In this study, a novel approach is developed for online state monitoring based on higher-order cumulants analysis (HCA). This approach applies higher-order cumulants to monitor a multivariate process, and while conventional approaches such as independent components analysis (ICA) uses variance to monitor process. Variance is lower-order statistics and is only sensitive to amplitude. In contrast, higher-order cumulants, the typical higher-order statistics, carry important information and are sensitive to both amplitude and phase, particularly for non-Gaussian distributions. The main idea of this novel approach is to monitor the cumulants of dominant independent components and residuals of the ICA model. Therefore, higher-order statistical information of multivariate processes can be monitored online. Furthermore, a variable contribution analysis scheme is developed for HCA to diagnose faults. The proposed approach is applied to the Tennessee Eastman (TE) process to exhibit its effectiveness. The results de...