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Phase I analysis of high-dimensional covariance matrices based on sparse leading eigenvalues
Journal of Quality Technology ( IF 2.5 ) Pub Date : 2020-05-04 , DOI: 10.1080/00224065.2020.1746212
Jinyu Fan 1 , Lianjie Shu 2 , Aijun Yang 3 , Yanting Li 4
Affiliation  

Abstract

In statistical process control (SPC), a proper Phase I analysis is essential to the success of Phase II monitoring. With recent advances in sensing technology and data acquisition systems, Phase I analysis of high-dimensional data is increasingly encountered. However, the high dimensionality presents a new challenge to the traditional Phase I techniques. A literature review reveals nearly no Phase I techniques in existence for analyzing high-dimensional process variability. Motivated by this, this paper develops a sparse-leading-eigenvalue-driven control chart for retrospectively monitoring high-dimensional covariance matrices in Phase I, denoted as the SLED control chart. The key idea of it is to track changes in the sparse leading eigenvalue between two covariance matrices. Compared to the L2-type and L-type methods, the proposed method can extract stronger signal with less noise. It is shown that the proposed method can gain high detection power, especially when the shift is weak and is not very dense, which is often the case in practical applications.



中文翻译:

基于稀疏前导特征值的高维协方差矩阵的第一阶段分析

摘要

在统计过程控制 (SPC) 中,适当的第一阶段分析对于第二阶段监测的成功至关重要。随着传感技术和数据采集系统的最新进展,越来越多地遇到高维数据的第一阶段分析。然而,高维对传统的第一阶段技术提出了新的挑战。文献综述显示几乎没有用于分析高维过程可变性的第一阶段技术。受此启发,本文开发了一个稀疏前导特征值驱动的控制图,用于回顾性监控阶段 I 中的高维协方差矩阵,表示为 SLED 控制图。它的关键思想是跟踪两个协方差矩阵之间的稀疏前导特征值的变化。与L 2相比- 类型和 类型的方法,所提出的方法可以提取更强的信号,噪声更少。结果表明,所提出的方法可以获得较高的检测能力,尤其是在偏移较弱且不是很密集的情况下,这在实际应用中很常见。

更新日期:2020-05-04
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