A Mixed Method for Estimating Parameters of Three-Parameter Weibull Distribution

Abstract

The three-parameter Weibull distribution has been widely used for modeling component lifetime and material strength. The parameter estimates obtained from the maximum likelihood estimation method (MLE) and maximum product of spacing (MPS) method can be biased or inexistent. Though many other approaches have been developed, none is always efficient. Therefore, it is still a challenging issue to develop more efficient estimation methods. This paper aims to address this issue by proposing a mixed approach. The proposed approach is based on a modified Weibull transformations and involves three main steps. The first step determines two reference points from the empirical distribution function. In the second step, the location parameter is estimated based on the ratios of the difference between the reference point and data points on the modified Weibull probability paper (MWPP) plot. The third step estimates the shape and scale parameters based on the linear relation of the MWPP plot. The accuracy and robustness of the proposed approach is illustrated by a numerical experiment and its usefulness is illustrated by a real-world example. The results shows that the proposed approach provides more accurate and robust estimates than the MLE and MPS.