A variance-based importance index for systems with dependent components.

© 2023. Elsevier This document is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ This document is the accepted version of a published work that appeared in final form in Fuzzy Sets and SystemsThis paper proposes a variance-based measure of importance for coherent systems with dependent and heterogeneous com-ponents. 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 estima-tion 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