Fault detection and diagnosis is important in ensuring the stability and safety of chemical processes. However, limited studies have focused on strong periodic disturbance and non-Gaussian process monitoring. By utilizing the data-driven monitoring method, we have proposed the residual analysis independent component analysis based on average multivariate cumulative sum (AMRA-ICA) method to avoid the influence of periodic disturbance in non-Gaussian chemical processes with periodic disturbance. Average multivariate cumulative sum (AM) is introduced in the AMRA-ICA method for disturbance cycle synchronization. Residual analysis (RA) is employed to remove the disturbance in the data set and to obtain the normal residual. The independent component analysis (ICA) method is then utilized to monitor the residual, and an improved contribution histogram method is proposed to identify the cause of the fault. The proposed method has been applied to the classic benchmark Tennessee Eastman process with and without periodic disturbance and to an ethylene compressor which is periodically affected by ambient temperature. Simulation results illustrate that the proposed AMRA-ICA method could solve the monitoring problem of non-Gaussian processes with periodic disturbance more effectively and accurately compared with the residual analysis PCA (RA-PCA) and the local tangent space alignment-ICA (LTSA-ICA). The AMRA-ICA method can also manage conventional processes without periodic disturbance.