An electronic tag is attached to a filter cartridge, which includes a filter. The electronic tag stores individual product information of the filter and wirelessly transmits the individual product information. A wireless receiver device is installed to a predetermined location of a vehicle, which is other than the filter cartridge and receives the individual product information transmitted from the electronic tag. A diagnostic device diagnoses whether the individual product information is received by the wireless receiver device or whether the filter cartridge installed in the vehicle has a desired filtering performance based on contents of the individual product information received by the wireless receiver device.