A numerical controller controlling a five-axis machining machine having three linear axes and two rotation axes acquires a linear-axis-caused compensation amount associated with a combination of an instructed linear axis position and linear axis movement direction and an rotation-axis-caused compensation amount associated with a combination of an instructed rotation axis position and rotation axis movement direction, calculate a translation/rotation compensation amount based on the linear-axis-caused compensation amount and the rotation-axis-caused compensation amount, and adds the calculated translation/rotation compensation amount to the instructed linear axis position.

A method for ascertaining and correcting the defective machine state and/or at least one defective component state of a machine tool includes ascertaining the state using imaging and analysis of a cut edge produced and comparing with selected machine parameters and making the correction by way of a maintenance instruction based on the machine state for maintaining the machine tool.