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Biasness Correction on Maximum Likelihood Estimator using Pivotal Method for Weibull Distribution for Right Censored Situation
Volume 12, Number 5, September 2016 - Paper 1 - pp. 403-412
YUAN FUQINGDepartment of Engineering and Safety, University of Tromsø, N-9037 Tromsø, NORWAY
(Received on July 12, 2016, revised on August 16, 2016)
Two-parameter Weibull distribution is widely used in reliability engineering. Maximum likelihood Estimation (MLE) is a classical approach to estimate the parameters. It has been well-known the MLE estimator is biased. For the small sample size and highly censored situation, the biasness is serious and it is necessary to be corrected. Considering the special structure of the first derivative of the likelihood function to its parameters, a state of art of pivotal method can be used, as it has found the ratio of the estimator for shape parameter to its true parameter is independent on the observed time to failure. This paper elaborates the pivotal method and provides a detailed simulation procedure to estimate the biasness correction factor for both complete data and censored data. Numerical examples are presented to apply the biasness correction factor to real cases for reliability evaluation.
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