Multivariate Exponentially Weighted Moving Covariance Matrix

Multivariate exponentially weighted moving average (MEWMA) charts are among the best control charts for detecting small changes in any direction. The well-known MEWMA is directed at changes in the mean vector. But changes can occur in either the location or the variability of the correlated multivar...

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Bibliographic Details
Published in:Technometrics 2008-05, Vol.50 (2), p.155-166
Main Authors: Hawkins, Douglas M., Maboudou-Tchao, Edgard M.
Format: Article
Language:English
Subjects:
Applied sciences
Average run length
Average run length bias
Changes
Charts
Computer science
control theory
systems
Control charts
Control theory. Systems
Covariance matrices
Data processing. List processing. Character string processing
Eigenvalues
Exact sciences and technology
Group size
Inventory control, production control. Distribution
Mathematical models
Mathematics
Memory organisation. Data processing
Methods
Operational research and scientific management
Operational research. Management science
Probability and statistics
Process control. Computer integrated manufacturing
Process controls
Quality assurance
Rational choice theory
Reading
Regression adjustment
Sciences and techniques of general use
Software
Standard error
Statistical variance
Statistics
Variables
Weighted averages
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Summary:Multivariate exponentially weighted moving average (MEWMA) charts are among the best control charts for detecting small changes in any direction. The well-known MEWMA is directed at changes in the mean vector. But changes can occur in either the location or the variability of the correlated multivariate quality characteristics, calling for parallel methodologies for detecting changes in the covariance matrix. This article discusses an exponentially weighted moving covariance matrix for monitoring the stability of the covariance matrix of a process. Used together with the location MEWMA, this chart provides a way to satisfy Shewhart's dictum that proper process control monitor both mean and variability. We show that the chart is competitive, generally outperforming current control charts for the covariance matrix.
ISSN:0040-1706
1537-2723
DOI:10.1198/004017008000000163