B737-500 AUTOFLIGHT FUNCTIONS ABNORMAL DURING INITIAL PORTION OF FLT. ON APCH; AIRSPEED AND FLT DIRECTOR MALFUNCTIONED. RAW DATA APCH FLOWN TO LNDG.

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ACFT HAD PROBS WITH 'ALT ACQ' AND 'ALT HLD' NOT WORKING WHILE IN A AUTOPLT FOR FIRST HALF OF FLT. B AUTOPLT WORKED BETTER. ACFT WOULD NOT CAPTURE ALT AND WE FLEW THROUGH ASSIGNED ALT BY 200 FT ON FIRST LEVELOFF AS WE LEFT. SO WE TALKED TO DISPATCH AND MAINT AND DECIDED THAT THE ACFT SHOULD NOT DO ANY AUTOLANDS AND THAT IF WX WAS BELOW CAT I WE WOULD DIVERT. WE ALSO DECIDED TO MAINTAIN 250 KIAS FOR ENTIRE FLT IN CASE WE ENDED UP NEEDING TO HAND-FLY AND TO SLOW CLBS AND DSCNTS IN CASE OF ANOTHER MISSED ALT ACQ. AT 800 FT AGL ON FINAL; THE MCP WENT BLANK; THE AIRSPD BUG FROZE AT OUR 150 KTS SPD AND THE FD'S FROZE IN PLACE SO RAW DATA WAS DIFFICULT TO INTERPRET AND I USED THE SAI TO VERIFY. THE APCH WAS UGLY BUT SAFE AND WE BROKE OUT AT ABOUT 250 FT AND LANDED SAFELY. THE MAINT OF THE B737 FLEET IS CONCERNING ME. IN THE PAST 2 1/2 MONTHS I HAVE REFUSED 9 ACFT; I HAVE HAD AUTOPLT NOT WORK AND HAD TO RTB AND I'VE HAD ACFT THAT I'VE TOLD DISPATCH THAT I WOULD NOT TAKE; THEN SIGNED OFF AND WAITING FOR ME AT THE GATE WITH DEFERRED ITEMS I STATED I WOULDN'T FLY WITH. I'VE PASSED CREWS AND THEIR PAX MOVING FROM THEIR ACFT TO MY ACFT AS PLANNING SWAPS JETS AND DISPLACES THE ENTIRE COMPLEMENT OF PEOPLE ON BOARD 'SHOPPING' THE ACFT I'VE REFUSED TO ANOTHER CREW. I'VE TAKEN DELAYS FOR A MYRIAD OF MAINT ISSUES AND I JUST SUBMITTED A RPT FOR WHEN 2 ACFT BROKE AND THEN WE RAN OUT OF DUTY ON THE 3RD ACFT AND CANCELLED A FULL FLT. EVEN MY SECOND FLT TODAY AFTER OUR AUTOPLT ISSUE WAS DELAYED AND THEN WE HAD A REPEAT WRITE-UP APU FAULT ON START THAT THE INBOUND CREW HAD TO REATTEMPT MULTIPLE TIMES TO GET ON LINE; AS DID WE; AND IT ALREADY HAD AN INOP FUEL GAUGE. IF YOU PULL UP CANCELLATIONS; THERE ARE MULTIPLE MAINT CANCELLATIONS FOR THE B-300 FLT. I DON'T KNOW WHERE THE BREAKDOWN IN MAINT ON THE B-300 FLEET IS OCCURRING; BUT I CAN TELL YOU IT'S NOT GOING UNNOTICED.