Count data monitoring: Parametric or nonparametric?

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.

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