When monitoring process dispersion, it is common to pay more attention to dispersion increases than to decreases for practical reasons. Nonetheless, it is also important to detect dispersion decreases for two reasons: (i) it deserves further investigations as to why the process has improved; and (ii) if the process has changed, the settings of the control chart would need to be adjusted for effective future monitoring. In this paper, we first propose an effective control chart for detecting multivariate dispersion decreases in phase II process monitoring, which is constructed using the same approach as that of the one-sided likelihood-ratio-test-based multivariate chart proposed recently in the literature for detecting dispersion increases. We then discuss a combined charting scheme by combining these two one-sided charts for detecting either dispersion increases or decreases. Comparative simulation studies show that the proposed combined control charting scheme outperforms several existing two-sided control charts in terms of the average run length when the process dispersion indeed increases or decreases. Two real-life examples are presented to demonstrate the applicability of the proposed charts. Copyright (c) 2011 John Wiley & Sons, Ltd.