INADVERTENT ENG SHUTDOWN DURING CLB.

Narrative

THIS WAS THE FIRST FLT OF THE DAY AND FE HAD DONE AN ORIGINATION PREFLT. DURING CLB THROUGH FL240; 30 NM SOUTH OF FOF; THE #3 ENG FLAMED OUT. ACCOMPLISHED ENG FAILURE PRECAUTIONARY SHUTDOWN CHKLIST. WHEN WE GOT TO THE STEP TO TURN OFF THE #3 ENG FUEL SHUTOFF SWITCH; WE SAW THAT IT WAS ALREADY CLOSED. WE SUSPECTED A PROB WITH THIS SWITCH WHICH HAD BEEN CYCLED DURING THE PREFLT CHK. PRIOR TO THE FAILURE; THE FE HAD NOT RECONFIGURED THE FUEL PANEL SINCE CLEANUP AFTER TKOF AND HE WAS LOOKING FORWARD AND NOT TOUCHING THE FE PANEL WHEN THE ENG FAILED. AFTER OBSERVING N1 AND N2 ROTATION; GOOD OIL PRESSURE AND TEMP; WE RESTARTED THE ENG USING THE INFLT RESTART CHKLIST. ENG RESTARTED NORMALLY. WITH ALL SYS REINSTATED TO NORMAL AND ENGS RUNNING NORMALLY; I DECIDED TO CONTINUE TOWARDS SJU. MIA WAS DEST. THE ALTERNATIVE WAS TO DIVERT TO FOF; BUT I DECIDED NOT TO DO THAT BECAUSE WE HAD 3 GOOD ENGS. I WAS UNFAMILIAR WITH FOF. WE WERE OVER WT FOR LNDG. NO WX FOR THERE AND WE WERE IN A NON RADAR AREA. BECAUSE ALL WAS OPERATING NORMALLY AND THE PROB DID NOT REOCCUR; WE CONTINUED TO DEST. THERE WERE MANY SUITABLE ALTERNATES ALONG THE WAY TO MIA WHERE WE PLANNED TO DIVERT IF NECESSARY.