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Mathematical Problems in Engineering
Volume 2014, Article ID 829597, 10 pages
Research Article

Reliability Modeling for Systems with Multiple Degradation Processes Using Inverse Gaussian Process and Copulas

1School of Reliability and Systems Engineering, Beihang University, Haidian District, Beijing 100191, China
2Beijing Institute of Space Long March Vehicle, Beijing 100076, China

Received 14 November 2013; Accepted 4 June 2014; Published 18 June 2014

Academic Editor: Fazal M. Mahomed

Copyright © 2014 Zhenyu Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We develop a reliability model for systems with s-dependent degradation processes using copulas. The proposed model accommodates assumptions of s-dependence among degradation processes and allows for different marginal distributions. This flexibility makes the model more attractive compared with the multivariate distribution model, which lay on the limitation of the homogeneous marginal distribution and can only describe linear correlation. Marginal degradation process is modeled by the inverse Gaussian (IG) process with time scale transformation. Furthermore, we incorporate random drift to account for the possible heterogeneity in population. This paper also develops the statistical inference method using EM algorithm with two-stage procedure. The comparison results of the reliability estimation under both s-dependent and s-independent assumptions are illustrated in the illustrative example to demonstrate the applicability of the proposed method.