Abstract: Fault diagnosis of a ball mill is a typical multi-dimensional data mining problem in complex industrial processes. The difficulty of this problem lies in the low accuracy and high time complexity of multi-dimensional data mining. We propose a FastVOA with local weight (LW-FastVOA) to solve the problem. First, we apply the angle-based outlier detection (ABOD) to measure the outlier factor. Then, we use the FastVOA algorithm to reduce the time complexity of ABOD. The algorithm projects the dataset on random hyperplanes orthogonally and then derives the variance with AMS sketches. The frequency moments of the points are approximated by summarizing and projecting on the random hyperplanes. Finally, we propose the LW-FastVOA algorithm to add the local weight of the data points and reduce the omission rate of outliers among clusters to improve the accuracy. Simulation results show that the LW-FastVOA algorithm improves the precision rate and recall rate in fault diagnosis, thereby verifying the effectiveness and feasibility of the algorithm.