Example implementations described herein involve a new data-driven analytical redundancy relationship (ARR) generation for fault detection and isolation. The proposed solution uses historical data during normal operation to extract the data-driven ARRs among sensor measurements, and then uses them for fault detection and isolation. The proposed solution thereby does not need to rely on the system model, can detect and isolate more faults than traditional data-driven methods, can work when the system is not fully observable, and does not rely on a vast amount of historical fault data, which can save on memory storage or database storage. The proposed solution can thereby be practical in many real cases where there are data limitations.