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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
  • 23 Downloads

Abstract

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.

Keywords

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

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Notes

Acknowledgements

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).

References

  1. 1.
    Jin, G.; Liu, Q.; Zhou, J.; Zhou, Z.: RePofe: reliability physics of failure estimation based on stochastic performance degradation for the momentum wheel. Eng. Fail. Anal. 22(2), 50–63 (2012)Google Scholar
  2. 2.
    Kharoufeh, J.P.; Cox, S.M.: Stochastic models for degradation-based reliability. IIE Trans. 37(6), 533–542 (2005)Google Scholar
  3. 3.
    Lu, C.J.; William, O.M.: Using degradation measures to estimate a time-to-failure distribution. Technometrics 35(2), 161–174 (1993)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Mohammadian, S.H.; Aït-Kadi, D.; Routhier, F.: Quantitative accelerated degradation testing: practical approaches. Reliab. Eng. Syst. Saf. 95(2), 149–159 (2010)Google Scholar
  5. 5.
    Nicolai, R.P.; Dekker, R.; Van Noortwijk, J.M.: A comparison of models for measurable deterioration: an application to coatings on steel structures. Reliab. Eng. Syst. Saf. 92(12), 1635–1650 (2007)Google Scholar
  6. 6.
    Oliveira, V.R.B.D.; Colosimo, E.A.: Comparison of methods to estimate the time-to-failure distribution in degradation tests. Qual. Reliab. Eng. 20(4), 363–373 (2004)Google Scholar
  7. 7.
    Wang, Z.H.; Cao, J.M.; Ma, X.B.; Qiu, H.Y.; Zhang, Y.B.; Fu, H.M.; Krishnaswamy, S.: An improved independent increment process degradation model with bilinear properties. Arab. J. Sci. Eng. (2017).  https://doi.org/10.1007/s13369-016-2383-0 Google Scholar
  8. 8.
    Singpurwalla, N.D.: Survival in dynamic environments. Stat. Sci. 10(1), 86–103 (1995)zbMATHGoogle Scholar
  9. 9.
    Wang, X.: Wiener processes with random effects for degradation data. J. Multivar. Anal. 101(2), 340–351 (2010)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Tseng, S.T.; Peng, C.Y.: Stochastic diffusion modeling of degradation data. J. Data Sci. 5(3), 315–333 (2007)Google Scholar
  11. 11.
    Park, C.; Padgett, W.J.: New cumulative damage models for failure using stochastic processes as initial damage. IEEE Trans. Reliab. 54(3), 530–540 (2005)Google Scholar
  12. 12.
    Whitmore, G.A.; Schenkelberg, F.: Modelling accelerated degradation data using Wiener diffusion with a time scale transformation. Lifetime Data Anal. 3(1), 27–45 (1997)zbMATHGoogle Scholar
  13. 13.
    Tseng, S.T.; Tang, J.; Ku, I.H.: Determination of burn-in parameters and residual life for highly reliable products. Nav. Res. Logist. 50(1), 1–14 (2003)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Park, C.; Padgett, W.J.: Stochastic degradation models with several accelerating variables. IEEE Trans. Reliab. 55(55), 379–390 (2006)Google Scholar
  15. 15.
    Meeker, W.Q.; Escobar, L.A.: Statistical Methods for Reliability Data. Wiley, London (2014)zbMATHGoogle Scholar
  16. 16.
    Chaluvadi, V.: Accelerated life testing of electronic revenue meters. Dissertations & Theses—Gradworks (2008)Google Scholar
  17. 17.
    Wang, Z.H.; Fu, H.M.; Zhang, Y.B.: Analyzing degradation by an independent increment process. Qual. Reliab. Eng. Int. 30(8), 1275–1283 (2014)Google Scholar
  18. 18.
    Wang, Z.H.; Zhang, Y.B.; Wu, Q.; Fu, H.M.; Liu, C.R.; Krishnaswamy, S.: Degradation reliability modeling based on an independent increment process with quadratic variance. Mech. Syst. Signal Process. 70–71, 467–483 (2016)Google Scholar
  19. 19.
    Zhang, Z.; Si, X.; Hu, C.; Kong, X.: Degradation modeling-based remaining useful life estimation: a review on approaches for systems with heterogeneity. Proc. Inst. Mech. Eng. Part O J. Risk Reliab. 229(4), 343–355 (2015)Google Scholar
  20. 20.
    Ahmad, M.; Sheikh, A.K.: Bernstein reliability model: derivation and estimation of parameters. Reliab. Eng. 8(3), 131–148 (1984)Google Scholar
  21. 21.
    Crowder, M.; Lawless, J.: On a scheme for predictive maintenance. Eur. J. Oper. Res. 176(3), 1713–1722 (2007)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Peng, C.Y.; Tseng, S.T.: Mis-specification analysis of linear degradation models. IEEE Trans. Reliab. 58(3), 444–455 (2009)Google Scholar
  23. 23.
    Lu, J.C.; Park, J.; Yang, Q.: Statistical inference of a time-to-failure distribution derived from linear degradation data. Technometrics 39(4), 391–400 (1997)zbMATHGoogle Scholar
  24. 24.
    Ye, Z.S.; Wang, Y.; Tsui, K.L.; Pecht, M.: Degradation data analysis using wiener processes with measurement errors. IEEE Trans. Reliab. 62(4), 772–780 (2013)Google Scholar
  25. 25.
    Jin, G.; Matthews, D.; Fan, Y.; Liu, Q.: Physics of failure-based degradation modeling and lifetime prediction of the momentum wheel in a dynamic covariate environment. Eng. Fail. Anal. 28, 222–240 (2013)Google Scholar
  26. 26.
    Nagi, Z.G.; Mark, A.L.; Rong, L.I.; Jennifer, K.R.: Residual-life distributions from component degradation signals: a Bayesian approach. IIE Trans. 37(6), 543–557 (2005)Google Scholar
  27. 27.
    Beasley, J.E.; Chu, P.C.: A genetic algorithm for the set covering problem. Eur. J. Oper. Res. 94(2), 392–404 (1996)zbMATHGoogle Scholar
  28. 28.
    Davis, L.: Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York (1991)Google Scholar
  29. 29.
    Kang, F.; Xu, Q.; Li, J.: Slope reliability analysis using surrogate models via new support vector machines with swarm intelligence. Appl. Math. Model. 40(11–12), 6105–6120 (2016)MathSciNetGoogle Scholar
  30. 30.
    Kang, F.; Han, S.; Salgado, R.; Li, J.: System probabilistic stability analysis of soil slopes using Gaussian process regression with Latin hypercube sampling. Comput. Geotech. 63, 13–25 (2015)Google Scholar

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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