B737-400 FLT CREW HAS A TRACK HDG DEV DURING THE HOLTZ7.HOLTZ RNAV DEP FROM LAX.

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THIS RPT IS ABOUT AN FMC POS DISCREPANCY VERSUS THAT OF LAX DEP CTL. WE WERE CLRED FOR TKOF ON RWY 25R; THEN TO FLY THE HOLTZ7 RNAV DEP WITH A TRM (THERMAL) TRANSITION. I CONFIRMED OUR FIRST FIX WITH THE TWR ON THE GND BEFORE TKOF; WHICH WAS HIIPR; THEN WAS SUBSEQUENTLY CLRED FOR TKOF. WHILE THE CAPT POSITIONED THE PLANE ON THE CTRLINE; I REACHED DOWN TO UPDATE OUR POS ON THE FMC SINCE OUR IRS'S HAD BEEN SITTING ON THE GND FOR APPROX 50 MINS AFTER A FULL ALIGNMENT. I TOOK OFF; THEN FOLLOWED THE RNAV PROC AS DEPICTED BY OUR FMC. AT ABOUT THE TIME WE WERE PASSING ADORE; ATC INQUIRED ABOUT WHAT PROC WE WERE FLYING; THEN ABOUT OUR POS; THEN ULTIMATELY OUR PRESENT HDG. IT BECAME APPARENT THAT SOMETHING WAS NOT RIGHT; SO I THEN TURNED ON AUTOPLT 'B' SO THAT I COULD BETTER ANALYZE THE SITUATION; THEN MY INITIAL FEELINGS WERE CONFIRMED WHEN AT POINT 'B' WE WERE BARELY NW OF SHAEF INTXN AND WERE LOOKING AT AN FMC GENERATED GUIDANCE TO TURN TO HDG 120 DEGS TO INTERCEPT THE LEG FROM SHAEF TO PEVEE (153 DEG COURSE). AT WHICH POINT WE TOLD THE CTLR OUR HDG AND THEN HE INSTRUCTED US TO FLY HDG 240 DEGS. AT THIS POINT IN THE CONFUSION; WE NOTICED THAT THE ANP ON OUR FMC WAS GREATER THAN 2.5 VERSUS AN RNP OF 1.0. FROM THIS POINT ON WE SUSPECTED AN IRS/FMC POS DEGRADATION AND IT WAS CONFIRMED AS OUR ANP CONTINUED TO BUILD UP TO 9.5 VERSUS AN RNP OF 2.0 DURING THE LENGTH OF THE TRIP. WE WENT TO RAW DATA AND THE CAPT MANUALLY TUNED IN TRM AND BLYTHE VOR'S AND NOTED AT THIS POINT IN CRUISE A 10 MI DIFFERENCE IN DME FROM THE NAVAIDS VERSUS WHAT OUR FMC TOLD US. ON TKOF BOTH RADIO BOXES WERE SET TO 'AUTO.' DURING TROUBLESHOOTING WE DOUBLECHKED THIS AND VERIFIED THAT THE RADIO UPDATING FEATURE WAS ENABLED OR 'ON.' FINALLY WHEN WITHIN 200 NM OF PHX ARPT; OUR ANP FINALLY FELL TO WITHIN RNP LIMITS AND OUR FMC-GENERATED POS SEEMED TO HAVE FINALLY CORRECTED ITSELF. SUPPLEMENTAL INFO FROM ACN 712635: AROUND THE SECOND FIX; THE FMS HAD US TURN MORE TO OUR L THAN WE HAD THOUGHT WE NEEDED TO. ABOUT THAT TIME ATC QUESTIONED US AS TO WHERE WE WERE HEADING. WHEN WE FOUND OUT WE WERE NOT GOING THE RIGHT DIRECTION; EVEN THOUGH THE FMS DIRECTED US TO KEEP TURNING L; WE RECEIVED A HDG FROM ATC AND STOPPED PROCEEDING ON THE DEP PROC. AT THAT TIME WE NOTICED ON THE FMS SCREEN THAT OUR ACTUAL POS WAS OFF BY JUST OVER 1 MI. LATER; ATC WOULD ALSO CONFIRM TO US WE WERE OFF COURSE BY 1 MI. THE FMS APPEARED TO BE NOT UPDATING ITS POS CORRECTLY. WE TOLD ATC WE WERE HAVING TROUBLE WITH OUR RNAV AND PROCEEDED THE REST OF THE FLT WITH RAW DATA FROM VOR'S. LATER; THE FMS WAS OFF BY OVER 7 MI COMPARED TO VOR/DME MILEAGE. WE ALSO RECEIVED IRS NAV ONLY MESSAGES EVEN THOUGH THE FMS APPEARED TO HAVE 2 GOOD VOR/DME'S WITHIN RANGE AND RECEIVING THEIR SIGNALS.