1. A component mounting method in a component mounting system having: a component mounting line formed by linking a plurality of component mounters which pick up components supplied to component supply positions by a plurality of tape feeders disposed on a carriage, and mount the components onto a board using a suction nozzle which is attached to a mounting head; and an external set-up device to which the carriage that is scheduled to be attached to one of the component mounters which is a set-up changing target is attachable in a detachable manner;the method comprising:
imaging the component supply positions of the tape feeders disposed on the carriage, in a state in which the carriage scheduled to be attached to the one of the component mounters of the set-up changing target is attached to the external set-up device,
calculating a shift amount of the component supply position of each tape feeder based on an image of the component supply position which is captured in the imaging,
storing supply position shifting data in which the shift amount calculated in the calculating is related to a feeder address and a feeder ID of each tape feeder, and
comparing the feeder ID of each of the tape feeders disposed on the carriage, with the feeder ID included in the component supply position shifting data in a state in which the carriage removed from the external set-up device is attached to the one of the component mounters of the set-up changing target.