Improving the ARL profile of the Poisson EWMA chart

The Poisson exponentially weighted moving average (PEWMA) chart was proposed by Borror et al. (1998) to monitor the mean of counts of nonconformities. This chart regrettably fails to have an in-control average run length (ARL) larger than any out-of-control ARL, i.e., the PEWMA chart is ARL-biased. Moreover, due to the discrete character of its control statistic the PEWMA it is difficult to set the control limits in such way that the in-control takes a desired value, say ARL0. In this paper, we propose an ARL-unbiased counterpart of the PEWMA chart and use the R statistical software to provide gripping illustrations of this chart with a decidedly improved ARL profile and an in-control ARL equal to ARL0. We also compare the ARL performance of the proposed chart with the one of a few competing control charts for the mean of i.i.d. Poisson counts.

Joint work with Sven Knoth (Department of Mathematics and Statistics — Faculty of Economics and Social Sciences — Helmut Schmidt University, Hamburg, Germany)