About this Journal Submit a Manuscript Table of Contents
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 953848, 11 pages
http://dx.doi.org/10.1155/2012/953848
Research Article

Applying Hierarchical Bayesian Neural Network in Failure Time Prediction

1Department of Business Management, National Taipei University of Technology, 10608, Taiwan
2Graduate Institute of Industrial and Business Management, National Taipei University of Technology, 10608, Taiwan

Received 31 December 2011; Accepted 21 February 2012

Academic Editor: Jung-Fa Tsai

Copyright © 2012 Ling-Jing Kao and Hsin-Fen Chen. 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. C. J. Lu and W. Q. Meeker, “Using degradation measures to estimate a time-to-failure distribution,” Technometrics, vol. 35, no. 2, pp. 161–174, 1993. View at Publisher · View at Google Scholar
  2. C. J. Lu, W. Q. Meeker, and L. A. Escobar, “A comparison of degradation and failure-time analysis methods for estimating a time-to-failure distribution,” Statistica Sinica, vol. 6, no. 3, pp. 531–546, 1996.
  3. W. Q. Meeker and M. Hamada, “Statistical tools for the rapid development & evaluation of high-reliability products,” IEEE Transactions on Reliability, vol. 44, no. 2, pp. 187–198, 1995. View at Publisher · View at Google Scholar
  4. K. A. Doksum and A. Hoyland, “Models for variable-stress accelerated life testing experiments based on Wiener processes and the inverse Gaussian distribution,” Technometrics, vol. 34, no. 1, pp. 74–82, 1992.
  5. J. M. Bernardo and A. F. M. Smith, Bayesian Theory, John Wiley & Sons, 1994. View at Publisher · View at Google Scholar
  6. A. Gelman, J. B. Carlin, H. S. Stern, and D. B. Rubin, Bayesian Data Analysis, Chapman & Hall, London, UK, 1995.
  7. C. P. Robert and G. Casella, Monte Carlo Statistical Methods, Springer, New York, NY, USA, 1999.
  8. S. I. Liu, “Bayesian model determination for binary-time-series data with applications,” Computational Statistics & Data Analysis, vol. 36, no. 4, pp. 461–473, 2001. View at Publisher · View at Google Scholar
  9. R. Zheng and B. R. Ellingwood, “Stochastic fatigue crack growth in steel structures subjected to random loading,” Structural Safety, vol. 20, no. 4, pp. 305–324, 1998.
  10. R. Zhang and S. Mahadevan, “Model uncertainty and Bayesian updating in reliability-based inspection,” Structural Safety, vol. 22, no. 2, pp. 145–160, 2000. View at Publisher · View at Google Scholar
  11. M. Akama, “Bayesian analysis for the results of fatigue test using full-scale models to obtain the accurate failure probabilities of the Shinkansen vehicle axle,” Reliability Engineering and System Safety, vol. 75, no. 3, pp. 321–332, 2002. View at Publisher · View at Google Scholar
  12. R. M. Neal, Bayesian Learning for Neural Networks, Springer, New York, NY, USA, 1996.
  13. P. Müller and D. Rios Insua, “Issues in bayesian analysis of neural network models,” Neural Computation, vol. 10, pp. 571–592, 1998.
  14. C. C. Holmes and B. K. Mallick, “Bayesian wavelet networks for nonparametric regression,” IEEE Transactions on Neural Networks, vol. 11, no. 1, pp. 27–35, 2000. View at Publisher · View at Google Scholar
  15. J. L. Bogdanoff and F. Kozin, Probabilistic Models of Cumulative Damage, John Wiely, New York, NY, UA, 1984.
  16. E. P. Liski and T. Nummi, “Prediction in repeated-measures models with engineering applications,” Technometrics, vol. 38, no. 1, pp. 25–36, 1996. View at Publisher · View at Google Scholar
  17. R. B. Chinnam, “On-line reliability estimation for individual components using statistical degradation signal models,” Quality and Reliability Engineering International, vol. 18, no. 1, pp. 53–73, 2002. View at Publisher · View at Google Scholar
  18. R. B. Chinnam and P. Baruah, “A neuro-fuzzy approach for on-line reliability estimation and condition based-maintenance using degradation signals,” International Journal of Materials and Product Technology, vol. 20, no. 1–3, pp. 166–179, 2004.
  19. J. G. Ibrahim, L. M. Ryan, and M.-H. Chen, “Using historical controls to adjust for covariates in trend tests for binary data,” Journal of the American Statistical Association, vol. 93, no. 444, pp. 1282–1293, 1998.
  20. B. P. Carlin and T. A. Louis, Bayes and Empirical Bayes Methods for Data Analysis, CRC Press, London, UK, 2000.
  21. S. P. Brooks, “Markov chain Monte Carlo method and its application,” Journal of the Royal Statistical Society D, vol. 47, part 1, pp. 69–100, 1998.
  22. A. E. Gelfand and A. F. Smith, “Sampling-based approaches to calculating marginal densities,” Journal of the American Statistical Association, vol. 85, no. 410, pp. 398–409, 1990.
  23. H. J. Kushner and P. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, vol. 24, Springer, New York, NY, USA, 2001.