Abstract In this paper we discuss the accuracy of probability of failure sensitivity analysis with sampling-based schemes. Three approaches commonly employed in literature are discussed: the Weak sensitivity analysis, the Direct employment of finite difference schemes and the Common Random Variable approach. Theoretical estimates for the bias, the coefficient of variation and the mean square error for each approach are presented. The results hold for a single random variable and the extension to more general situations should be pursued in future works. These results lead to the conclusion that the Common Random Variable approach is superior to the Direct approach from the theoretical point of view. The Weak approach, on the other hand, is equivalent to the Common Random Variable approach with central finite difference formula. The choice between these latter two approaches is then a matter of computational efficiency. The results of this work should contribute to further development of efficient algorithms for the problem under study.

中文翻译：

---

基于抽样的失效概率敏感性分析方案

摘要 在本文中，我们讨论了基于抽样方案的失效概率敏感性分析的准确性。讨论了文献中常用的三种方法：弱敏感性分析、有限差分方案的直接使用和公共随机变量方法。给出了每种方法的偏差、变异系数和均方误差的理论估计。结果适用于单个随机变量，并且应在未来的工作中扩展到更一般的情况。这些结果得出的结论是，从理论的角度来看，公共随机变量方法优于直接方法。另一方面，弱方法等效于具有中心有限差分公式的公共随机变量方法。后两种方法之间的选择则是计算效率的问题。这项工作的结果应该有助于进一步开发针对所研究问题的有效算法。