Arabian Journal for Science and Engineering

, Volume 44, Issue 3, pp 2751–2762 | Cite as

A Bilinear Degradation Model Considering Unit-Specific Property

  • Xinlei Wen
  • Zhihua WangEmail author
  • Junxing Li
  • Chengrui Liu
  • Yongbo Zhang
Research Article - Systems Engineering


The Wiener process model has been widely applied in degradation analysis for long-life and highly reliable products. However, the biggest challenge lies in how to properly describe the time-varying degradation mean and variance and the unit-specific property. Meanwhile, the current Wiener process degradation models cannot properly describe the degradation processes with increasing deterioration path and decreasing dispersity which do exist in real applications. Motivated by this practical problem and based on our previous study, an improved Wiener process degradation model is proposed. The degradation model can be widely adopted to depict practical degradation procedures illustrating a linear degradation mean and a quadratic variance. A random drift coefficient is further incorporated to properly consider the heterogeneity among items. The improvements can further expand the applicable scope and improve the statistical inference accuracy. Maximum likelihood estimations of unknown parameters are derived. The mean time to failure and the percentile of the failure time distribution are also constructed. Comparative results with reference methods from comprehensive simulation studies and practical applications both illustrate that the proposed method is more reasonable and can provide superior evaluation accuracy, even in limited sample size circumstances.


Degradation modeling Time-varying characteristic Linear degradation path Quadratic variance Unit-specific property 


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The authors are grateful to the anonymous reviewers, and the editor, for their critical and constructive review of the manuscript. This study was co-supported by the National Basic Research Program of China (Grant No. 2016YFF0202605) and National Natural Science Foundation of China (Grant No. 11501022).


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Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.School of Aeronautic Science and EngineeringBeihang UniversityBeijingChina
  2. 2.School of Mechatronical EngineeringHenan University of Science and TechnologyLuoyangChina
  3. 3.Beijing Institute of Control EngineeringBeijingChina

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