Model-based fault detection and diagnosis approaches based on statistical models for fault-free performance concurrently require a fault classifier database for diagnosis. On the other hand, a model with physical parameters would directly provide such diagnostic ability. In this paper we propose a generic model development approach, called the characteristic parameter approach, which is suitable for large engineering systems that usually come equipped with numerous sensors. Such an approach is applied to large centrifugal chillers, which are generally the single most expensive piece of equipment in heating, ventilating, air-conditioning, and refrigeration systems. The basis of the characteristic parameter approach is to quantify the performance of each and every primary component of the chiller (the electrical motor, the compressor the condenser heat exchanger the evaporator heat exchanger and the expansion device) by one or two performance parameters, the variation in magnitude of which is indicative of the health of that component. A hybrid inverse model is set up based on the theoretical standard refrigeration cycle in conjunction with statistically identified component models that correct for non-standard behavior of the characteristic parameters of the particular chiller Such an approach has the advantage of using few physically meaningful parameters (as against using the numerous sensor data directly), which simplifies the detection phase while directly providing the needed diagnostic ability. Another advantage to this generic approach is that the identification the correction models is simple and robust, since it requires regression rather than calibration. The entire methodology has been illustrated with actual monitored data from two centrifugal chillers (one a laboratory chiller and the other afield operated chiller). The sensitivity of this approach to sensor noise has also been investigated.