Research has been ongoing during the last several years on developing robust automated fault detecting and diagnosing (FDD) methods applicable for process faults in chillers used in commercial buildings. These FDD methods involve using sensor data from available thermal, pressure and electrical measurements from commercial chillers to compute characteristic features (CF) which allow more robust and sensitive fault detection than using the basic sensor data itself. One of the proposed methods is based on the analytical redundancy approach using polynomial black-box multiple linear regression models for each CF that are identified from fault-free data in conjunction with a diagnosis table. The second method is based on a classification approach involving linear discriminant analysis to identify the classification models whereby both the detection and diagnosis can be done simultaneously. This paper describes the mathematical basis of both methods, illustrates how they are to be tuned using the same fault-free data set in conjunction with limited faulty data, and then compares their performance when applied to different fault severity levels. The relative advantages and disadvantages of each method are highlighted and future development needs are pointed out.