method and apparatus for repairing an article , such as an air - cooled component , during which at least a portion of the component must be removed and replaced . the method and apparatus make use of one or more workpiece holders adapted to secure and position an component on the apparatus , a multi - axis head adapted for movement relative to the workpiece holder , a nozzle mounted to the multi - axis head and operable to remove at least a portion of the component with a jet of fluid discharged therefrom , an electrical - discharge electrode mounted to the multi - axis head and operable to form surface holes in the component by electrical - discharge machining , and a system for controlling the movement of the multi - axis head so that the waterjet and electrical - discharge machining operations are performed to yield a repaired component that closely duplicates the original .