Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 486368, 8 pages
http://dx.doi.org/10.1155/2014/486368
Research Article

A Bayesian Framework for Reliability Assessment via Wiener Process and MCMC

1Department of Industrial Engineering, Southeast University, Nanjing 211189, China
2Department of Mathematics, Hubei Engineering University, Xiaogan 432100, China

Received 27 August 2013; Revised 2 March 2014; Accepted 14 March 2014; Published 9 April 2014

Academic Editor: Sarp Adali

Copyright © 2014 Huibing Hao and Chun Su. 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.

Linked References

  1. W. Q. Meeker and L. A. Escobar, Statistical Method For Reliability Data, John Wiley & Sons, New York, NY, USA, 1998.
  2. W. Nelson, Accelerated Testing: Statistical Models, Test Plans, and Data Analysis, John Wiley & Sons, New York, NY, USA, 1990.
  3. M. J. Zuo, R. Y. Jiang, and R. C. M. Yam, “Approaches for reliability modeling of continuous state devices,” IEEE Transactions on Reliability, vol. 48, no. 1, pp. 9–18, 1999. View at Publisher · View at Google Scholar · View at Scopus
  4. S.-T. Tseng, N. Balakrishnan, and C.-C. Tsai, “Optimal step-stress accelerated degradation test plan for gamma degradation processes,” IEEE Transactions on Reliability, vol. 58, no. 4, pp. 611–618, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. Q. Duan, Z. Chen, and D. Zhao, “An expectation maximization algorithm to model failure times by continuous-time Markov chains,” Mathematical Problems in Engineering, vol. 2010, Article ID 242567, 16 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. H. W. Wang, J. Gao, and Z. Y. Liu, “Maintenance decision based on data fusion of aero engines,” Mathematical Problems in Engineering, vol. 2013, Article ID 628792, 10 pages, 2013. View at Publisher · View at Google Scholar
  7. C. Li and Y. Zhang, “Time-variant reliability assessment and its sensitivity analysis of cutting tool under invariant machining condition based on gamma process,” Mathematical Problems in Engineering, vol. 2012, Article ID 676923, 19 pages, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. S.-T. Tseng, J. Tang, and I.-H. Ku, “Determination of burn-in parameters and residual life for highly reliable products,” Naval Research Logistics, vol. 50, no. 1, pp. 1–14, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. Tang and T.-S. Su, “Estimating failure time distribution and its parameters based on intermediate data from a Wiener degradation model,” Naval Research Logistics, vol. 55, no. 3, pp. 265–276, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M.-Y. Lee and J. Tang, “A modified EM-algorithm for estimating the parameters of inverse Gaussian distribution based on time-censored Wiener degradation data,” Statistica Sinica, vol. 17, no. 3, pp. 873–893, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. C. Park and W. J. Padgett, “Stochastic degradation models with several accelerating variables,” IEEE Transactions on Reliability, vol. 55, no. 2, pp. 379–390, 2006. View at Publisher · View at Google Scholar · View at Scopus
  12. C.-Y. Peng and S.-T. Tseng, “Mis-specification analysis of linear degradation models,” IEEE Transactions on Reliability, vol. 58, no. 3, pp. 444–455, 2009. View at Publisher · View at Google Scholar · View at Scopus
  13. X. Wang, “Wiener processes with random effects for degradation data,” Journal of Multivariate Analysis, vol. 101, no. 2, pp. 340–351, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. X.-S. Si, W. Wang, C.-H. Hu, D.-H. Zhou, and M. G. Pecht, “Remaining useful life estimation based on a nonlinear diffusion degradation process,” IEEE Transactions on Reliability, vol. 61, no. 1, pp. 50–67, 2012. View at Publisher · View at Google Scholar · View at Scopus
  15. N. Z. Gebraeel, M. A. Lawley, R. Li, and J. K. Ryan, “Residual-life distributions from component degradation signals: a Bayesian approach,” IIE Transactions, vol. 37, no. 6, pp. 543–557, 2005. View at Publisher · View at Google Scholar · View at Scopus
  16. N. Z. Gebraeel and M. A. Lawley, “A neural network degradation model for computing and updating residual life distributions,” IEEE Transactions on Automation Science and Engineering, vol. 5, no. 1, pp. 154–163, 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. L. Bian and N. Gebraeel, “Computing and updating the first-passage time distribution for randomly evolving degradation signals,” IIE Transactions, vol. 44, pp. 974–987, 2012. View at Publisher · View at Google Scholar
  18. I. Ntzoufras, Bayesian Modeling Using WinBUGS, John Wiley & Sons, Hoboken, NJ, USA, 2009.
  19. D. J. Spiegelhalter, N. G. Best, B. P. Carlin, and A. van der Linde, “Bayesian measures of model complexity and fit,” Journal of the Royal Statistical Society B, vol. 64, no. 4, pp. 583–639, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. C. A. Santos and J. A. Achcar, “A Bayesian analysis in the presence of covariates for multivariate survival data: an example of application,” Revista Colombiana de Estadística, vol. 34, no. 1, pp. 111–131, 2011. View at Google Scholar · View at MathSciNet
  21. W. Wang, M. Carr, W. Xu, and K. Kobbacy, “A model for residual life prediction based on Brownian motion with an adaptive drift,” Microelectronics Reliability, vol. 51, no. 2, pp. 285–293, 2011. View at Publisher · View at Google Scholar · View at Scopus