An adaptive exponentially weighted moving average control chart for poisson processes

The Adaptive Exponentially Weighted Moving Average (AEWMA) control chart is known to be effective in detecting range of shifts simultaneously. Moreover, the AEWMA chart is known to diminish the inertia effect. The AEWMA chart is usually investigated while assuming that the monitored process follows a continuous distribution; commonly the normal distribution. In practice, however, monitored data could be of a discrete-type. We aim in this study to propose a discrete-version from the AEWMA chart; namely the Poisson AEWMA chart. The chart is compared with its counterparts; the Poisson EWMA chart and Poisson CUSUM chart using the ARL and RMI metrics. Our results show that the Poisson AEWMA chart performs more efficiently in detecting shifts of various sizes with an RMI value approaching zero. The Poisson CUSUM chart has the worst performance. Moreover, the proposed Poisson AEWMA chart is capable of detecting shifts faster than an approach based on normal approximation even for large values of the mean defects. In addition, the superiority of the Poisson AEWMA chart in diminishing the inertia effect is illustrated through a numerical example. The example shows that the Poisson AEWMA chart is capable of detecting out of control situations very fast even if the chart statistic is in a disadvantageous position before a shift occurs.