What was found
JUST PRIOR TO DESCENT INTO MIA AT FL 390, THE NR 4 ENGINE FLAMED OUT. THE ENGINE SHUT-DOWN CHECK LIST WAS COMPLETED AND THE IN-FLIGHT ENGINE START CHECK LIST WAS COMPLETED. THE FUEL FLOW INDICATED 3-400 POUNDS PER HOUR. ON THE FIRST TWO ATTEMPTS, THE FUEL FLOW DID NOT INCREASE, BUT EGT INCREASED WITH NO INCREASE IN N1 OR N2. ON THE THIRD ATTEMPT, AT APPROXIMATELY FL 320 AND 280 KNOTS, ENGINE RESTARTED. A NORMAL DESCENT AND APPROACH WAS MADE AT MIA. REPLACED NR 4 ENGINE FUEL FILTER, BOTH IGNITERS AND SUMPED ALL FUEL TANKS. ENGINE R/U NORMAL.