In this study, the convergent cross-mapping technique has been applied to non-linear dynamic systems for operation monitoring, detecting process abnormalities or faults, and identifying their root cause(s). Faults in sensor or controller are easier to detect and diagnose compared to process faults (e.g., change in composition of feed). Therefore, we have focused on sensor and process faults for two non-linear dynamic systems. Our fault detection and root cause diagnosis methodology uses convergent cross-mapping along with some standard statistical techniques. Moreover, causal link lists are deduced to visualize the propagation of a fault-the correctness of these data generated causal link lists have also been validated with existing process knowledge. © 2021 The Society of Instrument and Control Engineers-SICE.