Optimal linear regression estimator in the fitting of Weibull strength distribution
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The strength of ceramics is characterized by a wide scatter because of pre-existing cracks that occur during the manufacturing and machining processes. The Weibull distribution is one of the most widely used functions for the characterization of strength data. A linear regression method is generally applied in the estimation of Weibull parameters for its simplicity and low overestimation, in which probability estimators play an important role. In this paper, an optimal probability estimator for different sample sizes is obtained by using alumina strength data. In comparison with other commonly used estimators, the optimal probability estimator shows less bias and higher safety. The performance of the optimal probability estimator is also verified by other experimental strength data. In conclusion, an optimal probability estimator constant of 0.25 is suggested in practical applications.
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Davies, Ian (2017)© 2016 Elsevier Ltd The wide applicability of the Weibull distribution to fields such as hydrology and materials science has led to a large number of probability estimators being proposed, in particular for the widely ...
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Davies, Ian (2017)© 2017 Elsevier Ltd Unbiased estimation of the Weibull scale parameter using unweighted linear least squares (LLS) analysis was investigated in this work as a function of specimen number, N. Mean, median and mode values ...