The exponentially weighted moving (EWMA) control chart has been used successfully to monitor a process mean. Recently, extensions of the EWMA have been proposed that use an EWMA chart on the usual EWMA statistic; this is called the double EWMA, or DEWMA, chart. This effectively “double smooths” the original data. A multivariate version of the DEWMA chart, called the MDEWMA, is a straightforward extension of the DEWMA chart. The process output vectors are doubly smoothed, and a \(T^2\) statistic is computed and plotted. Sufficiently large values of the \(T^2\) statistic indicate a process shift. We compare the MEWMA chart with the newly proposed MDEWMA chart using the criterion of first-to-signal or “firstness.” For a given stream of output data, the chart that is most likely to signal first is considered the better chart. We estimate the firstness for the MEWMA and MDEWMA charts, along with the probability of a simultaneous signal. These firstness curves are estimated using simulation. We find that in most cases, the MEWMA chart signals first, or there is a simultaneous signal. Only rarely does the MDEWMA signal before the MEWMA.