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Mathematical Problems in Engineering
Volume 2016, Article ID 5246108, 13 pages
Research Article

Accelerated Degradation Process Analysis Based on the Nonlinear Wiener Process with Covariates and Random Effects

1Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China
2Science and Technology on Combustion and Explosion Laboratory, Xi’an, Shanxi 710065, China

Received 13 September 2016; Accepted 27 November 2016

Academic Editor: Eusebio Valero

Copyright © 2016 Li Sun 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.


It is assumed that the drift parameter is dependent on the acceleration variables and the diffusion coefficient remains the same across the whole accelerated degradation test (ADT) in most of the literature based on Wiener process. However, the diffusion coefficient variation would also become obvious in some applications with the stress increasing. Aiming at the phenomenon, the paper concludes that both the drift parameter and the diffusion parameter depend on stress variables based on the invariance principle of failure mechanism and Nelson assumption. Accordingly, constant stress accelerated degradation process (CSADP) and step stress accelerated degradation process (SSADP) with random effects are modeled. The unknown parameters in the established model are estimated based on the property of degradation and degradation increment, separately for CASDT and SSADT, by the maximum likelihood estimation approach with measurement error. In addition, the simulation steps of accelerated degradation data are provided and simulated step stress accelerated degradation data is designed to validate the proposed model compared to other models. Finally, a case study of CSADT is conducted to demonstrate the benefits of our model in the practical engineering.