Count Data Monitoring: Parametric or Nonparametric? Zhiqiong Wang 1 and Peihua Qiu 2 1 College of Management and Economics, Tianjin University 2 Department of Biostatistics, University of Florida Abstract Count data are common in practice, ranging from security protection, disease surveillance, to quality monitoring of a production process. To describe the distribution of a count data, we usually use a Poisson probability model or a similar parametric model (e.g., a Negative Binomial model). In practice, however, such a parametric model may not be able to describe the distribution of a count data well in some cases, because the count data are often affected by some confounding factors and such a confounding impact is difficult to accommodate by the parametric model. In this paper, we study the count data monitoring problem, and the consequence to use a parametric control chart in cases when the underlying parametric distribution model is invalid. Based on that study, we suggest using nonparametric charts to monitor count data when it is uncertain that the count data can be described by a parametric distribution model. Keywords: Count data; Data categorization; Distribution free; Parametric probability models; Pois- son distribution; Statistical process control. 1 Introduction In many sequential processes, major outcome variables are often in the form of counts of certain events that are related to the quality or performance of the related processes. For instance, in manufacturing industries, the number of specific defects found in a product sampled from a production line could be a quality variable to monitor. In road or internet traffics, the number of accidents is often a major index of concern. In public health, we are often concerned about the number of daily occurrences of a specific disease (e.g., lung cancer) in a region or country. Therefore, proper monitoring of count data is an important research problem with broad applications, which is the focus of this paper. In the statistical process control (SPC) literature, there have been some control charts for monitoring count data. In some applications, it is obvious that the distribution of the count data is binomial, because the count denotes the number of successes from a binomial experiment. Many control charts, including the classic p and mp charts, have been developed for monitoring binomial count data. See, for instance, Gan 1 , 1