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International Journal of Photoenergy
Volume 2015, Article ID 243648, 8 pages
Research Article

LED Lighting System Reliability Modeling and Inference via Random Effects Gamma Process and Copula Function

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

Received 13 December 2014; Accepted 15 January 2015

Academic Editor: Ahmad Umar

Copyright © 2015 Huibing Hao 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.


Light emitting diode (LED) lamp has attracted increasing interest in the field of lighting systems due to its low energy and long lifetime. For different functions (i.e., illumination and color), it may have two or more performance characteristics. When the multiple performance characteristics are dependent, it creates a challenging problem to accurately analyze the system reliability. In this paper, we assume that the system has two performance characteristics, and each performance characteristic is governed by a random effects Gamma process where the random effects can capture the unit to unit differences. The dependency of performance characteristics is described by a Frank copula function. Via the copula function, the reliability assessment model is proposed. Considering the model is so complicated and analytically intractable, the Markov chain Monte Carlo (MCMC) method is used to estimate the unknown parameters. A numerical example about actual LED lamps data is given to demonstrate the usefulness and validity of the proposed model and method.