A vehicle compressed air supply system includes a supply part with compressor, an air drying part and a consumer part including consumer circuits with brake circuits supplied with compressed air via a multi-circuit safety valve. The brake circuits, and optionally at least one other consumer circuit, include compressed air tanks. Pressure in the circuits is monitored by sensors and evaluated by an electronic control device. To determine system parameters in terms of tank size and compressor output, when filling circuits, the rate of pressure increase in a circuit is determined as a function of compressor speed, and air-drying regeneration is effected. The period of a pre-defined pressure drop or pre-defined pressure gradient is determined and air volume for completing regeneration is calculated from the magnitude of the pressure drop, regeneration time and throttle diameter. Tank volume is determined therefrom. Compressor output is calculated from tank volume and rate of pressure increase.