Global variance-based reliability sensitivity indices arise from a variance decomposition of the indicator function describing the failure event. The first-order indices reflect the main effect of each variable on the variance of the failure event and can be used for variable prioritization; the total-effect indices represent the total effect of each variable, including its interaction with other variables, and can be used for variable fixing. This contribution derives expressions for the variance-based reliability indices of systems with multiple failure modes that are based on the first-order reliability method (FORM). The derived expressions are a function of the FORM results and, hence, do not require additional expensive model evaluations. They do involve the evaluation of multinormal integrals, for which effective solutions are available. We demonstrate that the derived expressions enable an accurate estimation of variance-based reliability sensitivities for general system problems to which FORM is applicable.

翻译：全局方差基可靠性灵敏度指标源于对描述失效事件的指示函数进行方差分解。一阶指标反映各变量对失效事件方差的直接影响，可用于变量优先级排序；总效应指标表征各变量的总影响（包含其与其他变量的交互作用），可用于变量固定。本研究推导了基于一阶可靠性方法（FORM）的多失效模式系统方差基可靠性指标表达式。所推导的表达式以FORM计算结果为函数，因此无需额外进行昂贵的模型评估，但涉及多正态积分的计算（对此已有有效求解方案）。我们证明，对于FORM可适用的一般系统问题，该推导公式能够实现方差基可靠性灵敏度的精确估计。