**6. Concluding remarks**

In this chapter, we proposed an adaptive EWMA surveillance plan to monitor a counting process of which the time between its events is Weibull distributed. The proposed method can be applied to both homogeneous and nonhomogeneous processes. To implement the proposed surveillance plan, the scale and shape parameters for the underlying distribution of the TBEs are estimated using a distributional regression approach [15]. Then the threshold for the counts is established using the estimated parameters and the desired ARL. The proposed plan is applied to both simulated and real data. Simulation results indicate that the proposed method is applicable for detecting outbreaks of any magnitude and also signals them in a reasonable time after their incidence. In addition, simulations revealed that for the detection of the large outbreak, plans with larger smoothing parameter are superior. However, for the early detection of small outbreaks, we need to employ smaller smoothing weights. Applying the proposed surveillance method to real data, we conclude that the proposed method is capable of detecting outbreaks in nonhomogeneous counting processes.
