Abstract： In this paper, the fault detection of non-Gaussian processes was discussed. A modified sparse representationbased fault detection method was proposed. Two control thresholds  called reconstruction error control threshold (CLE) and distance control threshold (CLDint) were introduced, and the fault detection level was improved. Additionally, by introducing a time constant, a sparse representation-based small shift detection method was proposed based on the same framework above， enhancing the detection ability of small shift. Two numerical examples demonstrate the effectiveness of these two methods, and a comparison between the proposed methods and the classic PCA-based fault detection method shows that the proposed methods are superior.