Two different types of algorithms were developed and applied to detect the partial faults of a multi-type air conditioning system. Partial faults include the compressor valve leakage, the refrigerant pipe partial blockage, the condenser fouling, and the evaporator fouling. The first algorithm was developed by using mathematical models and parity relations, and the second algorithm was developed by using mathematical models and a RBF neural network. Test results showed that the second algorithm was better than the first algorithm in detecting various partial faults of the system. Therefore, the algorithm developed by using mathematical models and a RBF neural network may be used for the detection of partial faults of an air-conditioning system.