-based rare event estimation method. That is, no additional evaluations of the computational model are required. We demonstrate the approach on a test function and two engineering problems.

翻译：可靠性灵敏度分析关注于衡量系统不确定输入参数对其失效概率的影响。统计上依赖的输入在计算和解释这些灵敏度指标时均构成挑战；此类依赖关系需要区分由描述系统输入的概率模型与描述系统本身的计算模型所产生的变量交互作用。为在可靠性灵敏度分析中实现这种效应分离，我们扩展了Mara和Tarantola（2012）最初针对非稀有事件模型输出提出的思想。我们计算所有输入对稀有事件指示函数方差的独立贡献（通过计算模型的影响）和完整贡献（通过计算与概率模型的共同影响）。我们利用单组失效样本计算稀有事件指示函数的完整方差基灵敏度指标集。这是通过考虑从原始d维依赖输入空间到标准正态空间的d种不同层次结构的等概率变换来实现的。该方法便于利用单次基于样本的稀有事件估计方法所产生的单组失效样本副产品，来计算完整的方差基可靠性灵敏度指标集。即，无需额外评估计算模型。我们在一个测试函数和两个工程问题中验证了该方法。