Process monitoring techniques are used in the chemical industry to improve both product quality and plant safety. In chemical process systems, real-time process monitoring is one of the most crucial and challenging tasks for efficient quality control of the final products and process optimization. The existing multiscale process monitoring techniques use offline decomposition tools that restrict their applications to real-time process monitoring. In this study, to improve the performance of monitoring real-time process data, we have combined moving window-based wavelet transform and kernel principal component analysis (KPCA). A case study is performed on a typical continuous stirred tank reactor system. Performance analysis (based on T-2 and squared prediction error statistics and contribution plots) shows that the technique successfully detects and identifies process disturbances, sensor bias, and process faults. Moreover, a comparison with PCA and KPCA methods shows that the proposed approach provides a 100% fault detection rate for the step-change fault patterns and has considerably improved detection rates for the random and ramp-change fault patterns.