基于广义逆威布尔分布的应力强度模型可靠度估计

Reliability Estimation of Stress Strength Model Based on Generalized Inverse Weibull Distribution

威布尔分布及其拓展分布在可靠性领域有着重要的作用和地位。文章给出广义逆威布尔分布应力强度模型可靠度的极大似然估计以及置信区间,其中强度变量和应力变量相互独立。鉴于极大似然估计迭代过程的不稳定性,文中对迭代进行了约束,从而得到收敛的极大似然估计。相应的运用参数变换后的信息阵,得到模型可靠度的渐近分布与渐进置信区间。通过随机模拟和单碳纤维的实例来说明所采用方法的效果。

The Weibull distribution and its expansion play an important role in the field of reliability.This paper gives the maximum likelihood estimation and confidence interval of the reliability of generalized inverse Weibull stress strength model,in which the strength variables and stress variables are independent of each other.Considering the instability of the iterative process of the maximum likelihood estimation,the paper constrains the iteration to obtain the maximum likelihood estimation of conver⁃gence.The asymptotic distribution and the asymptotic confidence interval of model reliability are obtained by using the informa⁃tion matrix after parameter transformation.Finally,the paper illustrates the effect of the method by a random simulation and a sin⁃gle carbon fiber example.