The triple exponentially weighted moving average control chart for monitoring Poisson processes

In many real applications, the quality characteristics of interest, such as the number of nonconformities in a production unit or the annual incidence rate, may follow the Poisson distribution. In the present article, we propose a triple exponentially weighted moving average control chart for monitoring Poisson processes (regarded as PTEWMA chart). One- and two-sided schemes of the proposed chart are designed and are compared with the existing PEWMA and PDEWMA charts in terms of the average run-length (ARL). The results show that for small values of the smoothing parameter lambda, the PTEWMA chart is more effective than its competitors in detecting small shifts while its superiority increases as the value of lambda increases. Moreover, the two-sided PTEWMA chart is less ARL-biased for small downward shifts than the other two charts. Two illustrative examples are provided to demonstrate the application of the proposed chart.