Multivariate Control Charts for Monitoring Covariance Matrix: A Review

Arthur B. Yeh · Dennis K. J. Lin · Richard N. McGrath

118 citations0/0 files storedQuality Technology & Quantitative Management

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Advanced Statistical Process Monitoring Statistical Methods and Applications Fault Detection and Control Systems

Abstract

In this paper, we review multivariate control charts designed for monitoring changes in a covariance matrix that have been developed in the last 15 years. The focus is on control charts developed for multivariate normal processes, assuming that independent subgroups of observations or independent individual observations are sampled as process monitoring proceeds. Control charts developed between 1990 and 2005 are reviewed according to the types of the control chart: multivariate Shewhart chart, multivariate CUSUM chart and multivariate EWMA chart. In addition to these developments, a new multivariate EWMA control chart is proposed. We also discuss comparisons of chart performance that have been carried out in the literature, as well as the issue of diagnostics. Some potential future research ideas are also given.

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References

1992Introduction to Statistical Quality Control 1992A Multivariate Exponentially Weighted Moving Average Control Chart 1995A review of multivariate control charts 1999Research Issues and Ideas in Statistical Process Control 2012Statistical Process Control 2000Controversies and Contradictions in Statistical Process Control 1985Multivariate CUSUM Quality-Control Procedures 1991Multivariate Quality Control Based on Regression-Adjusted Variables

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2007Monitoring Multivariate Process Variability for Individual Observations 2013Control Charts for Monitoring Linear Profiles with Within-Profile Correlation Using Gaussian Process Models 2012Monitoring the covariance matrix via penalized likelihood estimation 2015Monitoring the ratio of two normal variables using Run Rules type control charts 2013A Multivariate Sign Chart for Monitoring Process Shape Parameters 2010Variation reduction for multistage manufacturing processes: a comparison survey of statistical‐process‐control vs stream‐of‐variation methodologies

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