基于经验似然比检验的高维非参EWMA控制图  

High-Dimensional Nonparametric EWMA Control Chart Based on Empirical Likelihood Test

作　　者：钟文[1] 刘浏 ZHONG Wen;LIU Liu(College of Mathematics and Physics,Chengdu University of Technology,Chengdu 610059;School of Big Data and Statistics,Sichuan Tourism University,Chengdu 610100)

机构地区：[1]成都理工大学数理学院,成都610059 [2]四川旅游学院大数据与统计学院,成都610100

出　　处：《系统科学与数学》2024年第3期862-878,共17页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(12075162)资助课题。

摘　　要：随着传感技术和数据采集系统的逐渐完善,大量复杂高维数据可以被收集,对多变量和高维数据流进行监控往往是现代制造业和质量管理部门的一个基本要求.然而,在高维数据监控领域中,由于“维数的诅咒”以及变量的分布通常是复杂未知的,大多数传统的多元控制图不再适用.针对这种情况,一些研究者讨论了对分布未知且复杂高维数据的均值向量的各种检验,但这些检验很少适用于Phase Ⅱ阶段的过程监控.文章提出了一种基于高维经验似然比检验的EWMA型非参数监控方案,该方案可用于多元过程和高维过程均值向量的监控,并且适用于子组数据流.所提出的控制图不仅易于实现和解释,而且蒙特卡罗数值模拟结果显示该控制图在对称、偏态、厚尾分布中都能有效地监测均值漂移.最后,将所提出的控制图应用于半导体制造过程,结果显示文章的方法对未通过测试的半导体具有良好的监控效果.With the gradual improvement of sensor technology and data acquisition system,a large number of complex high-dimensional data can be collected.Monitoring multi-variable and high-dimensional data streams are often a basic requirement of modern manufacturing and quality management departments.However,in the field of high dimensional data monitoring,most of the traditional multivariate control charts are no longer applicable due to the“curse of dimension”and the complicated and unknown distribution of variables.In response to this situation,some researchers have discussed various tests for the mean vector of complex high-dimensional data with unknown distribution.But these tests are rarely applicable to Phase Ⅱ process monitoring.In this paper,we propose an EWMA-type nonparametric monitoring scheme based on high-dimensional empirical likelihood ratio test,which can be used to monitor the mean vector of multi-dimensional and highdimensional processes,and is suitable for subgroup data streams.The proposed control chart is not only easy to implement and interpret,but also the Monte Carlo numerical simulation results show that the proposed control chart can effectively detect the mean shift in symmetric,skewed and heavy-tailed distributions.Finally,the proposed control chart is applied to the semiconductor manufacturing process,and the results show that the proposed method has a good monitoring effect on the semiconductor that has not passed the test.

关 键 词：高维 非参 多元统计过程控制 经验似然比检验 控制图 

分 类 号：O212.1[理学—概率论与数理统计]