A numerical procedure using integral equations is presented for the tabulation of moments of run lengths of exponentially weighted moving average (EWMA) charts. Both average run lengths (ARL's) and standard deviations of run lengths (SDRL's) are presented for the two-sided EWMA chart assuming normal observations, along with an example illustrating how to design such a chart. The procedure given extends easily to many nonnormal cases and to one-sided versions of the EWMA chart.