Three-Parameter Estimation Method of Multiple Hybrid Weibull Distribution Based on the EM Optimization Algorithm

The hybrid Weibull distribution model can describe the failure rules of electromechanical products more accurately than the single Weibull distribution model, and it can improve the accuracy of reliability analysis. However, the hybrid Weibull distribution model is also more complex, and the multi-parameter estimation is more difficult. In this paper, a reliability mathematical model based on the two-fold three-parameter hybrid Weibull distribution model was established, an EM optimization algorithm was derived for its solution, and a practical initial parameter selection scheme was designed. The validity of the model and the algorithm were verified, and goodness-of-fit tests were conducted through an arithmetic example. The results showed that the initial value selection scheme proposed in this paper and the corresponding solution algorithm could solve all the parameters and weight coefficients to be estimated for each sub distribution, and the obtained failure probability fitting curve had a high fit with the actual sample data, which effectively solved the multi-parameter estimation problem of the multiple mixed Weibull distribution model.