This paper proposes a control chart useful for detecting small shifts in the mean of a double-bounded process, such as fractions and proportions, in the presence of control variables. For this purpose, we consider the cumulative sum (CUSUM) control chart applied to different residuals of the beta regression model. We conduct an extensive Monte Carlo simulation study to evaluate and compare the performance of the proposed control chart with two other control charts in the literature in terms of run length analysis. The numerical results show that the proposed control chart is more sensitive to detect changes in the process than its competitors and that the quantile residual is the most suitable residual to be used in our proposal. Finally, based on the quantile residual, we present and discuss applications to real and simulated data to show the applicability of the proposed control chart.