What was found
AT FL380, THE CREW OBSERVED DECREASING PARAMETERS ON THE NR 4 ENGINE. THE COM PROCEDURES WERE FOLLOWED BUT THE ENGINE REMAINED AT IDLE. ALL INDICATIONS REMAINED IN THE NORMAL RANGE, SO THE ENGINE WAS LEFT AT IDLE POWER. WHEN DESCENDING THROUGH 8000 FEET ON APPROACH, THE ENGINE ROLLED BACK BELOW IDLE AND THE CREW SECURED THE ENGINE. THE FLIGHT CONTINUED TO ITS DESTINATION LANDING WITHOUT INCIDENT. MAINTENANCE REPLACED THE ENGINE DRIVEN FUEL PUMP, FUEL CONTROL, AND FUEL HEAT VALVE. AN ENGINE RUN AND LEAK CHECK WERE COMPLETED WITH NORMAL INDICATIONS.