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Accelerated Degradation Model of Nonlinear Wiener Process Based on Fixed Time Index

Author

Listed:
  • Hanzhong Liu

    (School of Automation, Nanjing Institute of Technology, Nanjing 211167, China)

  • Jiacai Huang

    (School of Automation, Nanjing Institute of Technology, Nanjing 211167, China)

  • Yuanhong Guan

    (School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China)

  • Li Sun

    (School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China)

Abstract

In the process of extrapolating a lifetime distribution function under normal storage conditions through nonlinear accelerated degradation data, time indexes under the normal storage conditions are usually set to the mean value of time indexes under various accelerated stresses. However, minor differences in time indexes may lead to great changes in the assessment results. For such a problem, an accelerated degradation model of a nonlinear Wiener process based on a fixed time index is established first and meanwhile, the impact of the measurement error is considered. Then, the probability density function is normalized, and multiple unknown parameters are estimated by using fminsearch function in MATLAB and multiple iterations. Finally, the model is validated by accelerated degradation test data of accelerometers and the O-type rubber sealing rings. The results show that there is a difference of 30,710 h for accelerometers between the mean time to failure under normal storage conditions obtained by the proposed method and the mean time to failure when the time indexes are the mean value of those under various accelerated stresses, and the main cause of the difference is compared and analyzed. A similar phenomenon is observed in the case study of O-type rubber sealing rings.

Suggested Citation

  • Hanzhong Liu & Jiacai Huang & Yuanhong Guan & Li Sun, 2019. "Accelerated Degradation Model of Nonlinear Wiener Process Based on Fixed Time Index," Mathematics, MDPI, vol. 7(5), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:416-:d:229744
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    References listed on IDEAS

    as
    1. Yuan, X.-X. & Pandey, M.D., 2009. "A nonlinear mixed-effects model for degradation data obtained from in-service inspections," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 509-519.
    2. Wang, Xiaolin & Balakrishnan, Narayanaswamy & Guo, Bo, 2014. "Residual life estimation based on a generalized Wiener degradation process," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 13-23.
    3. Zhi‐Sheng Ye & Min Xie, 2015. "Rejoinder to ‘Stochastic modelling and analysis of degradation for highly reliable products’," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(1), pages 35-36, January.
    4. Zhi‐Sheng Ye & Min Xie, 2015. "Stochastic modelling and analysis of degradation for highly reliable products," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(1), pages 16-32, January.
    5. Shengjin Tang & Xiaosong Guo & Chuanqiang Yu & Haijian Xue & Zhijie Zhou, 2014. "Accelerated Degradation Tests Modeling Based on the Nonlinear Wiener Process with Random Effects," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-11, May.
    6. Huang, Jianlin & Golubović, Dušan S & Koh, Sau & Yang, Daoguo & Li, Xiupeng & Fan, Xuejun & Zhang, G.Q., 2016. "Lumen degradation modeling of white-light LEDs in step stress accelerated degradation test," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 152-159.
    Full references (including those not matched with items on IDEAS)

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