A B737-500 FLT CREW CONTINUES THEIR CATII APCH ONTO RWY 14R AFTER THEIR EGPWS SIGNALS A 'PULL UP' AT 200 FT AGL AFTER IT HAD SIGNALED 'TERRAIN' AT 300 FT AGL WHEN THE CREW SUSPECTED A MAP SHIFT; AT ORD; IL.

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ORD WX WAS RPTED OVCST 2 MI; 1/4 SM VISIBILITY IN FOG AND DRIZZLE; RVR RWY 14R 1600 FT VERSUS 1800 FT. FLYING AN AUTO COUPLED CATII APCH TO AN AUTOLAND. INTERCEPTED LOC AT APPROX 16.5 DME OUTSIDE SEXXY INTXN AT 5000 FT MSL. INTERCEPTED GS AT SEXXY; ENGAGED 'B' AUTOPLT; AND PROCEEDED DOWN THE APCH AT 180 KIAS. FMC SUDDENLY DUMPED; BUT REBOOTED ABOUT 5 SECONDS LATER. FO (PNF) RESELECTED AUTO ON NAV #2 FOR FMC UPDATE; AND COURSE LINE MATCHED UP WITH THE LOC. AT CHESTER LOM; THE MARKER BEACON SOUNDED AND BLUE LIGHT FLASHED; BUT I NOTICED THAT WE WERE STILL ABOUT 2.5 MI PRIOR TO THE FIX ON THE MAP DISPLAY. I ANNOUNCED THAT THE MAP WAS STILL OFF QUITE A BIT. CONFIGURED ACFT FOR LNDG; FINAL DSCNT CHKLIST COMPLETED; AND WAS STABLE AT 40 DEGS FLAPS AT 1000 FT AGL. THEN; WHILE ON PROFILE PASSING APPROX 300 FT AGL; THE EGPWS SOUNDED WITH 'TERRAIN.' I CONFIRMED WITH THE LOC AND GS THAT WE WERE STILL ON PROFILE; AND AFTER A MOMENT REALIZED THAT THE EGPWS WARNING WAS DUE TO THE MAP SHIFT. AT 200 FT AGL; IT SOUNDED 'PULL UP.' AT ABOUT THE SAME TIME; THE APCH LIGHTS WERE IN VIEW; AND I ELECTED TO CONTINUE THE APCH TO AN UNEVENTFUL AUTOLAND. THE OUTCOME WAS THAT WE DID NOT EXECUTE A GAR WITH THE WARNING. THE LNDG WAS NORMAL AND THE APCH WAS NORMAL. WE WERE AT THE END OF A LONG DAY; AND I STILL HAD ONE MORE LEG TO GO; SO THERE WAS A SENSE OF URGENCY TO LAND THE ACFT. THE VISIBILITY WAS DROPPING ALSO; AND WITH A GAR THERE WAS A POSSIBILITY THAT THE VISIBILITY WOULD BE WORSE THE SECOND TIME AROUND. ALSO UNDER CONSIDERATION WAS THE FACT THAT THE FMC WAS NOT RELIABLE. I DEEMED THE SIT SAFE TO CONTINUE THE APCH. IT WAS CONFUSING FOR A MOMENT; AND PROCS CALLED FOR A GAR. IF WE WERE NOT RIGHT ON PROFILE AND STABLE; WITH THE NAVAIDS PROPERLY IDENTED AND PROPER CATII OPS WERE IN EFFECT ON THAT RWY; I WOULD HAVE GONE AROUND. SUPPLEMENTAL INFO FROM ACN 599017: I DECIDED TO GO BACK TO NAV #2 AUTO DUE TO A LARGE MAP SHIFT OF THE FMC (AROUND 2-3 MI L OF COURSE). THE FMC UPDATED ITS POS BACK TO THE LOC COURSE. I WENT BACK TO MANUAL WITH A NORMAL IDENT. CONTINUED APCH AND; AT AROUND 300 FT AGL; WE GOT A TERRAIN WARNING FROM EGPWS. ALL INDICATIONS FROM LOC AND GS WERE NORMAL ON ALL 3 ADI'S. WE FIGURED THIS WAS DUE TO THE MAP SHIFT AND CONTINUED. HUMAN FACTORS: LATE AT NIGHT; TIRED; BAD WX; FMC PROB. WE DISCUSSED THIS AFTER LNDG AND DECIDED WE SHOULD HAVE GONE AROUND PER THE FLT MANUAL.