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

Asymptotic Distribution of the Delay Time in Page's Sequential Procedure