  In this paper the asymptotic distribution of the stopping time in Page's
sequential cumulative sum (CUSUM) procedure is presented. Page as well as
ordinary cumulative sums are considered as detectors for changes in the mean of
observations satisfying a weak invariance principle. The main results on the
stopping times derived from these detectors extend a series of results on the
asymptotic normality of stopping times of CUSUM-type procedures. In particular
the results quantify the superiority of the Page CUSUM procedure to ordinary
CUSUM procedures in late change scenarios. The theoretical results are
illustrated by a small simulation study, including a comparison of the
performance of ordinary and Page CUSUM detectors.
