Parameter estimation of three-parameter Weibull probability model based on outlier detection

The Weibull probability model used in statistical analysis has become more popular in the inconsistency evaluation of used Li-ion batteries due to its flexibility in fitting asymmetrically distributed data. However, despite its better fitting of data with a non-zero minimum, the three-parameter Weibull model is less used because of its complicated calculation. Additionally, the Weibull family is likely to overfit and shows inference from outliers. Although conventional estimation methods for Weibull parameters based on dispersion and symmetry of the overall distribution lead to derivation from the actual data features, there is little research into methods to solve the contradiction between estimation accuracy and proper outlier detection. In this study, a Weibull parameter estimation method was proposed that features simplified computation and eliminates the interference from outliers. The outliers were identified based on the obtained Weibull parameters and excluded from the sample data. The method was implemented for fitting the capacity distribution of Li-ion batteries, which was verified by a chi-square test at a confidence of 95% and the Anderson–Darling test. It showed a higher goodness-of-fit and less error than the results of the maximum likelihood estimated Weibull model as well as the normal distribution. The optimal presetting of column number and peak reference point selection were determined by parameter discussion.