A WDB CREW; ON A LINE CHK; HAD A GROSS NAVIGATIONAL ERROR. THE IRS SHOWED W LONGITUDE VICE THE PROPER E.

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I AM A LCA GIVING A IOE ON THIS WDB. AFTER INITIAL COCKPIT SET-UP; I HAD THE IOE FO DO THE CAPT PORTION OF CDU PROGRAMMING; SO HE WOULD BE FAMILIAR WITH THESE DUTIES AND TO DETERMINE IF HE KNEW THESE PROCS. HE PERFORMED THIS PROGRAMMING ACCORDING TO SOP. SETTING THE IRS POS WAS ACCOMPLISHED USING SIN GATE POS. WE SUBSEQUENTLY GOT AN 'ENTER IRS POS' MESSAGE ON CDU. GTE POS WAS REENTERED ONCE AND WAS ACCEPTED. I THEN VERIFIED THE POS WITH THE COORDS AT THE SINGAPORE GATE W THEY WERE SAME. RTE WAS ENTERED USING CO STORED RTE; AND WAS THEN CHKED BY BOTH MYSELF AND FO IN THE PLAN MODE. THE COMPLETE RTE CHKED OK. REMAINDER OF PUSHBACK START AND TAXI WAS NORMAL. DURING THIS TIME WE DID NOT GET AN 'INSUFFICIENT FUEL' MESSAGE. (THIS IS IMPORTANT). IN THE BRIEFING I HAD TOLD FO WE WOULD MAKE RAW DATA DEP USING VOR RADIALS TO ILLUSTRATE THAT IF PLT WERE TO LOSE THE MAP OR MAGENTA LINE HE COULD STILL FLY THE DEP. IN THIS REGARD WE WERE CLRED FOR A ROLLING TKOF (FO FLYING) AND THEN SWITCHED TO NAV DISPLAY (ND) TO VOR MODE AND TRACKED THE VOR RADIAL. WE WERE EVENTUALLY CLRED DIRECT TO MEVAS WAYPOINT. I MADE MEVAS THE ACTIVE WAYPOINT ON LEGS PAGE BUT GOT NO DASHED LINE AND NOTICED THAT MAGENTA LINE WAS FROM L SIDE OF ND (IN MAP MODE) TO MEVAS AND NOT FROM AIRPLANE SYMBOL TO MEVAS. I ASKED FOR AND RECEIVED A VECTOR FOR MEVAS. THEN I BEGAN CHKING TO SEE WHAT WAS WRONG. I CHKED LEGS PAGE AND RTE PAGE FIRST. I THEN CHKED OUR POS ON POS INIT PAGE AND FOUND THE PROBLEM. POS (ALL IRS'S AND FMC) WERE IN 'W' LONGITUDE AND SHOULD HAVE BEEN E. CALLED COMPANY ADDRESS AND DISCUSSED PROBLEM. DECIDED TO RETURN TO SIN. WE WERE VECTORED TO FINAL APCH COURSE. I MANUALLY TUNED THE ILS FREQ TO PRECLUDE ANY OTHER ERROR. AFTER PARKING AT SIN GATE I TURNED IRS'S OFF; THEN TO NAV AND ONCE AGAIN INSERTED THE GATE LAT/LONG FROM THE SIGN AT THE GATE. POS WAS ACCEPTED; (AND THIS IS ALSO IMPORTANT) AND WE DID NOT GET ANY 'ENTER IRS POS' MESSAGE. I PUT IN RTE AGAIN AND CHKED OK REMAINDER OF TRIP WAS NORMAL. IN CONCLUSION. NO ONE CAN BE 100 PERCENT POSITIVE; BUT I AM 95 PERCENT POSITIVE THAT THE GAE POS WAS CORRECT. I BELIEVE THIS PROBLEM WAS DUE TO EITHER A SOFTWARE PROBLEM OR SOME KIND OF MAP SHIFT. THE REASON IS THAT WE ONLY HAD TO REENTER IRS POS ONCE. WE DID NOT GET ANY INSUFFICIENT FUEL MESSAGE AND BACK AT THE SIN GATE (RETURN GATE) WE ONLY HAD TO INSERT THE GATE POS ONE TIME.