Abstract
The three-parameter Weibull distribution is a continuous distribution widely used in the study of reliability and life data. The estimation of the distribution parameters is an important problem that has received a lot of attention by researchers because of theirs effects in several measurements. In this research, we propose a particle swarm optimization (PSO) to estimate the three-parameter Weibull distribution and then to estimate the reliability and hazard functions. The real data results indicate that our proposed estimation method is significantly consistent in estimation compared to the maximum likelihood method. In terms of log likelihood and mean time to failure (MTTF).
Highlights
The widespread interest in study of reliability is due to the fast development of the world, especially in the field of technology
We propose a particle swarm optimization (PSO) to estimate the three-parameter weibull distribution and to estimate the reliability and hazard functions
In order to test the fitting of the both data sets for 3-parameter weibull distribution, the kolmogorov-smirnov test was used with values 0.15554 and 0.13448 and the corresponding P-values are 0.43999 and 0.54466 respectively
Summary
The widespread interest in study of reliability is due to the fast development of the world, especially in the field of technology. The estimating parameters is the key to the life model, it can predict the life of product accurately in the reliability (Jun et al, 2017). The process of estimating 3-parameter weibull distribution is important because of the difficulty of obtaining the estimated parameters. The estimation process by using the maximum likelihood function requires iterative methods and requires considerable time and effort. We propose a particle swarm optimization (PSO) to estimate the three-parameter weibull distribution and to estimate the reliability and hazard functions. The real data results indicate that our proposed estimation method is significantly consistent in estimation compared to the maximum likelihood method
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