B737-300 DEPARTED FROM CLRED RTE DUE TO FMC MALFUNCTION OR FMC OPERATOR ERROR.

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NAV; FML; LNAV/OFF COURSE. FLT WAS UNEVENTFUL UNTIL WE WERE CLRED DIRECT BTY VOR TRAGR 2 ARR LAS. AFTER CLRNC; WE WERE GIVEN 2 10-DEG TURNS; VECTORS FOR TFC. SHORTLY AFTER ATC CLRED US DIRECT FUZZY TRAGR2. ON THE FMC SCRATCH PAD DISPLAY; WE WERE ALERTED 'VERIFY POS.' WE CHKED LNAV. IT WAS IN USE. FMC WAS SHOWING DIRECT FUZZY; RNP/ACTUAL SHOWING 2.00/.26. PLACED BOTH MSI SWITCHES TO NAV. RE-ENTERED DIRECT FUZZY. ATC QUERIED; 'COMPANY NUMBER; ARE YOU DIRECT FUZZY?' WE CHKED AGAIN AND TOLD ATC AFFIRMATIVE. ATC SAID 'YOU ARE DRIFTING OFF COURSE.' WE CHKED FMC AGAIN. RE-ENTERED DIRECT FUZZY AND TOLD ATC. SEVERAL MINS LATER ATC SAID 'COMPANY NUMBER; YOU ARE NW OF FUZZY NOT PROCEEDING DIRECT; OFF COURSE BY 30 DEGS! TURN L 095 DEGS DIRECT FUZZY.' I CHKED FMC AND NO ALERT WAS SHOWN. BUT RNP/ACTUAL WAS SHOWING WE WERE OFF COURSE BY 9 MI R OF COURSE. I TOLD ATC WE WOULD NEED VECTORS TO FUZZY AND CHANGED OUR EQUIP TYPE TO ALPHA. WE PROCEEDED TO LAS. UNEVENTFUL APCH AND LNDG VIA FUZZY 2 ARR RWY 25R USING RAW DATA. INFORMED OUTBOUND CREW OF SIT; SUGGESTED FULL IRS ALIGNMENT. OUTBOUND CAPT AGREED AND SAID HE WOULD HANDLE ANY DISCREPANCIES. QUESTION: ON RNAV SID/STARS; HOW CAN WE VERIFY POS IF FMC IRS ARE ONLY SOURCE OF NAV? WOULD 2 FMC'S IN ACFT MAKE A DIFFERENCE?