A process for controlling the length of a purge and the purge rate of a fuel cell stack at system shut-down so as to provide the desired amount of stack humidity. The membrane humidification is measured at system shut-down by a high frequency resistance sensor that detects membrane humidification and provides the measurement to a controller. The controller controls the compressor that provides cathode input air to the fuel cell stack so that the time of the purge and the flow rate of the purge provide a desired membrane humidity for the next start-up.