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Title: Dependence evaluation for reliability monitoring data by using the multivariate Farlie-Gumbel-Morgenstern copula Authors:  Shuhei Ota - Kanagawa University (Japan) [presenting]
Mitsuhiro Kimura - Hosei University (Japan)
Abstract: In the research field of reliability engineering, multivariate distributions are frequently used to assess the probability that systems fail dependently. We focus on the multivariate Farlie-Gumbel-Morgenstern (FGM) copula that is one of the multivariate distributions. The problem of estimating the multivariate FGM copula parameters is that the maximum likelihood estimation is not practical because the multivariate FGM copula has many parameters to be estimated, and the parameter constraints are complex. We propose an efficient estimation algorithm for the multivariate FGM copula based on the theory of the inference functions for margins. We show that the estimator given by our estimation algorithm has asymptotic normality as well as its performance determined through simulation studies. Finally, we apply the estimation algorithm to real data analysis of the reliability of ball bearings.