Nonlinear Least Squares Estimation for Parameters of Mixed Weibull Distributions by Using Particle Swarm Optimization

Mixed Weibull distributions are widely used in lifetime modeling of products with multiple failure modes. It is difficult to estimate parameters of the mixed Weibull distribution since it contains multiple parameters. A parameter estimation model for the mixed Weibull distributions is proposed based on nonlinear least squares estimation (LSE). An approach of determining parameters' approximate values and rough bounds is presented for selecting good starting points used in the particle swarm optimization (PSO) procedure. The PSO solution of the nonlinear LSE method is proposed by a step-by-step procedure. A case study is given to illustrate the accuracy and efficiency of our proposed method. Compared with the genetic algorithm (GA)-based nonlinear LSE method, our method shows advantages in both accuracy and efficiency. And compared with the maximum likelihood estimation (MLE) method, our method shows significant advantages in efficiency.