Multivariate control charts are widely used in various industries to monitor the shifts in process mean and process variability. In Phase I monitoring, control limits are computed using the historical data, and control charts based on classical estimators (sample mean and the sample covariance) are highly sensitive to the outliers in the data. We propose robust control charts with high breakdown robust estimators based on the re-weighted minimum covariance determinant and the re-weighted minimum volume ellipsoid to monitor the process variability of multivariate individual observations in Phase I data under multivariate exponentially weighted mean square error and multivariate exponentially weighted moving variance schemes. The control limits are computed empirically, and the performance of the proposed charts is assessed with Monte Carlo simulations by considering different data scenarios. The proposed robust control charts are shown to perform better than charts based on classical estimators. Copyright © 2013 John Wiley & Sons, Ltd.