This paper presents an on-line Statistical Process Control (SPC) technique, based on a Generalized Likelihood Ratio Test (GLRT), for detecting and estimating mean shifts in autocorrelated processes that follow a normally distributed Autoregressive Integrated Moving Average (ARIMA) model. The GLRT is applied to the uncorrelated residuals of the appropriate time-series model. The performance of the GLRT is compared to two other commonly applied residual-based tests – a Shewhart individuals chart and a CUSUM test. A wide range of ARIMA models are considered, with the conclusion that the best residual-based test to use depends on the particular ARIMA model used to describe the autocorrelation. For many models, the