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Non-Gaussian dynamic processes are ubiquitous due to the presence of non-Gaussian distributed variables. Therefore, fault detection of non-Gaussian dynamic processes plays a vital role to maintain the safe operation of systems and symmetry of data distribution. In this paper, a dynamic generalized likelihood ratio (DGLR)-based fault detection method is proposed for non-Gaussian dynamic processes. Different from the conventional principal component analysis (PCA)-based, dynamic PCA-based, and PCA-based GLR fault detection methods, the novelty of the proposed method is that the GLR is extended to non-Gaussian dynamic processes, and the randomized algorithm is integrated for threshold setting to attenuate the influence of non-Gaussian. The application scope of these methods is also discussed. The proposed method is compared with four existing fault detection methods on a numerical simulation and the continuous stirred-tank reactor (CSTR) process. The achieved results show that the proposed method is able to significantly improve the detection performance in terms of fault detection rate and prompt response to faults. [ABSTRACT FROM AUTHOR]