The paper concentrates on modeling the data that can be described by a homogeneous or non-homogeneous Poisson process. The goal is to decide whether the intensity of the process is constant or not. In technical practice, e.g., it means to decide whether the reliability of the system remains the same or if it is improving or deteriorating. We assume two situations. First, when only the counts of events are known and, second, when the times between the events are available. Several statistical tests...