Abstract
Abstract In recent decades, it has been found that the three parameter Weibull distribution plays an increasingly important role in the fields of structural fatigue and reliability. However, due to the complexity of the methods for estimating these three parameters, the application of the three parameter Weibull distribution has been greatly affected. The author has successively proposed the Zhentong Gao method and the generalized Zhentong Gao method in recent years, which have better solved this problem. Later, by using the characteristics of the Monte Carlo method and the Metropolis-Hastings algorithm to upgrade the Zhentong Gao method and the generalized Zhentong Gao method, it is further found that they can be used to improve the Bayesian method. This paper mainly discusses how to improve the Bayesian method so that the improved Bayesian method is more convenient than the commonly used Gibbs method, and can also estimate the three parameters of the Weibull distribution, and at the same time give their confidence intervals.
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