In this study, fault detection and fault reconstruction methods are developed using matrix factorization of component vectors obtained with independent component analysis (ICA). Two monitoring statistics are used for fault detection in a detailed analysis of the ICA data model. A fault reconstruction technique is proposed that can determine the normal value and an estimate of the fault magnitude from the measurements. A semi-supervised Laplacian regularization (SLR) kernel density estimation approach is introduced to determine the normal operating region, which can significantly reduce the false alarm rate. These methods are applied to a hot galvanizing pickling waste liquor treatment process (HGPWLTP) to evaluate the performance of the proposed approach. The test results show that the proposed approach has satisfactory performance.