1. A device management method comprising: periodically performing a complete test involving the entire number of devices in a large group of managed devices to determine whether the devices are operating normally or have a malfunction; recording a test result in a management database for each cycle of the complete test, and repairing or replacing a device that has been found to be malfunctioning; and determining the suitability of a device model or selecting a suitable device model for each of the managed devices on the basis of history information about each of the managed devices obtained from the test result of the complete test that spans a plurality of cycles, as recorded in the management database.