缺失数据过程的自适应多元EWMA控制图  

An Adaptive Multivariate EWMA Control Chart for Monitoring Missing Data

作　　者：濮晓龙[1] 项冬冬[1] 陈昕妍 PU Xiaolong;XIANG Dongdong;CHEN Xinyan(KLATASDS-MOE,School of Statistics,East China Normal University,Shanghai,200062,China)

机构地区：[1]华东师范大学统计学院,统计与数据科学前沿理论及应用教育部重点实验室,上海200062

出　　处：《应用概率统计》2024年第2期343-363,共21页Chinese Journal of Applied Probability and Statistics

摘　　要：随着生产过程的日益复杂,多元统计过程控制(SPC)领域对在线算法的关注与日俱增.然而,基于完整数据和均匀时间间隔假设的传统方法在存在缺失数据时表现并不理想.为了最大化利用可用信息,我们提出了一种自适应指数加权移动平均(EWMA)控制图,它采用了加权插补方法,能够充分利用完整数据和不完整数据之间的关系.具体而言,我们首先引入了两种恢复方法:改进的K近邻方法和传统的单变量EWMA方法.然后,我们构造了一个自适应加权函数来结合这两种方法,即当样本信息表明过程超出控制的可能性增加时,会降低EWMA统计量的权重,反之亦然.通过模拟结果和一个实际案例,我们证明了所提出方案的稳健性和敏感性.With the increasing complexity of production processes,there has been a growing focus on online algorithms within the domain of multivariate statistical process control(SPC).Nonetheless,conventional methods,based on the assumption of complete data obtained at uniform time intervals,exhibit suboptimal performance in the presence of missing data.In our pursuit of maximizing available information,we propose an adaptive exponentially weighted moving average(EWMA)control chart employing a weighted imputation approach that leverages the relationships between complete and incomplete data.Specifically,we introduce two recovery methods:an improved K-Nearest Neighbors imputing value and the conventional univariate EWMA statistic.We then formulate an adaptive weighting function to amalgamate these methods,assigning a diminished weight to the EWMA statistic when the sample information suggests an increased likelihood of the process being out of control,and vice versa.The robustness and sensitivity of the proposed scheme are shown through simulation results and an illustrative example.

关 键 词：在线监控 完全随机缺失 加权插补 指数加权移动平均 改进的K近邻 

分 类 号：O213.1[理学—概率论与数理统计]