Public health surveillance consists of the systematical collection, analysis and interpretation of public health data in order to (i) understand trends, (ii) detect changes in disease incidence and death rates, and (iii) plan, implement and evaluate public health policies. The monitoring of incidence rate of an event of interest (e.g., cancer incidence, surgical failures, etc.) is the main scope of public-health surveillance methods. For example, an increase in the incidence rate of a disease represents an increased risk to the public. Hence, the quick and accurate detection of such changes will lead to the development of effective medical and non-medical intervention strategies that will delay or reduce the impact of the outbreak in the community.The monitoring of public-health data over time is a scientific area closely related to the domain of statistical process control (SPC); the primary tool of SPC is the control chart. In case of public-health surveillance, the data are often discrete, assuming to follow a specific probability distribution. Thus, the application of ordinary control charting techniques is not valid. Therefore, new improved schemes are needed in order to deal effectively with the health-related processes, without leading to incorrect assessments and ambiguous conclusions. Also, the performance and the statistical design of the new control schemes should be evaluated under non-standard, more realistic, situations.Several procedures suitable for the monitoring of public health surveillance data have proposed and studied in the literature. However, further research is needed in the area. The basic aim of the proposed research is dual: (i) The development of improved monitoring procedures for attributes with specific applications in public-health surveillance problems and (ii) to assess the effect of several violations of the main assumptions on the performance of the proposed schemes, suggesting effective solutions and adjustments.