Establishing Control Limits

Control limits are generally set depending on an acceptable false alarm rate. The control limits are set in such a manner that there is a very less possibility of out-of-control (limits) points occuring (say, one time out of 100 sample points). This logic easily extends to multivariate control charting.

Control limits based on probabilities for a multivariate statistic
In the Hotelling T2 chart, the control limit is determined based on the multivariate T2 statistic. The multivariate T2 statistic for multivariate normal distributions has a known sampling distribution. So the rationale of how an appropriate control limit is determined, and how out-of-control alarms are interpreted is essentially the same to that applied to univariate charts, for example, X-bar and S charts.
ARL-based limits
For the MEWMA chart, no simple multivariate statistic is available. In this case, you can set theccontrol limits based on the expected ARL of the respective chart, under the assumption of an in-control process. For example, a vector of cumulative sums of deviations from means for multiple variables (a MCUSUM chart). By applying Monte Carlo simulation methods, you can create thousands of charts for processes that are randomly generated for an in-control process. The control limit is then simply set so that, given an in-control multivariate process, alarms occur on average after 100, 200, and successive samples. Hence the control limits are adjusted consistent with an acceptable false-alarm rate, and while the computations are more complex, the basic interpretation and application of the control limits is the same.