Fast initial response features for EWMA control charts

The exponentially weighted moving average (EWMA) control 49 chart became very popular during the last decade. It is characterized by simple handling and good performance. It turns out, however, that the most popular EWMA scheme with fixed-width control limits - the asymptotic control limits are taken and do not change over time - detects early changes rather slowly. For the competing CUSUM chart the so-called fast initial response (head-start) feature is developed which permits rapid response to an initial out-of-control situation. Meanwhile, in some papers similar modifications for EWMA schemes are described. We compare these approaches by using precise computation techniques, which are based on numeric quadrature rules and allow higher accuracy than earlier studies. Moreover, previous comparisons are restricted to the evaluation of the detection speed by comparing the average run lengths (ARLs), that is, the parameter of interest is constant during the whole monitoring period. Here, we consider more possible change point locations, which gives the EWMA control chart user a better insight into the scheme performance for early changes.