This paper proposes a variance-based measure of importance for coherent systems with dependent and heterogeneous components. The particular cases of independent components and homogeneous components are also considered. We model the dependence structure among the components by the concept of copula. The proposed measure allows us to provide the best estimation of the system lifetime, in terms of the mean squared error, under the assumption that the lifetime of one of its components is known. We include theoretical results that are useful to calculate a closed-form of our measure and to compare two components of a system. We also provide some procedures to approximate the importance measure by Monte Carlo simulation methods. Finally, we illustrate the main results with several examples.

翻译：本文针对具有相依性和异质性部件的相干系统，提出了一种基于方差的重要性度量方法。同时考虑了部件独立与同质性的特殊情况。我们采用连接函数概念对部件间的相依结构进行建模。所提出的度量方法能够在已知某一部件寿命的条件下，以均方误差为准则，为系统寿命提供最优估计。我们给出了可用于计算该度量闭式解及比较系统两个部件的理论结果，同时提供了通过蒙特卡洛模拟方法近似计算重要性度量的若干算法。最后，通过多个算例对主要结果进行了演示。