Multivariate statistical process control (MSPC) has been successfully applied to chemical processes. In order to improve the performance of fault detection, two kinds of advanced methods, known as moving principal component analysis (MPCA) and DISSIM, have been proposed. In MPCA and DISSIM, an abnormal operation can be detected by monitoring the directions of principal components (PCs) and the degree of dissimilarity between data sets, respectively. Another important extension of MSPC was made by using multiscale PCA (MS-PCA). In the present work, the characteristics of several monitoring methods are investigated. The monitoring performances are compared with using simulated data obtained from the Tennessee Eastman process. The results show that the advanced methods can outperform the conventional method. Furthermore, the advantage of MPCA and DISSIM over conventional MSPC (cMSPC) and that of the multiscale method are combined, and the new methods known as MS-MPCA and MS-DISSIM are proposed.