B747-400 ENG SHUT DOWN AT CRUISE ALT OVER THE PACIFIC RESULTED IN A DIVERT LNDG.

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WE WERE FLYING FROM HONG KONG TO LAX. AFTER FLYING FOR ABOUT 6 HRS; MOST OF IT WITH OVER 150 KT TAILWIND. AS WE PASSED ABOUT 170 DEGS E AN ENG STARTED TO VIBRATE BADLY AND THE EGT (#3) INCREASED RAPIDLY. NARITA JAPAN WAS THE CLOSEST ARPT AND WOULD SEEM LIKE THE BEST PLACE TO GO; BUT WITH A 175 KT TAILWIND AND KNOWING ONLY THE DISTANCES TO ANC AND HNL; WE HAD TO DECIDE WHERE TO GO IN A HURRY! OUR DISPATCH SAID HE RAN THE NUMBERS AND RECOMMENDED A RETURN TO NARITA. AFTER WE TURNED AROUND; HE TOLD US HE HAD RERUN THE NUMBERS AND ANC WAS LESS TIME AWAY. I THINK THAT IT WOULD BE BEST TO HAVE A 3 ENG POINT OF EQUAL TIME AVAILABLE; NOT ONLY BTWN 'UNDESIRABLE' (SHEMYA; ADAK; ETC) ARPTS; WHERE YOU WOULD ONLY WANT TO GO IF YOU HAD A FIRE ON BOARD OR MORE SERIOUS EMER. A PET COULD BE WORKED OUT BY DISPATCH WHILE RUNNING THE FLT PLAN; THAT WOULD GIVE US SOME IMMEDIATE GUIDANCE THAT WOULDN'T BE ARRIVED AT IN A HURRY WITH THE WIND BLOWING US THE WRONG WAY AS THE QUICK *NECESSARY) DECISION IS MADE. OUR MOST CRITICAL PET THAT NIGHT WAS SHEMYA (WE WEREN'T BY SHEMYA YET; BUT IT WAS CLOSE. WE LANDED NRT WITH 20000 LB OF FUEL! JUST COMFORTABLE IN A 747! 5 HRS AFTER ENG SECURED.