On the reaction time of moving sum detectors

In this paper, we quantify the reaction time of on-line monitoring schemes for changes in the mean based on moving sums. The corresponding sequential test procedure requires a historical sample of size m   as a baseline, while decisions are made based on a window of size h=h(m)h=h(m) containing the h most recent observations. Perhaps surprisingly, the limit distribution (obtained as m tends to infinity) of the associated stopping time crucially depends on the asymptotic relation of these two quantities, posing potential problems in applications. In the empirical part of the paper, we study therefore the finite sample behavior of the monitoring schemes. We provide tables of critical values for the various limit distributions and guidelines for practitioners via a simulation study.