A diagnostic system for a vehicle includes a first sensor that generates a first status signal, which is indicative of an engine speed of an engine. A second sensor generates a second status signal that is indicative of an actual accessory speed of an accessory. The accessory is coupled to the engine via a belt system. A control module determines an expected accessory speed based on the engine speed and determines a residual accessory speed based on the expected and actual accessory speeds. The control module also detects a fault in the belt system based on the residual accessory speed.