A variance-based importance index for systems with dependent components

TL;DR

This paper introduces a variance-based importance index for systems with dependent and heterogeneous components, utilizing copulas to model dependence and providing methods for estimation and comparison.

Contribution

It presents a novel importance measure for systems with dependent components, including theoretical formulas and Monte Carlo procedures for practical computation.

Findings

The importance index can be explicitly calculated using copula-based models.

The measure effectively compares component contributions in dependent systems.

Monte Carlo methods provide accurate approximations of the importance measure.

Abstract

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.