Multivariate Control Charts for Monitoring Covariance Matrix: A Review

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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