Parameter estimation of the initial failure period for a three-parameter Weibull distribution in a small sample

The Weibull distribution is a continuous distribution widely used in studies of reliability and lifetime data. In the parameter estimation of a two-parameter Weibull distribution with shape and scale parameters, the maximum likelihood method works well and parameter estimation can be performed easily. In addition, the parameter estimation of the three-parameter Weibull distribution, where the location parameter is added, may not work with the maximum likelihood method. Indeed, various methods of parameter estimation have been proposed. We proposed a method for estimating three parameters through an iterative method using a minimum variance linear unbiased estimator for the location parameter of a three-parameter Weibull distribution. We assessed the proposed method's effectiveness using numerical simulations with the root mean squared error and finally applied it to real data.