Abstract: Taking two-parameter Weibull distribution as the basis function, an optimization model is established based on the maximum likelihood method for parameter estimation, and the model is solved by improved Expectation-Maximization (EM) algorithm. Bayesian random classification algorithm, which is used for parameter initialization, is proposed in the improved EM algorithm. Radial basis function interpolation is used to solve the transcendental equation in the maximization step of the EM algorithm. The performance of the improved EM algorithm is compared with traditional algorithms by case study. Approximation performance of finite Weibull mixture distributions is analyzed with specific cases. The distribution law of the reliability data of ten punching machine tools, which come from testing field, is investigated by Weibull mixture distributions. The relationship between KS test statistic and the number of Weibull distributions is analyzed. The case study suggests that the fourfold Weibull mixture distributions could be better reflect the real law of the punching machine tools in early stage.

Key words: machinery manufacturing automation, reliability of machine tools, finite Weibull mixture distributions, maximum likelihood method, EM algorithm, Bayesian random classification, radial basis function interpolation, KS test