In the present study, data-driven fault diagnosis (FD) systems of chemical plants dealing with frequent and rare faults are investigated. Although different faults occur with different frequencies in chemical plants, this issue has scarcely been addressed in developing a process FD system. A novel diagnostic framework based on the Bayesian network (BN) is proposed to incorporate fault frequencies. This probabilistic method can readily involve non-uniform probability distribution of faults and non-Gaussian probability distribution of features. The proposed approach includes not only a combination of tools but also information management. In fact, the imbalanced dataset, established by frequent and rare faults, promotes recursive updating of prior probabilities of faults. The performance of the BN was evaluated and compared with the conventional C4.5 method in the Tennessee-Eastman process benchmark. It was shown in this work that the diagnostic performance of the proposed approach versus the C4.5 method is more efficient. The importance of taking into account non-uniform probability distribution of faults for designing a FD system was highlighted. Furthermore, the effect of independent component analysis (ICA) of the imbalanced dataset on the FD was examined. The proposed framework versus the C4.5 method promises 37 % FD performance improvement for the dataset with a 10:1 imbalance index.