B737 WITH A HISTORY OF MAP SHIFTS REQUIRES VECTOR FROM ATC WHEN FMS DOES NOT PROVIDE ACCURATE COURSE INTERCEPT.

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ACFT MAINT HISTORY REVEALED AN FMS MAP SHIFT 3 DAYS PRIOR TO OUR FLT. THE ACFT HAD FLOWN 5 LEGS THIS DAY PRIOR TO OUR FLT WITH NO PROB NOR ANY NOTED AFTER THE WRITE-UP. NEVERTHELESS; IN ADDITION TO NORMAL SOP MAP CONFIRMATION PRIOR TO USING FMS FOR NAV I MONITORED OUR COURSE INTERCEPT; ON THE BUCKEYE TWO DEP PHX; WITH RAW DATA DISPLAYED USING LNAV ENGAGED. EVERYTHING INDICATED THE FMS WAS OPERATING CORRECTLY. NO PROBS WERE NOTED ENRTE. ON THE L TURN TO INTERCEPT RWY 25L AT LAX FROM PDZ 277 DEG RADIAL; HOWEVER; SOCAL TOLD US TO CONTINUE OUR TURN TO 220 DEGS (249 DEGS IS THE COURSE) TO INTERCEPT THE LOC. I SWITCHED TO RAW DATA TO FIND THE LOC OFF SCALE. RAW DATA WAS NOT USED TO THIS POINT BECAUSE WE HAD NOT BEEN CLRED FOR THE APCH AND WE WERE MORE THAN 25 MI FROM THE FIELD WHICH REQUIRES BOTH RADIOS BE IN AUTO TO INSURE FMC UPDATE. THE SYS (FMS) WAS CHKED BY MAINT AT LAX WITH NO PROB FOUND. ON THE NEXT LEG ENRTE NAV LNAV WORKED FINE; YET WE DID NOTE A MAP SHIFT SHORTLY AFTER WE WENT FROM AUTO TO MANUAL FOR THE FINAL APCH INTO OAK (APPROX 1 MI). WHY THIS HAPPENED AT LAX WITH BOTH VOR SWITCHES IN AUTO CAN ONLY BE POSTULATED THAT BOTH RADIOS LOST VOR LOCK AND THE IRS DRIFTED. SUPPLEMENTAL INFO FROM ACN 451004: ON PARADISE 3 ARR INTO LAX; FMC MAP DISPLAY DRIFTED APPROX 5 NM. NOT RECOGNIZED UNTIL APCH CTL VECTORED US BACK TO FINAL. FMC DISPLAYED ON COURSE WHICH WAS INCORRECT. WE FLEW REMAINDER IN RAW DATA. MAY HAVE BEEN CAUSED BY A SOFTWARE BUG IN THE RECENTLY UPDATED DATABASE. FMC MAP ERRORS ARE SOMEWHAT INSIDIOUS.