  The classic N p chart gives a signal if the number of successes in a sequence
of inde- pendent binary variables exceeds a control limit. Motivated by
engineering applications in industrial image processing and, to some extent,
financial statistics, we study a simple modification of this chart, which uses
only the most recent observations. Our aim is to construct a control chart for
detecting a shift of an unknown size, allowing for an unknown distribution of
the error terms. Simulation studies indicate that the proposed chart is su-
perior in terms of out-of-control average run length, when one is interest in
the detection of very small shifts. We provide a (functional) central limit
theorem under a change-point model with local alternatives which explains that
unexpected and interesting behavior. Since real observations are often not
independent, the question arises whether these re- sults still hold true for
the dependent case. Indeed, our asymptotic results work under the fairly
general condition that the observations form a martingale difference array.
This enlarges the applicability of our results considerably, firstly, to a
large class time series models, and, secondly, to locally dependent image data,
as we demonstrate by an example.
