1 ENG OF A B727 QUIT DURING HIGH ALT CRUISE; APPARENTLY DUE TO FUEL STARVATION.

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XFEED STARTED FROM L TO R TANK TO BAL 200 LBS. SEVERAL MINS LATER #3 ENG QUIT. DISCOVERED WHEN ESSENTIAL PWR LOST AND AUTOPLT DISENGAGED. BECAUSE IT TOOK SEVERAL MINS TO WIND DOWN AND SUPPORTING INSTS TO SHOW; WE THOUGHT INITIALLY IT WAS GENERATOR FAILURE. RAN ENG FAILURE; WINDMILLING ENG; AND ENG START INFLT CHKLISTS (3 SEPARATE CHKLISTS). RETURNED TO NGO FOR FUEL AND MAINT INSPECTION. ENG RESTART NORMAL; INSPECTED OK. 3 POSSIBLE REASONS COME TO MIND. 1) XFEED PROC DONE INCORRECTLY. NOT LIKELY; BUT POSSIBLE. I'VE GOT 5 YRS AND 3000 HRS AS 727 FE. TO GO FROM TANK TO ENG TO XFEED MEANS MOVING EACH XFEED VALVE AND TURNING OFF R BOOST PUMPS. PRETTY SIMPLE. STILL; SIMPLE THINGS BECOME ROTE AND THAT LEADS TO COMPLACENCY. 2) XFEED VALVE DIDN'T OPEN. A BLUE LIGHT FLASHES MOMENTARILY (LESS THAN 1 SECOND) TO SHOW VALVE CHANGES POS -- DOESN'T SHOW POS. I DON'T REMEMBER IF THE LIGHT FLASHED OR NOT. NEXT TIME -- ALL THE NEXT TIMES -- I'LL MAKE SURE LIGHT CHANGES EVEN IF I HAVE TO CHANGE IT SEVERAL TIMES TO CATCH IT. 3) FUEL LEVEL WAS MAX FOR OUR WT (WAS OPTIMAL) SO THE ENGS WERE AT FULL PWR. I SUPPOSE THE 2 PUMPS IN L TANK MAY NOT HAVE BEEN ABLE TO SUPPLY FUEL TO BOTH ENGS WHEN WE WERE SO HIGH AND SO HVY. FUEL CTL? I DON'T KNOW WHAT HAPPENED -- RATHER WHY IT HAPPENED. I DO KNOW I'LL WATCH MORE CAREFULLY WHEN I MAKE CHANGES TO FUEL CONDITIONS.