We propose a Bayesian approach to the cumulative sum (CUSUM) control chart to perform under different distributions without the need of a data transformation. Different loss functions are considered to inform the framework of the charts for the Normal and Poisson conjugate cases. Using a comprehensive simulation study, we assess the method via a sensitivity analysis for the control chart decision parameters, shift sizes, and distribution hyper-parameters; where performance measurements are average run length (ARL), standard deviation of the run length (SDRL), average time to signal (ATS), and standard deviation of time to signal (SDTS). For CUSUM literature, a data transformation is often required when using non-Guassian data, so we also consider a comparative study with the classical CUSUM chart. To showcase their efficacy on over-dispersed count data, we model a count series of respiratory disease related hospitalizations in São Paulo, Brazil and implement our Bayesian charts.