In this paper, an alternative data-driven fault detection technique is developed focusing on complex industrial systems with uncertainties. To deal with inconstant uncertainties, industrial data matrices are constructed including the information of mean. Based on the Riemannian manifold of symmetric positive definite matrices, the Riemannian mean is defined as the mean of data matrices, and the Riemannian metric is employed as the monitoring index to assess the variation of data matrices. Threshold is set using randomized algorithms with an acceptable false alarm rate. The detection decision could be made according to the monitoring index and the threshold. Verification are carried out with a numerical system and a continuous stirred tank heater system.