Weibull parameter estimation and reliability analysis with zero-failure data from high-quality products

This paper deals with an old and fundamental problem in reliability—estimation of Weibull parameters and reliability with zero-failure data. Because the maximum likelihood estimation is no longer applicable, the conventional method uses the 50% confidence limit as a point estimator for the Weibull scale parameter. However, since this method was proposed several decades ago, little progress has been made on the solution to this fundamental problem. New estimation techniques are developed in this study. In contrast to those Bayesian methods found in the literature which usually leverage historical data and/or technical knowledge, the new methods do not require prior information. In particular, an unbiased estimator for the Weibull scale parameter is discovered for the first time, which is demonstrated to have much better statistical performance than the conventional estimator as well as other new estimators proposed in this study. The unbiased estimator also provides significant new insights into the problem under study. An efficient confidence interval is also derived for the Weibull scale parameter, which is demonstrated through simulation to have satisfactory coverage probabilities.