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 demonstrate that HCA outperforms ICA and dynamic ICA significantly and the variable contribution analysis of HCA can diagnose faults successfully.