**4. Simulation results**

To assess the validity and applicability of our proposed adaptive method, we employ simulations studies. We restrict our attention to plans that have 10<*E c*ð Þ*<sup>i</sup>* <50 which limits the volume of simulations that are required to make a realistic judgment. This is also the range where the EWMA counts become competitive for small changes in the scale parameter (see [4] and Sparks et al., 2020). To do so, we consider four counting processes with daily aggregations. The shape parameters for the TBE distributions when the processes are in-control are equal to 0.85, 0.95, 1.15, and 1.25. The in-control scale parameter for each process is equal to 0.02, 0.025, 0.03, and 0.035, respectively. We intentionally imposed outbreaks in the simulated data to assess if the proposed method is capable of detecting them. In the simulation study, we assume that the outbreaks result in a decrease in the scale parameter. Various surveillance plans are devised to monitor each process. The *ATS*<sup>0</sup> for the plans associated with the first process (with shape and scale
