Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 203618, 15 pages
http://dx.doi.org/10.5402/2011/203618
Research Article

Estimating and Planning Accelerated Life Test Using Constant Stress for Generalized Logistic Distribution under Type-I Censoring

1Department of Mathematical Statistics, Institute of Statistical Studies and Research, Cairo University, Cairo 12613, Egypt
2Department of Statistics, Faculty of Economics and Political Science, Cairo University, Cairo, Egypt

Received 24 September 2011; Accepted 16 October 2011

Academic Editors: F. Jauberteau, T. Y. Kam, and S. Sture

Copyright © 2011 A. F. Attia 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. J. F. Lawless, “Confidence interval estimation in the inverse power law model,” Journal of the Royal Statistical Society: Series C, vol. 25, no. 2, pp. 128–138, 1976. View at Google Scholar
  2. J. I. McCool, “Confidence limits for weibull regression with censored data,” IEEE Transactions on Reliability, vol. R-29, no. 2, pp. 145–150, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. D. S. Bai and S. W. Chung, “An accelerated life test model with the inverse power law,” Reliability Engineering and System Safety, vol. 24, no. 3, pp. 223–230, 1989. View at Publisher · View at Google Scholar · View at Scopus
  4. M. M. Bugaighis, “Properties of the MLE for parameters of a Weibull regression model under type I censoring,” IEEE Transactions on Reliability, vol. 39, no. 1, pp. 102–105, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. A. J. Watkins, “On the analysis of accelerated life-testing experiments,” IEEE Transactions on Reliability, vol. 40, no. 1, pp. 98–101, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. A. A. Abdel-Ghaly, A. F. Attia, and H. M. Aly, “Estimation of the parameters of pareto distribution and the reliability function using accelerated life testing with censoring,” Communications in Statistics Part B, vol. 27, no. 2, pp. 469–484, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. E. A. El-Dessouky, On the use of bayesian approach in accelerated life testing, M.S. thesis, Institute of Statistical Studies and Research, Cairo University, Egypt, 2001.
  8. W. Q. Meeker, L. A. Escobar, and C. J. Lu, “Accelerated degradation tests: modeling and analysis,” Technometrics, vol. 40, no. 2, pp. 89–99, 1998. View at Publisher · View at Google Scholar
  9. W. Nelson and T. J. Kielpinski, “Theory for optimum censored accelerated life tests for normal and lognormal life distributions,” Technometrics, vol. 18, no. 1, pp. 105–114, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. W. Nelson, Accelerated Life Testing: Statistical Models, Test Plan and Data Analysis, John Wiley & Sons, New York, NY, USA, 1990.
  11. G. B. Yang, “Optimum constant-stress accelerated life-test plans,” IEEE Transactions on Reliability, vol. 43, no. 4, pp. 575–581, 1994. View at Publisher · View at Google Scholar
  12. C. Ding, C. Yang, and S. K. Tse, “Accelerated life test sampling plans for the Weibull distribution under type I progressive interval censoring with random removals,” Journal of Statistical Computation and Simulation, vol. 80, no. 8, pp. 903–914, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, vol. 2 of Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, John Wiley & Sons, New York, NY, USA, 2nd edition, 1995.
  14. S. Nadarajah and S. Kotz, “A generalized logistic distribution,” International Journal of Mathematics and Mathematical Sciences, vol. 2005, no. 19, pp. 3169–3174, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. A. M. Mathai and S. B. Provost, “On the distribution of order statistics from generalized logistic samples,” International Journal of Statistics, vol. 62, no. 1, pp. 63–71, 2004. View at Google Scholar
  16. K. Tolikas, “Value-at-risk and extreme value distributions for financial returns,” Journal of Risk, vol. 10, pp. 31–77, 2008. View at Google Scholar
  17. M. R. Alkasasbeh and M. Z. Raqab, “Estimation of the generalized logistic distribution parameters: comparative study,” Statistical Methodology, vol. 6, no. 3, pp. 262–279, 2009. View at Publisher · View at Google Scholar
  18. K. Tolikas and G. D. Gettinby, “Modelling the distribution of the extreme share returns in Singapore,” Journal of Empirical Finance, vol. 16, no. 2, pp. 254–263, 2009. View at Publisher · View at Google Scholar
  19. A. Shabri, U. N. Ahmad, Z. A. Zakaria et al., “TL-moments and L-moments estimation of the generalized logistic distribution,” Journal of Mathematical Research, vol. 10, no. 10, pp. 97–106, 2011. View at Google Scholar · View at Zentralblatt MATH
  20. K. Tolikas, “The rare event risk in African emerging stock markets,” Managerial Finance, vol. 37, no. 3, pp. 275–294, 2011. View at Publisher · View at Google Scholar
  21. H. Shin, T. Kim, S. Kim, and J. H. Heo, “Estimation of asymptotic variances of quantiles for the generalized logistic distribution,” Stochastic Environmental Research and Risk Assessment, vol. 24, no. 2, pp. 183–197, 2010. View at Publisher · View at Google Scholar
  22. R. K. Rai, S. Sarkar, and V. P. Singh, “Evaluation of the adequacy of statistical distribution functions for deriving unit hydrograph,” Water Resources Management, vol. 23, no. 5, pp. 899–929, 2009. View at Publisher · View at Google Scholar
  23. S. Kim, H. Shin, T. Kim, and J. Heo, “Derivation of the probability plot correlation coefficient test statistics for the generalized logistic distribution,” in Proceedings of the International Workshop Advances in Statistical Hydrology, Taormina, Italy, 2010.
  24. G. Molenberghs and G. Verbeke, “On the Weibull-Gamma frailty model, its infinite moments, and its connection to generalized log-logistic, logistic, Cauchy, and extreme-value distributions,” Journal of Statistical Planning and Inference, vol. 14, no. 2, pp. 861–868, 2011. View at Publisher · View at Google Scholar
  25. E. Gouno, “Optimum step-stress for temperature accelerated life testing,” Quality and Reliability Engineering International, vol. 23, no. 8, pp. 915–924, 2007. View at Publisher · View at Google Scholar