Bias correction for the least squares estimator of Weibull shape parameter with complete and censored data

Reliability Engineering and System Safety

Volumn 91, Issue 8, 2006, Pages 930-939

  Zhang, L F ^a   Xie, M ^a   Tang, L C ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Bias correction; Censored data; Shape parameter; Weibull distribution

Indexed keywords

COMPUTER SIMULATION; DATA REDUCTION; FUNCTION EVALUATION; LEAST SQUARES APPROXIMATIONS; PARAMETER ESTIMATION; PROBABILITY;

BIAS CORRECTION; CENSORED DATA; LEAST SQUARES ESTIMATION (LSE); MAXIMUM LIKELIHOOD ESTIMATION (MLE); SHAPE PARAMETER;

WEIBULL DISTRIBUTION;

EID: 33646078342     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2005.09.010     Document Type: Article

References (21)

1. Hossain A.M., and Zimmer W.J. Comparison of estimation methods for Weibull parameters: complete and censored samples. J Stat Comput Simul 73 2 (2003) 145-153
2. Hisada K., and Arizino I. Reliability tests for Weibull distribution with varying shape-parameter, based on complete data. IEEE Trans Reliab 51 3 (2002) 331-336
3. Keats J.B., Nahar P.C., and Korbel K.M. A study of the effects of mis-specification of the Weibull shape parameter on confidence bounds based on the Weibull-to-exponential transformation. Qual Reliab Eng Int 16 1 (2000) 27-31
4. Xie M., Yang Z.L., and Gaudoin O. More on the mis-specification of the shape parameter with Weibull-to-exponential transformation. Qual Reliab Eng Int 16 4 (2000) 281-290
5. Montanari G.C., Mazzanti G., Cacciari M., and Fothergill J.C. In search of convenient techniques for reducing bias in the estimation of Weibull parameter for uncensored tests. IEEE Trans Dielect Electr Insul 4 3 (1997) 306-313
6. Jacquelin J. Generalization of the method of maximum likelihood. IEEE Trans Dielect Electr Insul 28 1 (1993) 65-72
7. Ross R. Formulas to describe the bias and standard deviation of the ML estimated weibull shape parameter. IEEE Trans Dielect Electr Insul 1 2 (1994) 247-253
8. Ross R. Bias and standard deviation due to Weibull parameter estimation for small date sets. IEEE Trans Dielect Electr Insul 3 1 (1996) 28-42
9. Hirose H. Bias correction for the maximum likelihood estimates in the two parameter Weibull distribution. IEEE Trans Dielect Electr Insul 6 1 (1999) 66-68
10. Cacciari M., Mazzanti G., and Montanari G.C. Comparison of maximum likelihood unbiasing methods for the estimation of the Weibull parameters. IEEE Trans Dielect Electr Insul 3 1 (1996) 18-27
11. Montanari G.C., Mazzanti G., Cacciari M., and Fothergill J.C. Optimum estimators for the Weibull distribution of censored data: singly-censored tests. IEEE Trans Dielect Electr Insul 4 4 (1997) 462-469
12. Engelhardt M., and Bain L.J. Simplified statistical procedures for the Weibull or extreme-value distribution. Technometrics 19 3 (1977) 323-331
13. White J.S. The moments of log-Weibull order statistics. Technometrics 11 2 (1969) 65-72
14. Hung W.L. Weighted least squares estimation of the shape parameter of the Weibull distribution. Qual Reliab Eng Int 17 6 (2001) 467-469
15. Lu H.L., Chen C.H., and Wu J.W. A note on weighted least-squares estimation of the shape parameter of the Weibull distribution. Qual Reliab Eng Int 20 6 (2004) 579-586
16. Yang Z.L., and Xie M. Efficient estimation of the Weibull shape parameter based on a modified profile likelihood. J Stat Comput Simul 73 2 (2002) 115-123
17. Fothergill J.C. Estimating the cumulative probability of failure data points to be plotted on weibull and other probability paper. IEEE Trans Electr Insul 25 3 (1990) 489-492
18. Bernard A., and Bosi-Levenbach E.C. The plotting of observations on probability paper. Stat Neerl 7 (1953) 163-173
19. Herd GR. Estimation of reliability from incomplete data. Proceedings of the sixth international symposium on reliability and quality control; 1960.
20. Johnson L.G. The statistical treatment of fatigue experiments (1964), Elsevier, New York
21. Nelder J.A., and Mead R. A simplex method for function minimization. Comput J 7 (1965) 308-313