Many of the current multivariate statistical process monitoring techniques (such as principal component analysis (PCA) or partial least squares (PLS)) do not utilize the non-Gaussian information of process data. This paper proposes a new monitoring method based on independent component analysis-principal component analysis (ICA-PCA). The Gaussian and non-Gaussian information can be extracted for fault detection and diagnosis. Moreover, a new mixed similarity factor is proposed. This similarity factor is used to identify the fault mode. Because of the non-orthogonal nature of the extracted independent components, a "main angle" is proposed to calculate the ICA-based similarity factor. To handle the cases where two datasets have similar principal components or independent components but the numerical values of the process variables are different, two distance similarity factors are used for complement. A case study of the Tennessee Eastman (TE) benchmark process indicates that the proposed fault detection and mode identification methods are more efficient, compared to the alternative methods.