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Mathematical Problems in Engineering
Volume 2014, Article ID 510929, 11 pages
Research Article

Bivariate Nonlinear Diffusion Degradation Process Modeling via Copula and MCMC

1Department of Industrial Engineering, Southeast University, Nanjing 211189, China
2Department of Mathematics, Hubei Engineering University, Xiaogan 432100, China

Received 27 October 2013; Revised 12 February 2014; Accepted 14 February 2014; Published 30 March 2014

Academic Editor: Xi Frank Xu

Copyright © 2014 Huibing Hao and Chun Su. 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.


A novel reliability assessment method for degradation product with two dependent performance characteristics (PCs) is proposed, which is different from existing work that only utilized one dimensional degradation data. In this model, the dependence of two PCs is described by the Frank copula function, and each PC is governed by a random effected nonlinear diffusion process where random effects capture the unit to unit differences. Considering that the model is so complicated and analytically intractable, Markov Chain Monte Carlo (MCMC) method is used to estimate the unknown parameters. A numerical example about LED lamp is given to demonstrate the usefulness and validity of the proposed model and method. Numerical results show that the random effected nonlinear diffusion model is very useful by checking the goodness of fit of the real data, and ignoring the dependence between PCs may result in different reliability conclusion.