When CWS is present, CWS should be taken into account to the sufficient reduction method as ignoring CWS delays detection and gives more false alarms. Sufficient reduction methods derived for independent observations (1, 2) do not take CWS into account; therefore, the effect of CWS is still present in their derived series of sufficient statistics. This effect violates the assumptions of EWMA chart, for which data are assumed to be independent and then produces a high FAR. Although the sufficient reduction method proposed by Wessman (1) allows for CBS, it does not allow CWS. Incorporating both CWS and CBS in our proposed sufficient reduction method substantially improves the performance in detecting a mean shift in multivariate surveillance data.