The Poisson distribution is a discrete model widely used to analyze count data. Statistical control charts based on this distribution, such as the c$c$ and u$u$ charts, are relatively well‐established in the literature. Nevertheless, many studies suggest the need for alternative approaches that allow for modeling overdispersion, a phenomenon that can be observed in several fields, including biology, ecology, healthcare, marketing, economics, and industry. The one‐parameter Poisson mixture distributions, whose literature is extensive and essential, can model extra‐Poisson variability, accommodating different overdispersion levels. The distributions belonging to this class of models, including the Poisson‐Lindley (PL), Poisson‐Shanker (PSh), and Poisson‐Sujatha (PSu) models, can thus be used as interesting alternatives to the usual Poisson and COM‐Poisson distributions for analyzing count data in several areas. In this paper, we consider the class of probabilistic models mentioned above (as well as the cited three members of such a class) to develop novel and useful statistical control charts for counting processes, monitoring count data that exhibit overdispersion. The performance of the so‐called one‐parameter Poisson mixture charts, namely the PLc$\text{PL}_c$‐PLu$\text{PL}_u$, PShc$\text{PSh}_c$‐PShu$\text{PSh}_u$, and PSuc$\text{PSu}_c$‐PSuu$\text{PSu}_u$ charts, is measured by the average run length in exhaustive numerical simulations. Some data sets are used to illustrate the applicability of the proposed methodology.