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Mathematical Problems in Engineering
Volume 2015, Article ID 681232, 8 pages
http://dx.doi.org/10.1155/2015/681232
Research Article

Weibull Failure Probability Estimation Based on Zero-Failure Data

1College of Information System and Management, National University of Defense Technology, Changsha 410073, China
2College of Continuing Education, National University of Defense Technology, Changsha 410073, China

Received 27 May 2014; Revised 4 September 2014; Accepted 15 October 2014

Academic Editor: Wenbin Wang

Copyright © 2015 Ping Jiang et al. 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. E. L. Welker and M. Lipow, “Estimating the exponential failure rate from data with no failure events,” in Proceedings of the Annual Reliability and Maintainability Symposium, pp. 420–427, 1974.
  2. H. F. Martz Jr. and R. A. Waller, “A bayes zero-failure(BAZE) reliability demonstration testing procedure,” Journal of Quality Technology, vol. 11, no. 3, pp. 128–137, 1979. View at Google Scholar · View at Scopus
  3. H. Qi, S. Ganesan, and M. Pecht, “No-fault-found and intermittent failures in electronic products,” Microelectronics Reliability, vol. 48, no. 5, pp. 663–674, 2008. View at Publisher · View at Google Scholar · View at Scopus
  4. R. T. Bailey, “Estimation from zero-failure data,” Risk Analysis, vol. 17, no. 3, pp. 375–380, 1997. View at Publisher · View at Google Scholar · View at Scopus
  5. W. Wang and D. R. Langanke, “Comparing two designs when the new design has few or no failures—is the new design better than previous one?” in Proceedings of the International Symposium on Product Quality and Integrity, pp. 322–325, January 2001. View at Scopus
  6. K. W. Miller, L. J. Morell, R. E. Noonan et al., “Estimating the probability of failure when testing reveals no failures,” IEEE Transactions on Software Engineering, vol. 18, no. 1, pp. 33–43, 1992. View at Publisher · View at Google Scholar · View at Scopus
  7. P. Jiang, J.-H. Lim, M. J. Zuo, and B. Guo, “Reliability estimation in a Weibull lifetime distribution with zero-failure field data,” Quality and Reliability Engineering International, vol. 26, no. 7, pp. 691–701, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. J. D. Chen, W. L. Sun, and B. X. Li, “The confidence limits in the case of no failure data,” Acta Mathematicae Applicatae Sinica, vol. 18, no. 1, pp. 90–100, 1995 (Chinese). View at Google Scholar · View at MathSciNet
  9. L. Wang and B. Wang, “Statistical analysis for no-failure data-modified likelihood function method,” Mathematical Statistics and Applied Probability, vol. 11, no. 1, pp. 64–70, 1996 (Chinese). View at Google Scholar
  10. J. Ning, Reliability assessment on zero-failure data of liquid rocket engine [M.S. thesis], National University of Defense Technology, 2005 (Chinese).
  11. F. Li, Statistical analysis on zero-failure data [M.S. thesis], Anhui Normal University, 2006.
  12. S. Mao and C. Luo, “Reliability analysis of no failure data,” Mathematic Statistics and Applied Probability, vol. 4, no. 4, pp. 489–506, 1989 (Chinese). View at Google Scholar
  13. D. Ling, Research on Weibull distribution and its applications in mechanical reliability engineering [Dissertation thesis], University of Electronic Science and Technology of China, 2010, (Chinese).
  14. M. Han and Y.-Q. Li, “Hierarchical Bayesian estimation of the products reliability based on zero-failure data,” Journal of Systems Science and Systems Engineering, vol. 8, no. 4, pp. 467–471, 1999. View at Google Scholar
  15. Z. Zhang, “Statistical analysis of data only one failure under normal case,” Chinese Journal of Applied Probability, vol. 14, no. 2, pp. 185–190, 1998 (Chinese). View at Google Scholar
  16. M. Han, “Confidence limits of reliability parameters for weibull distribution,” Journal of Mechanical Strength, vol. 31, no. 1, pp. 59–62, 2009 (Chinese). View at Google Scholar · View at Scopus
  17. P. Jiang, X. Jia, and B. Guo, “Failure probability estimation in the Weibull distribution with zero-failure data,” in Proceedings of the 8th IMA International Conference on Modelling in Industrial Maintenance and Reliability (MIMAR '14), pp. 131–136, 2014.
  18. L. Xiong, Statistical analysis of reliability about zero-failure data [M.S. thesis], Jiling University, 2004, (Chinese).
  19. D. C. Li and L. S. Lin, “A new approach to assess product lifetime performance for small data sets,” European Journal of Operational Research, vol. 230, no. 2, pp. 290–298, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus