摘要
本文,我们结合统计过程控制方法,使用一种新的统计量用于在样本数量不充足的情况下监测高维数据。统计量利用样本协方差规范化技术避免协方差矩阵的奇异性,同时采用软阈值技术来挑选多维数据中重要的维度进行监测以减少监测噪音。本文在提出统计量后用matlab随机产生各种维度的高维数据样本进行仿真分析,并将该统计量与基于Hotelling T^2并采取广义逆矩阵的统计量进行比较。结果表明,本文使用的统计量的监测效果优于采取广义逆矩阵的方法。本文提出的方法可以应用于多指标产品生产的快速异常检测,特别是难以得到大量检测数据的产品,如检测需要破坏产品本身或者检测成本太高的产品。
In this paper we combine basic statistical process control method,using a new statistic to monitor high-dimensional data when the sample size is not big enough.The statistic applies sample covariance regularization to overcome the singularity.Besides,it applies a soft-thresholding technique to reduce random noise and improve the testing power.Then we use matlab to do Monte Carlo simulation by generating random multivariate data and applies the data to the new method as well as the statistic which based on the Hotelling T^2.The comparative result shows that our statistic is better than the statistic based on the Hotelling T^2 in the testing power.Our method can be applied to fast monitoring changes in multi-parameter products,especially the products that is hard to get enough testing data,such as when the test is a destructive test or the test costs to much.
出处
《数理统计与管理》
CSSCI
北大核心
2015年第3期420-426,共7页
Journal of Applied Statistics and Management
基金
国家自然学科基金项目(70902070)
关键词
多元过程控制
软阈值技术
样本协方差规范化
单样本
平均运行长度
multivariate process control
soft-thresholding technique
sample covariance regularization
one-sample
average run length
