A self-starting non-restarting CUSUM chart for monitoring Poisson count data with time-varying sample sizes

Abstract

Many studies have focused on monitoring the incidence rate of Poisson count data with time-varying sample sizes, with control charts being widely used. However, almost all of the existing reports mainly focus on solving the problem of time-varying sample sizes. Rare attention is paid to the real-life problems where the data cannot restart. Besides, these studies aim at Phase II with the in-control parameters known, which is unrealistic in real applications. As far as we know, there is no research on the non-restarting and unknown in-control parameters control charts, but it is essential and critical for extending applications of control charts. To address these limitations, this study offered two self-starting non-restarting cumulative sum (CUSUM) control charts based on the modified test to monitor the incidence rate of non-restarting Poisson data with time-varying sample sizes. The methods can be applied to other control charts and take into account both Phase I and Phase II without assumptions of time-varying sample sizes. Moreover, the monitor can be carried out with small Phase I samples. Simulation results show that the second control chart proposed in this study (SSNR-CUSUM-P2) is optimal compared to the common non-restarting control chart (E) and the first control chart proposed in this study (SSNR-CUSUM-P1). The SSNR-CUSUM-P2 chart has the highest similarity to the control chart with known parameters (T) in both post-outbreak false alarm rate and outbreak time point set. Finally, a dataset on German measles patients and a dataset on US employment are used to illustrate the application of the methods.