排序集抽样下Weibull分布的产品可靠度估计  

Estimation of Product Reliability for Weibull Distribution under Ranked Set Sampling

作　　者：张良勇 董晓芳 ZHANG Liangyong;DONG Xiaofang(College of Statistics and Mathematics,Hebei University of Economics and Business,Shijiazhuang 050061,China)

机构地区：[1]河北经贸大学统计与数学学院,河北石家庄050061

出　　处：《运筹与管理》2024年第6期100-105,共6页Operations Research and Management Science

基　　金：河北省教育厅科学研究项目(ZD2022062)。

摘　　要：排序集抽样方法用于样本单元排序容易但测量困难的情形。产品可靠度是描述产品可靠性的重要度量指标,Weibull分布在可靠性试验中占有非常重要的地位。为了提高Weibull分布产品可靠度的估计效率,本文采用排序集抽样方法,研究了产品可靠度的极大似然估计,计算了Weibull分布形状参数和尺度参数的Fisher信息阵,证明了极大似然估计量的渐近正态性,并给出了新估计量的渐近方差。渐近相对效率和模拟相对效率的计算结果表明:排序集抽样下极大似然估计量的估计效率一致高于简单随机抽样下极大似然估计量。最后,单碳纤维强度数据的实际分析结果验证了排序集抽样方法的高效率性。The ranked set sampling method is a method for improving sampling efficiency,and it is appropriate for a situation in which the visual ranking of sampling units is easy but the quantification of units is difficult.Although the ranked set sampling protocol was first introduced to solve agriculture problems,it has been applied to various fields since then,including reliable engineering,clinical medicine,ecological environment,etc.Product reliability is an important metric for describing product lifetime.In recent years,some scholars have studied the estimation problem of product reliability under ranked set sampling.Through the comparison of estimation efficiency,it has been proven that the ranked set sampling method is superior to the simple random sampling method.However,most of the product lifetimes studied by these scholars follow an exponential distribution.Weibull distribution plays a very important role in reliability testing,which can describe the lifetime of components,equipment,and other products.When the population distribution is known,the maximum likelihood estimation method is an important method for seeking point estimates and has a wide range of applications.In order to improve the estimation efficiency of the product reliability for Weibull distribution,this paper studies the maximum likelihood estimation problem of the product reliability using ranked set sampling.Firstly,the maximum likelihood estimators of the shape parameter and scale parameter of Weibull distribution under ranked set sampling are analyzed.On the basis of the invariance of maximum likelihood estimation,the maximum likelihood estimator of the product reliability using ranked set sampling is given.Secondly,the Fisher information matrix of the shape parameter and scale parameter of Weibull distribution under ranked set sampling are computed.The proposed maximum likelihood estimator is shown to have asymptotic normality,and the asymptotic variance of the new estimator is calculated using the Fisher information matrix of the shape p

关 键 词：产品可靠度 排序集抽样 WEIBULL分布 极大似然估计 FISHER信息阵 

分 类 号：O213.2[理学—概率论与数理统计]