The present invention is directed to a mathematical approach to detect faults by reconciling known data driven techniques with a physical understanding of the HVAC system and providing a direct linkage between model parameters and physical system quantities to arrive at classification rules that are easy to interpret, calibrate and implement. The fault modes of interest are low system refrigerant charge and air filter plugging. System data from standard sensors is analyzed under no-fault and full-fault conditions. The data is screened to uncover patterns though which the faults of interest manifest in sensor data and the patterns are analyzed and combined with available physical system information to develop an underlying principle that links failures to measured sensor responses. These principles are then translated into online algorithms for failure detection.