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Phase I analysis of high-dimensional covariance matrices based on sparse leading eigenvalues
Fan, Jinyu1; Shu, Lianjie2; Yang, Aijun3; Li, Yanting4
2021-08-08
Source PublicationJournal of Quality Technology
ISSN0022-4065
Volume53Issue:4Pages:333-346
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 L -type and (Formula presented.) -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.

KeywordStatistical Process Control Two-sample Tests Eigenvalues Control Chart
DOI10.1080/00224065.2020.1746212
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaEngineering ; Operations Research & Management Science ; Mathematics
WOS SubjectEngineering, Industrial ; Operations Research & Management Science ; Statistics & Probability
WOS IDWOS:000533261600001
Scopus ID2-s2.0-85084319484
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Citation statistics
Document TypeJournal article
CollectionDEPARTMENT OF ACCOUNTING AND INFORMATION MANAGEMENT
Corresponding AuthorShu, Lianjie
Affiliation1.School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou, China
2.Faculty of Business, University of Macau, Macao
3.College of Economics and Management, Nanjing Forest University, Nanjing, China
4.Department of Industrial Engineering and Logistics Management, Shanghai Jiao Tong University, Shanghai, China
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Fan, Jinyu,Shu, Lianjie,Yang, Aijun,et al. Phase I analysis of high-dimensional covariance matrices based on sparse leading eigenvalues[J]. Journal of Quality Technology, 2021, 53(4), 333-346.
APA Fan, Jinyu., Shu, Lianjie., Yang, Aijun., & Li, Yanting (2021). Phase I analysis of high-dimensional covariance matrices based on sparse leading eigenvalues. Journal of Quality Technology, 53(4), 333-346.
MLA Fan, Jinyu,et al."Phase I analysis of high-dimensional covariance matrices based on sparse leading eigenvalues".Journal of Quality Technology 53.4(2021):333-346.
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