ACR DEVIATED FROM FINAL APCH FIX AND COURSE ON IAP AS A RESULT OF AN FMS MAP SHIFT. FLC CORRECTED ERROR.

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AIRLINE FLT # XXXX SDQ (MDSD) TO JFK. WHILE BEING VECTORED FOR VOR RWY 13L APCH AT JFK ARPT APPROX 10 MI S OF CRI VOR THE CTLR GAVE US A HDG OF 010 DEGS FOR THE APCH. I NOTICED THE HDG WAS DIRECT TO THE VOR. WHEN STATED TO APCH AS SUCH HE CLRED US DIRECT CRI MAINTAIN 1500 FT CLRED FOR THE APCH. BOTH PLTS HAD 112.3; 043 DEG INBOUND COURSE. WHEN CLRED DIRECT IT WAS ENTERED INTO THE FMC. AT APPROX CRI VOR ON THE FMC WE EXPERIENCED A 2.7 MI MAP SHIFT WHICH WAS VERIFIED ON THE RMI AS W OF COURSE 2.7 MI. WE SOON PICKED UP VISUAL CUES WITH THE GND AND IMMEDIATELY INITIATED A 085 DEG HDG AFTER PICKING UP THE ARPT. SHORTLY THEREAFTER THE CTLR CONCURRED WITH THE PHRASE SAYING 'YOU'RE TOO FAR W TURN HDG 085 DEGS.' WE CALLED THE ARPT IN SIGHT AND PROCEEDED VISUALLY. I HAVE APPROX 4000 HRS IN TYPE ON THIS ACFT. WHILE I'VE HEARD OF MAP SHIFTS ON THIS FMS MAP I'VE NEVER SEEN ONE. ALSO I'VE BEEN BASED IN NEW YORK AND I HAVE DONE THIS APCH HUNDREDS OF TIMES. WE HAD THE RAW DATA AS A BACK UP BUT NEVER REALIZED PASSAGE OF INBOUND RADIAL 043 DEGS. COULD HAVE BEEN CONE OF CONFUSION? MAYBE. AT ANY RATE I CANNOT SAY WHY THE SUDDEN MAP SHIFT OF 2.7 MI. CLOSER MONITORING OF THE RMI MAY HAVE ALERTED US TO THE FACT OF A RADIAL SHIFT HAD TAKEN PLACE.