FLC OF ACR WDB ACFT DEVIATED FROM ASSIGNED STAR CLRNC BY NOT STARTING DSCNT AT THE DESIGNATED FIX AND SUBSEQUENTLY EXCEEDING DSCNT SPD DUE TO AN FMC PROB.

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ACFT CRUISING AT FL410 DIRECT COLLIER COUNTY VORTAC FOR THE COLLIER 3 ARR TO MIAMI INTL. ZMA BEGAN OUR DSCNT ROUGHLY 50 MI W OF COLLIER DOWN TO FL310; THEN FL240; AND EVENTUALLY TO FL210. AS THE DSCNT BEGAN WE LOST OUR FMC. COCKPIT NAV INFO (LNAV) WAS UNRELIABLE. THE FO WENT TO RAW DATA TO NAV DIRECT TO CCE; STILL DSNDING AS REQUESTED BY CTR. THE FMC CAME BACK UP AND THE DATA LOOKED GOOD. TOLD TO EXPECT SNOKE AT 11000 FT; 250 KTS THE FMC WAS THEN PROGRAMMED TO FLY A VERT NAV PATH (VNAV) TO MAKE THE XING. WE WERE ALSO TOLD TO DSND AT 300 KTS WHICH WAS ALSO ENTERED IN THE FMC. THEN THE FMC 'DUMPED' AGAIN. THE FO WENT TO RAW DATA ONCE AGAIN. WHEN THE FMC CAME BACK UP (2-3 MINS) THE RTE HAD BEEN DEACTIVATED. THE CAPT REACTIVATED THE RTE AND THE COLLIER 3 ARR. LNAV AND VNAV WERE REENGAGED FOR COMPUTER OP. WE WERE NOW CLRED TO CROSS SNOKE AT 11000 FT; 250 KTS. THE ACFT WAS NOW ROUGHLY AT FL215. THE HSI PICTORIAL DISPLAY INDICATED TOP-OF-DSCNT IN ROUGHLY 15 MI. CTR INQUIRED WHY WE WERE DELAYING OUR DSCNT. A QUICK REEXAMINATION OF THE HSI SCREEN SHOWED SNOKE 15 MI AWAY. IDLE PWR AND SPD BRAKES WERE IMMEDIATELY APPLIED. THE ACFT MADE THE ALT RESTRICTION; ALBEIT A LITTLE FAST. WE WERE SUBSEQUENTLY DIRECTED TO INTERCEPT THE 9R LOC FOR APCH AND AN UNEVENTFUL LNDG AT MIAMI. LATER; WE REALIZED WHAT HAD HAPPENED. WHEN THE FMC 'DUMPED' THE SECOND TIME IT ALSO DUMPED THE XING RESTRICTIONS AS WELL AS THE RTE. OUR TOP- OF-DSCNT GUIDANCE FOR THE BEST ECONOMICAL PROFILE WAS NOW BASED ON THE ELEVATION OF THE TOUCHDOWN ZONE FOR RWY 9R NOT SNOKE 250 KTS; 11000 FT. SWITCHING BTWN RAW NAV DATA AND COMPUTER DATA DURING A DSCNT WAS NOT WISE. WE WERE LUCKY. OUR EXPERIENCE IN THE ACFT ENABLED US TO ET DOWN TO 11000 FT. A LESS EXPERIENCED CREW WOULD CERTAINLY HAVE HAD TROUBLE. FOR THE REMAINDER OF OUR TRIP SEQUENCE THE CAPT AND FO BRIEFED THAT IF ANOTHER FMC MALFUNCTION WERE TO OCCUR; THE PF WOULD SWITCH TO RAW DATA; AND STAY ON RAW DATA UNTIL THE PNF REPROGRAMS THE FMC AND VERIFIES THAT ALL ALT/SPD ENTRIES HAVE BEEN REENTERED AND CONFIRMED.