TY - JOUR
T1 - Bias correction for the least squares estimator of Weibull shape parameter with complete and censored data
AU - Zhang, L. F.
AU - Xie, M.
AU - Tang, L. C.
PY - 2006/8
Y1 - 2006/8
N2 - Estimation of the Weibull shape parameter is important in reliability engineering. However, commonly used methods such as the maximum likelihood estimation (MLE) and the least squares estimation (LSE) are known to be biased. Bias correction methods for MLE have been studied in the literature. This paper investigates the methods for bias correction when model parameters are estimated with LSE based on probability plot. Weibull probability plot is very simple and commonly used by practitioners and hence such a study is useful. The bias of the LS shape parameter estimator for multiple censored data is also examined. It is found that the bias can be modeled as the function of the sample size and the censoring level, and is mainly dependent on the latter. A simple bias function is introduced and bias correcting formulas are proposed for both complete and censored data. Simulation results are also presented. The bias correction methods proposed are very easy to use and they can typically reduce the bias of the LSE of the shape parameter to less than half percent. © 2006.
AB - Estimation of the Weibull shape parameter is important in reliability engineering. However, commonly used methods such as the maximum likelihood estimation (MLE) and the least squares estimation (LSE) are known to be biased. Bias correction methods for MLE have been studied in the literature. This paper investigates the methods for bias correction when model parameters are estimated with LSE based on probability plot. Weibull probability plot is very simple and commonly used by practitioners and hence such a study is useful. The bias of the LS shape parameter estimator for multiple censored data is also examined. It is found that the bias can be modeled as the function of the sample size and the censoring level, and is mainly dependent on the latter. A simple bias function is introduced and bias correcting formulas are proposed for both complete and censored data. Simulation results are also presented. The bias correction methods proposed are very easy to use and they can typically reduce the bias of the LSE of the shape parameter to less than half percent. © 2006.
KW - Bias correction
KW - Censored data
KW - Shape parameter
KW - Weibull distribution
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-33646078342&origin=recordpage
U2 - 10.1016/j.ress.2005.09.010
DO - 10.1016/j.ress.2005.09.010
M3 - 21_Publication in refereed journal
VL - 91
SP - 930
EP - 939
JO - Reliability Engineering and System Safety
JF - Reliability Engineering and System Safety
SN - 0951-8320
IS - 8
ER -