三参数威布尔分布的参数估计及置信限计算方法  

PARAMETER ESTIMATION AND CONFIDENCE LIMIT CALCULATION METHOD OF THREE-PARAMETER WEIBULL DISTRIBUTION

作　　者：张剑锋 徐芳 张燕 黄小波 贾卓翰 ZHANG JianFeng;XU Fang;ZHANG Yan;HUANG XiaoBo;JIA ZhuoHan(Department of Material Engineering,AECC Commercial Aircraft Engine Co.,Ltd.,Shanghai 201108,China;Department of Manufacturing Engineering,AECC Commercial Aircraft Engine Co.,Ltd.,Shanghai 201108,China)

机构地区：[1]中国航发商用航空发动机有限责任公司材料工程部,上海201108 [2]中国航发商用航空发动机有限责任公司制造工程部,上海201108

出　　处：《机械强度》2024年第5期1136-1142,共7页Journal of Mechanical Strength

基　　金：国家自然科学基金项目(52105163);上海市科技启明星项目(22QB1406400)资助。

摘　　要：针对三参数威布尔分布参数估计及置信限计算精度较低问题,提出了相关-回归法的参数估计及置信限计算方法。所提方法充分利用了相关系数法(简称“傅氏法”)对三参数威布尔分布参数估计的便捷性,以及非线性回归法的优良估计效果,将傅氏法和非线性回归法二者优势相结合。为验证其有效性,将相关-回归法应用于某合金强度值数据三参数威布尔分布的参数估计及置信限计算,并将不同样本量情况下的计算结果与傅氏法、极大似然估计与经验公式相结合的方法(简称“MMPDS法”)进行比较。结果表明,相关-回归法具有较高的参数估计和置信限计算精度,当样本量小于100时优势更为显著,能够准确计算威布尔分布的参数及置信限。A correlation-regression method was proposed to solve the problem of low accuracy of parameter estimation and confidence limit calculation of the three-parameter Weibull distribution.The method was combined by the correlation coefficient method(Fu method)and the nonlinear regression method which makes full use of the convenience of Fu method and the excellent estimation effect of the nonlinear regression method in estimating the three-parameter Weibull distribution.In order to verify the effectiveness of the proposed method,the correlation-regression method,Fu method and the method combining maximum likelihood estimation and empirical formulae(referred to as the“MMPDS method”)were applied to the parameter estimation and confidence limit calculation of the data distribution of a certain alloy strength value with different sample sizes,and calculation consequence of different methods was compared and analyzed.Results show that the correlation-regression method has higher parameter estimation and confidence limit calculation accuracy among the above methods.When the sample size is less than 100,its advantage is more significant,and it can accurately calculate the parameters and confidence limits of the Weibull distribution.

关 键 词：威布尔分布 参数估计 置信限 

分 类 号：V438.4[航空宇航科学与技术—航空宇航推进理论与工程]