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Shock and Vibration
Volume 2016, Article ID 2315916, 15 pages
Research Article

Reliability Analysis with Multiple Dependent Features from a Vibration-Based Accelerated Degradation Test

1Science and Technology on Reliability and Environmental Engineering Laboratory, School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
2Department of Industrial Engineering, University of Arkansas, Fayetteville, AR 72701, USA

Received 14 July 2016; Accepted 27 October 2016

Academic Editor: Minvydas Ragulskis

Copyright © 2016 Fuqiang 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.


Accelerated degradation testing (ADT) has been widely used for reliability prediction of highly reliable products. In many applications, ADT data consists of multiple degradation-related features, and these features are usually dependent. When dealing with such ADT data, it is important to fully utilize the multiple degradation features and take into account their inherent dependency. This paper proposes a novel reliability-assessment method that combines Brownian motion and copulas to model ADT data obtained from vibration signals. In particular, degradation feature extraction is first carried out using the raw vibration signals, and a feature selection method quantifying feature properties, such as trendability, monotonicity, and robustness, is adopted to determine the most suitable degradation features. Then, a multivariate s-dependent ADT model is developed, where a Brownian motion is used to depict the degradation path of each degradation feature and a copula function is employed to describe the dependence among these degradation features. Finally, the proposed ADT model is demonstrated using the vibration-based ADT data for an electric motor.