疲劳中Lognormal和Weibull分布的等价性及一种新的参数估计方法

ON THE EQUIVALENCE OF LOGNORMAL AND WEIBULL DISTRIBUTION IN FATIGUE AND A NEW PARAMETER ESTIMATION METHOD

据大量统计分析表明,疲劳寿命大都服从Lognormal分布和Weibwll分布;对于前者,各方面的研究比较成熟,而对于后者,只有两参数Weibull处理方法,或是使用编制好的专用计算程序进行数值求解。本文基于疲劳问题中寿命既服从Lognorreal分布,又服从Weibull分布的前提,用特征函数研究该两种分布之间的等价性和逼近性,取得了两个分布参数之间的关系式。理论上沟通了两分布间的联系,从而得到一种新的三参数Weibull分布的估计方法(LW法),此法的正确性和适用范围并得到验证。

For estimating the parameters of Weibull distribution in fatigue, the equivalence and relation between Lognormal and Weibull distribution from their characteristic functions are studied. Based on the above studies a new method for estimating three parameters of Weibull distribution has been developed, aad proved to be simple, practical and easy to use.