Comparison of Estimators for Stress-Strength Reliability in the Gompertz Case

Year 2009, Volume: 38 Issue: 3, 339 - 349, 01.03.2009

Bugra Saraçoglu M.f. Kaya A.m. Abd-elfattah

https://izlik.org/JA86JN46TR

Keywords

-

References

• Awad, A. M. and Gharraf, M. K. Estimation of P (Y < X) in the Burr case: A comparative study, Commun. Statist. Simul. Comp. 15 (2), 389–403, 1986.
• Birnbaum, Z. W., 1956. On a use of the Mann-Whitney statistic (Proceedings of the Third Berkeley Symposium Math. Statistic Probability I, 1956), 13–17.
• Chao, A. On comparing estimators of P (Y < X) in the exponential case, IEEE Trans. Reliab. 31 (4), 389–392, 1982.
• Church, J. D. and Harris, B. The estimation of reliability from stress strength relationships, Technometrics 12, 49–54, 1970.
• Constantine, K. and Karson, M. Estimators of P (Y < X) in the gamma case, Commun. Statist. Simul. Comp. 15, 365–388, 1986.
• Ismail, A. A. On the optimal design of step-stress partially accelerated life tests for the Gompertz distribution with type-I censoring, 2006.
• http://interstat.statjournals.net/articles/0606001.pdf
• Jaheen, Z. F. A Bayesian analysis of record statistics from the Gompertz model, Appl. Math. Comp. 145 (2-3), 307–320, 2003.
• Khedhairi, A. and Gohary, A. E. A new class of bivariate Gompertz distributions and its mixture, Int. J. Math. Anal. 2 (5), 235–253, 2008.
• Kotz, S., Lumelskii, Y. and Pensky, M. The Stress-Strength Model and its Generalizations: Theory and Applications(World Scientific Publishing, Singapore, 2003).
• Kundu, D. and Gupta R. D. Estimation of P (Y < X) for the generalized exponential dis- tribution, Metrika 61 (3), 291–308, 2005.
• Lumelski, Ya. P. and Sapoznikov, P. N. Unbiased estimators of probabilities densities, Theor. Veroyat. Primen. 14, 372–380, 1969.
• Mokhlis, N. A. Reliability of a stress-strength model with Burr Type III distributions, Com- mun. Statist.Theory Meth. 34 (7), 1643–1657, 2005.
• Raqab M. Z. and Kundu, D. Comparison of different estimators of P (Y < X) for a scaled Burr type X distribution, Commun. Statist. Simul. Comp. 34 (2), 465–483, 2005.
• Sara¸co˘glu, B. and Kaya, M. F. Maximum likelihood estimation and confidence intervals of system reliability for Gompertz distribution in stress-strength models, Sel¸cuk J. Appl. Math. 8(2), 25–36, 2007.
• Surles, J. G. and Padgett, W. J. Inference for reliability and stress-strength for a scaled Burr-type X distribution, Lifetime Data Analy. 7, 187–200, 2001.
• Wu, S. J., Chang, C. T. and Tsai, T. R. Point and interval estimations for the Gompertz distribution under progressive type-II censoring, Metron - International J. Stat. LXI (3), 403–418, 2003.
• Wu, J. W., Hung, W. L. and Tsai, C. H. Estimation of parameters of the Gompertz distri- bution using the least squares method, Appl. Math. Comp. 158 (1), 133–147, 2004.
• Wu, C. C., Wu, S. F. and Chan, H. Y. MLE and the estimated expected test time for the two-parameter Gompertz distribution under progressive censoring with binomial removals, Appl. Math. Comp. 181 (2), 1657–1670, 2006.