基于概率加权矩的三参数Weibull分布母体百分位值和可靠度置信限估计的新方法

A Practical and Effective Method for Estimating Confidence Limits of Population Percentile and Reliability of Three-Parameter Weibull Distribution on Probability Weighted Moment

利用概率加权矩对Weibull分布三个参数的无偏估计以及Bootstrap方法再抽样的统计特性,文章提出了一种三参数Weibull母体百分位值置信限和可靠度置信限估计的新方法,所提方法概念清晰且易于实现。大量的数字模拟表明:所提方法在计算精度和效率方面均优于已有的估计方法,实际应用算例也表明所提方法具有较高的工程实用性。

Aim. The introduction of the full paper points out what we believe to be the shortcomings of Ref. 1 authored by Fu Huimin et al. We explain in sections 1 and 2 a new method that is, in our opinion, not only more effective but also suitable for engineering problems. The core of sections 1 and 2 is： ＂we propose a new method for estimating confidence limits of population percentile and reliability for three-parameter Weibull distribution by using the unbias of probability weighted moment in Refs. 2 and 3 and the good statistic properties of Bootstrap method in Refs. 4 and 5, our method has clear concepts and is easy to implement. ＂ Section 3 analyzes two numerical exampies and experimental data on fatigue life. The analysis results, given in Tables 1 and 2, show preliminarily that our method is more effective in terms of computation efficiency and precision than the existing estimation methods. The analysis of the experimental data in Ref. 2 on an engineering example verifies that our method is suitable for solving engineering problems.