VERTICAL BOX CONTROL CHART FOR THE PROCESS MEAN EWARYST RAFAJ LOWICZ, MIROS LAW PAWLAK, ANSGAR STELAND Abstract. Our aim is to discuss a Vertical Box Control Chart (V- Box Chart). The chart is designed for quick detection of changes in the mean of a process. V-Box Chart is as simple as the Shewart chart, but outperforms it in the probability of detecting out-of- control state with zero delay. Theoretical bounds on in-control and out-of-control behavior of the chart are provided together with simulation studies. 1. Introduction Classical control charts, such as CUSUM, EWMA and the Shewart chart, are the most widely used tools for detecting changes in the mean value of a process. For this reason they are still of interest for re- searchers. The above mentioned charts have a common feature, namely, they utilize a kind of averaging of past observations in order to decide whether a jump of a quality occurred or not. This feature allows to tune in-control average run length and to accumulate results of small changes in a quality of a controlled process. On the other hand, av- eraging observations before and after the jump occurrence results in delay of its detection. For the above reason we propose a new approach to constructing control charts, which does not average past observations, but – instead – the number of past observations which fell into a box is calculated. The box changes its position together with the most recent observation and therefore it is later called V-Box Chart. A leading position of the most recent observation makes it possible to detect jumps of a moderate size (almost) immediately. The construction of V-Box Chart does not uses a priori knowledge on underlying probability distribution. Also specification of a trajectory of getting out-of-control is not necessary, but in the theoretical considerations we shall use the step like jump. The research of the E. Rafaj lowicz was supported by Council for Scientific Re- search of Poland under grant ranging from 2002 to 2006. 1