Chemical and petrochemical processes require continuous monitoring to detect abnormal events and to sustain normal operations. Furthermore, process monitoring enhances productivity, efficiency, and safety in process industries. Here, we propose an innovative statistical approach that exploits the advantages of multiscale partial least squares (MSPLS) models and generalized likelihood ratio (GLR) tests for fault detection in processes. Specifically, we combine an MSPLS algorithm with wavelet analysis to create our modeling framework. Then, we use GLR hypothesis testing based on the uncorrelated residuals obtained from the MSPLS model to improve fault detection. We use simulated distillation column data to evaluate the MSPLS-based GLR chart. Results show that our MSPLS-based GLR method is more powerful than the PLS-based Q and GLR method and MSPLS-based Q method, especially in early detection of small faults with abrupt or incipient behavior.