Reliability evaluation of components with multiple failure modes based on mixture Weibull distribution using expectation maximization algorithm

The mixture Weibull distribution is widely used in the reliability analysis of lifetime data of components, especially for those caused by multiple failure modes. In order to accurately estimate the parameters of mixture Weibull distributions, an optimized expectation maximization (EM) algorithm is proposed based on the particle swarm optimization (PSO) algorithm. The Weibull probability plot (WPP) method is introduced to determine the approximate values and rough limits of unknown parameters, and the approximate values will be used as the initial points in the optimization of the EM procedure. By taking the maximum of the Q function as the optimization goal and the rough limits of each parameter as the constraints, a parameter estimation model of the mixture Weibull distribution is built. The PSO algorithm has been introduced into the maximization step of the EM algorithm to deal with the transcendental equations. Numerical cases are used to illustrate the accuracy of our method in the parameter estimation for the mixture Weibull distribution, and an engineering case is used to show the application of our method in the reliability evaluation of components with multiple failure modes. Compared with the least squares estimation and the maximum likelihood estimation, our method shows advantages in both accuracy and efficiency.