In this paper, we consider the double sampling (DS) (X) over bar control chart for monitoring processes in which the observations can be represented as a first-order autoregressive moving average (ARMA(1, 1)) model. The properties of the DS (X) over bar control chart with the sampling intervals driven by the rational subgroup concept are studied and compared with the Shewhart chart and the variable sample size (VSS) chart, both properly modified to account for the serial correlation. Numerical results show that the correlation within subgroups has a significant impact on the properties of the charts. For processes with low to moderate correlation levels, the DS (X) over bar chart is substantially more efficient in detecting process mean shifts.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)