Multivariate Farlie-Gumbel-Morgenstern Copula and Its Application to Reliability Data Analysis

Abstract

The dependence among multiple components (subsystems and components) that construct large-scale and complex systems should be considered for reliability analysis of the system. In this article, we introduce a method of reliability analysis by using multivariate Farlie-Gumbel-Morgenstern（FGM）copulas. We first explain the properties of the FGM copula. Next, to assess statistical dependence among components, we provide two likelihood-based estimation methods, the method of simultaneous estimation and the method of inference functions for margins, for parameters of the FGM copula. In particular, we derive standard errors and confidence intervals of estimators and investigate their properties. Finally, we demonstrate reliability analysis for an actual dataset of the reliability of ball bearings.