MD88 FLC FAILS TO CATCH THEIR FMS PROGRAM ERROR WHILE ENRTE ON A STAR ARR. ATC CATCHES THE OFF COURSE DEV AND SENDS THEM DIRECT TO THEIR NEXT POINT.

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FLT DEPARTED IND VIA THE DAWNN 1 DEP/BWG TRANSITION AND WAS FLT PLANNED TO ATL VIA THE ROME 8 ARR FROM BWG. SHORTLY AFTER PASSING BWG ZME REQUESTED OUR NEXT NAV FIX; WE RESPONDED RMG AND CTR STATED HE SHOWED OUR POS E OF COURSE. WE WERE NOW 20-40 NM S OF BWG HDG 160 DEGS TO RMG. FMS WAS OPERATIONAL AND BEING TRACKED BY AUTOPLT. AT THIS POINT WE DETERMINED THE TRANSITION OVER BWG HAD NOT TAKEN US VIA THE ROME 8 BWG TRANSITION BUT DIRECTLY TO RMG (HDG APPROX 15 DEGS E OF COURSE). AS WE WERE XREFING OUR POS; CTR STATED NO PROB AND JUST PROCEED DIRECT RMG. FLT CONTINUED WITHOUT INCIDENT. 2 POSSIBLE CAUSES WERE DISCUSSED BY FLC. 1) ON INITIAL FMS PROGRAMMING THE ARR TRANSITION WHICH SHARED A COMMON FIX WITH THE DEP TRANSITION ACCEPTED THE COMMON FIX OF BWG BUT WAS ENTERED IN SUCH A MANNER THE FMS TOOK THE ENTRY AS A REQUEST FOR DIRECT BWG-RMG AND NOT THE BWG TRANSITION TO RMG. 2) THE FMS WAS PROGRAMMED AS FLT PLANNED AND A SUBSEQUENT ENTRY CHANGED THE TRANSITION TO A DIRECT LEG. BOTH PLTS HAD REVIEWED THE DATA ENTRY ON PREFLT. RTE AND FLT PLAN WERE VERIFIED. CREW BELIEVES THEY WOULD HAVE NOTICED THE DIFFERENCE IN HEADING/RTE AS CHANGE FROM DEP CHART TO ARR CHART WAS MADE. THIS WAS IN PROCESS OF HAPPENING AFTER PASSING COMMON POINT OF BWG AND ABOUT THE TIME CTR CONTACTED THE FLT.