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.

可靠性敏感性分析涉及测量系统的不确定输入参数对其故障概率的影响。统计相关的输入对计算和解释这些敏感性指数提出了挑战；这种依赖性需要辨别描述系统输入的概率模型和描述系统本身的计算模型产生的变量相互作用。为了在可靠性敏感性分析的背景下实现这种效应分离，我们扩展了 Mara 和 Tarantola (2012) 最初提出的与罕见事件无关的模型输出的想法。我们计算所有输入对罕见事件指标函数方差的独立（通过计算模型的影响）和完整（通过计算和概率模型的影响）贡献。我们使用一组故障样本来计算罕见事件指标的全套基于方差的敏感性指数。这是可能的，通过考虑$d$这组故障样本与原始样本的不同层次结构的等概率变换$d$标准正态空间的依赖输入的维空间。该方法有助于使用作为基于样本的罕见事件估计方法的单次运行的副产品获得的单组故障样本来计算全套基于方差的可靠性灵敏度指数。也就是说，不需要对计算模型进行额外的评估。我们在测试功能和两个工程问题上演示了该方法。