Recent work has demonstrated the effectiveness of the principal component analysis (PCA)-independent component analysis (ICA) method for non-Gaussian process monitoring; however, the focus is on fault detection and isolation. The fault diagnosis issue has not been sufficiently investigated. This paper aims to introduce a PCA-ICA integrated with a Bayesian fault diagnosis method for non-Gaussian processes. First, PCA is employed to project the source signals into the dominant subspace. Second, ICA is employed to extract the independent components from the PCA dominant subspace. Then fault signature evidence is generated, and a Bayesian fault diagnosis system is established to identify the process status. Considering the significant amount of calculation in Bayesian diagnosis, a subset of optimal evidence sources are selected via a stochastic optimization algorithm. The efficiency and feasibility of the proposed method are exemplified by a numerical example and, the Tennessee Eastman benchmark process.