Cumulative sum (CUSUM) control charts are constructed under the assumption that the observations taken from the process of interest are independent over time. However, the observations in many industrial cases are actually correlated. Serial correlation of observations will result in poor performance of control charts. The effect of serial correlation on the performance of control charts is analyzed through mathematical analysis method. Positive serial correlation decreases the average run length (ARL) of CUSUM control chart, resulting in too many false alarms. Negative serial correlation increases the ARL of CUSUM control chart, which possibly results in missing faults. In addition, a fault detection method for autocorrelated processes is presented by using residual-based CUSUM control chart. The residuals between the process error and its predication are generated using autoregressive time-series models. Then, CUSUM control charts are used to monitor the residuals which are statistically independent. The residualbased CUSUM control chart can improve the accuracy of fault detection through eliminating the effects of serial correlation on the performance of control charts. Some case studies show that the residual-based CUSUM control chart is an effective tool in detecting faults of autocorrelated processes, and the fault detection method has good robustness and high accuracy rate.