Unbiased estimation of Weibull parameters with the linear regression method

Monte Carlo simulations were used to search for the probability estimator for the unbiased estimate of the Weibull parameters in the linear regression method. Compared with commonly-used probability estimators, the estimator proposed gives a more accurate estimation of the Weibull modulus and the same estimation precision of the scale parameter. It is found that the estimator proposed is more conservative than the estimator Pi = (i − 0.5)/n recommended by previous authors, and hence results in a higher safety in reliability predictions. The unbiased properties of the estimated Weibull parameters were validated with actual experimental data. It is also concluded that the estimated Weibull modulus from actual experimental data is more dispersive than that from Monte Carlo simulation, which arises from the fact that the strength data from actual experiments does not perfectly follow the Weibull statistics.