B757 FLC ENCOUNTERS FMS/FMC MALFUNCTION WHEN ENTERING MULTIPLE APCH AMENDMENTS AS ATC CHANGES RWY SEQUENCE.

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WE WERE FILED TO CIVET AND THEN TO LOS ANGELES. WE WERE FLYING A B757 AND MY FO HAD JUST RECENTLY COMPLETED HIS INITIAL B757 TRAINING. HE HAD INDICATED THAT HE HAD ONLY BEEN TO LAX ONCE SINCE COMPLETING HIS B757 TRAINING. I WAS THE PLT FLYING AND I STARTED TO DISCUSS THE ARR PROC WHILE WE WERE OVER NEBRASKA. I SELECTED THE MITTS ONE ARR IN ROUTE ONE AND TIED IT UP TO THE ILS RWY 24R. I THEN SELECTED THE CIVET FOUR ARR IN ROUTE TWO AND TIED IT UP TO THE ILS RWY 25L. I THEN HAD A CONVERSATION WITH MY FO ABOUT HOW WE WOULD DO ROUTE CHANGES IF THAT BECAME NECESSARY. THE BIGGEST PROB WITH FLYING INTO LAX IS THE FREQ OF ARR AND RWY CHANGES. THIS BECOMES A BIT OF A PROB ON THE B757 BECAUSE IT IS A LITTLE SLOW TO MAKE ROUTE CHANGES. THE CTLR SAID TO LOOK UP KONZL INTXN ON THE PDZ 3 ARR AND TO PROCEED DIRECT ONCE WE FOUND IT. WE WERE THEN INSTRUCTED TO DSND TO 17000 FT. WE PROGRAMMED THE PDZ 3 ARR AND ALSO PROGRAMMED THE ARR TO INCLUDE RWY 25L PER INSTRUCTIONS PRINTED ON THE TOP OF THE ARR. WE WERE THEN ASSIGNED 16000 FT AND TOLD TO EXPECT RWY 24R. SHORTLY AFTER THIS; OUR ROUTE TOTALLY DISAPPEARED AND THE FMC'S STARTED TO RESYNCHRONIZE. WE DO HAVE THE CAPABILITY TO FLY MANUALLY BUT WHEN I SELECTED PDZ VOR; IT DID NOT SHOW UP ON MY HSI. I WAS ABLE TO NAV OFF THE RDMI WHICH GAVE ME BEARING AND DISTANCE. THIS IS NOT AN EASY TASK WHILE MAKING SPD CHANGES AND FLYING AN ARR WITH COURSE CHANGES AND PUBLISHED XING RESTRICTIONS. WE FINALLY GOT THE ARR PROGRAMMED AFTER TEJAY AND I WAS SLIGHTLY L OF COURSE AND CORRECTING. WE STILL DID NOT HAVE RWY 24R PLUS DENAY AND DUNZL PROGRAMMED SO I HAD THE FO MANUALLY TUNE THE LOC AND I FLEW THE APCH AND USED THE DME TO MAKE THE REQUIRED XING RESTRICTIONS AT DENAY AND DUNZL. WHEN WE REACHED 8000 FT; APCH SAID IF WE HAD RWY 24L IN SIGHT WE COULD HAVE A VISUAL. MY FO WAS SO BUSY TRYING TO CATCH UP AND LISTEN TO ME THAT HE NEVER EVEN HEARD THAT CALL FROM APCH. WE REPORTED RWY 24L IN SIGHT AND DID COMPLETE A VISUAL TO THAT RWY FOR LNDG. I FEEL THAT WE WOULD HAVE HAD A MUCH EASIER TIME ACCOMPLISHING THE ARR IF WE COULD SIMPLY BE ASSIGNED THE ARR AND THE RWY SOONER. THIS HAS LONG BEEN A 'HUGE' PROB AT LAX. I SUPPOSE IT WILL TAKE AN ACCIDENT BEFORE ANYTHING HAPPENS TO IMPROVE IT. I HAVE WRITTEN PREVIOUS REPORTS ABOUT THE NUMEROUS LAST MINUTE CHANGES WHILE ARRIVING AT LAX. THIS SEEMS TO BE A COMMON COMPLAINT WHEN PLTS START TO TALK ABOUT LAX. WE ALL KNOW THAT THERE WILL BE MANY CHANGES AND WE TRY TO PREPARE FOR IT. MOST ARPTS WE ARE ASSIGNED ONE ARR AND THEN PERHAPS WE GET ONE RWY CHANGE. I HAVE CALLED APCH CTL TO TALK ABOUT MY CONCERNS. I DO NOT SEE ANY IMPROVEMENTS AND NOW WITH THE PDZ 3; WE HAVE ONE MORE APCH TO BE SWITCHED TO WITH LITTLE NOTICE. THE FO AND I TALKED ABOUT HOW THE FMC LOCKED UP AND STARTED TO RESYNC. I THINK IT IS TIME TO ADDRESS THE NUMBER OF CHANGES BEING GIVEN FOR THE ARR INTO LAX. WE DO NOT ENCOUNTER THESE MULTIPLE AND LAST MINUTE CHANGES AT ANY OTHER ARPTS THAT WE FLY TO. THIS IS DEFINITELY A SAFETY PROB AND IT NEEDS TO BE CORRECTED.