Self-information-based weighted CUSUM charts for monitoring Poisson count data with varying sample sizes

In many applications, the Poisson count data with varying sample sizes are monitored using statistical process control charts. Among these applications, the weighted CUSUM charts are developed to deal with the effect of the varying sample sizes. However, some of them use limited information of the sample size or the count data while assigning the weights. To gain more information of the process, the self-information weight functions are developed based on both the sample size and the observed count data. Then, the weighted CUSUM charts are proposed with the self-information-based weight. Simulation studies show the self-information-based weighted CUSUM charts perform better than the benchmark methods in detecting small shifts. Moreover, the performance of proposed method with estimated parameters is investigated via simulation. Finally, an example is given to illustrate the application of the proposed weighted CUSUM charts.