随机区组区间删失场合下威布尔分布模型的参数估计  

Parameter Estimation for the Weibull Distribution under Interval Censored Test Plan with Random Blocks

作　　者：周晓东 吴琳 岳荣先[2,3] ZHOU Xiao-dong;WU Lin;YUE Rong-xian(School of Statistics and Information,Shanghai University of International Business and Economics,Shanghai 201620,China;College of Mathematics and Science,Shanghai Normal University,Shanghai 200234,China;College of Liberal Arts and Sciences,Fuyao University of Science and Technology,Fuzhou 350109,China)

机构地区：[1]上海对外经贸大学统计与信息学院,上海201620 [2]上海师范大学数理学院,上海200234 [3]福耀科技大学文理学院,福建福州350109

出　　处：《数理统计与管理》2024年第6期1010-1024,共15页Journal of Applied Statistics and Management

基　　金：国家自然科学基金项目(11971318,11871143)。

摘　　要：区间删失数据是工业和生物医学中一种常见的不完全数据类型。以往对区间删失数据的分析通常假定数据独立同分布,然而在实际应用中,试验产品所用原材料、试验平台等因素的影响使得试验数据之间存在区组结构,导致同一区组下的数据存在相关性。首先,本文考虑随机区组区间删失场合下威布尔分布模型的统计推断问题。给出了模型参数估计以及产品寿命特征预测的两步估计法、极大似然估计方法以及贝叶斯估计方法。其次,本文探讨了最优区间删失方案的设计,给出了基于蒙特卡罗模拟的最优设计方法。模拟和实际数据分析结果表明所给方法是可行且有效的。Interval censoring is frequently encountered in industrial and biomedical data analysis.Previous studies usually assumed that the data were independent identically distributed.However,in practical applications,the raw materials used by test units,test platforms and other factors can make the data have an obvious block structure,which leads to the correlation of data under the same block.In this paper,statistical analysis for the Weibull distribution model to the interval censored data with random block effects is considered.Three estimation methods,including two-stage,maximum likelihood and Bayes,are proposed to estimate the model parameters and predict the life times of the products.Meanwhile,a method based on Monte Carlo simulation is proposed to find the optimal test plan.The numerical results based on the simulated data and the real life example show that the proposed methods are feasible and effective.

关 键 词：随机区组效应 区间删失 威布尔分布 GIBBS抽样 Gauss-Hermite近似 最优试验方案 

分 类 号：O212[理学—概率论与数理统计] O212.6[理学—数学]