An EWMA-type sign chart with exact run length properties

In this paper, a new phase II EWMA-type chart for count data, based on the sign statistic, is proposed and applied to the monitoring of the location of an unknown continuous distribution. The most valuable characteristics of this new chart are that: a) it only uses positive integer-valued weights to account for the past process history, b) the plotted statistic is always an integer, and c) its run length properties can be exactly obtained without resorting to expensive simulations or unreliable approximations. We provide the methodology to compute the exact run length properties of the proposed chart and the algorithms to obtain the optimal chart parameters through the minimization of the out-of-control average run length. We also compare the statistical performance of this new EWMA-type sign chart vs. two classical continuous type EWMA sign charts, a CUSUM-type sign chart and a GWMA-type sign chart. The computational evaluations show that the proposed EWMA control chart outperforms the other control charts for a wide range of location shifts. Finally, two examples implementing this new EWMA type sign chart are given.