Parameter estimation of three-parameter Weibull distribution by hybrid gray genetic algorithm with modified maximum likelihood method with small samples

Due to the increased cost and reliability, only few life failure data can be gathered. Therefore, it is significant to improve the parameter estimation accuracy of Weibull distribution with small samples. In this study, a Weibull parameter estimation method based on hybrid gray genetic algorithm with modified maximum likelihood method (HGLM) is proposed. In the HGLM, the solution model for the location parameter is established by using gray genetic algorithm. On the basis of the location parameter, the shape and scale parameters are acquired with improved maximum likelihood method. Then, a full Monte-Carlo sampling simulation study is conducted to compare the parameter estimation accuracy and fitting of the HGLM with three existing methods. Results show the HGLM can accurately and stably estimate the Weibull parameters with small samples. Finally, two cases are analyzed to demonstrate the application of the HGLM method and the feasibility of sample expansion is also discussed.