The CUSUM and the EWMA head-to-head

The cumulative sum (CUSUM) and the exponentially weighted moving average (EWMA) control charts are alternatives to the Xbar chart. The CUSUM's theoretical optimality suggests that it should outperform the EWMA for detecting persistent shifts, but practitioners have long thought that the two perform about equally. Each also involves design decisions on the likely shift in the process. This article quantifies the effect of these choices and concludes that, though the CUSUM outperforms the EWMA at the shift for which each was designed, if the actual shift is smaller than that used in the design, the EWMA may respond faster.