Cumulative sum control charts for covariance matrix

Lai K. Chan

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

Abstract

Cumulative sum (CUSUM) charts for controlling the covariance matrix are proposed via the projection pursuit method. Unlike traditional charts for covari- ance, the proposed charts can be used in a low-volume or short-run environment. It is shown that the proposed procedures are more effective than various exist- ing ones. Their applications to monitoring a process with paired measurements are demonstrated. The CUSUM chart based on the likelihood ratio is also investigated. The performances of the two new kinds of CUSUM charts are similar. However, the likelihood ratio-based CUSUM chart requires that the size of each subgroup is larger than the dimension of the quality characteristics.

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References

1992Introduction to Statistical Quality Control 1992A Multivariate Exponentially Weighted Moving Average Control Chart 1998Cumulative Sum Charts and Charting for Quality Improvement 2000Statistical Methods for Quality Improvement 1995A review of multivariate control charts 1994Multivariate statistical process control—recent results and directions for future research 1997Assessment of Multivariate Process Control Techniques 1995A Cumulative Sum Control Chart for Monitoring Process Variance

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2013A LASSO Chart for Monitoring the Covariance Matrix 2005Monitoring the cross-covariances of a multivariate time series 2007Multivariate Control Charts for Monitoring the Process Mean and Variability Using Sequential Sampling 2019Monitoring process variation using modified EWMA 2020A review of dispersion control charts for multivariate individual observations 2000Some issues in the design of EWMA Charts

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