Parameter Estimation of Mixed Weibull Distribution Based on Genetic Algorithm and Gradient Descent Method

Complex mechanical products usually contain multiple failure modes. Mixed Weibull distribution is often used to analyze their reliability, and their parameter estimation is more complex than single Weibull distribution. In this paper, a nonlinear least square parameter estimation method of mixed Weibull distribution based on genetic algorithm (GA) and gradient descent method (GDM) is proposed. This method uses the optimization algorithm of the combination of GDM and GA to estimate the parameters of mixed Weibull distribution. In the analysis and calculation of the example, according to the parameter estimation results obtained by this method, the relevant reliability indexes can be obtained, and compared with the real reliability index values, it is found that they are very close to the real values. Combined with the goodness of fit test, the effectiveness of this method is proved. The normalized root mean square error (NRMSE) is used to measure the accuracy of parameter estimation results. The results obtained by this method are more accurate than those obtained by single GA and single GDM. Through the comparative analysis of the sample group, it is found that the more accurate parameter estimation results can be obtained when the sample data is more uniform.