Recent approaches to independent component analysis (ICA) have introduced kernel function to obtain highly accurate solutions, particularly where classical linear methods experience difficulty in non-Gaussian process monitoring. These approaches are developed based on the statistics with normal data. However in some industry processes, certain fault data can be pre-separated from the normal data manually. In order to utilize this part of data, fault-related kernel independent component analysis (FKICA) is put forward as an improved algorithm of KICA in this paper. FKICA can make full use of the historical fault data by decomposing the data space into four subspaces and make the algorithm more sensitive to certain fault. The proposed methods are applied to monitoring of fused magnesia furnace smelting process. The experiment results show that the proposed methods are more sensitive to the known faults.