A DSNDING B737-300 EXPERIENCES A PROB WITH ITS AUTOPLT; ALLOWING THE ACFT TO EXCEED THE PLANNED RATE OF DSCNT AND FINALLY OVERSHOOTING ITS ASSIGNED LEVELOFF ALT WITHOUT ANY AURAL ALERT TO THE CREW WHILE W OF SMO; CA.

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EXPERIENCED PITCH CTL PROBS WITH AUTOPLT ENGAGED DURING DSCNT INTO LAX FROM THE N ON SADDE 6 ARR. SIMILAR PROBS HAD OCCURRED ON CLBOUT FROM SFO. AFTER PASSING SYMON INTXN AND CLRED BY ATC TO MAINTAIN 10000 FT; ACFT BEGAN DEVELOPING AN EXCESSIVE DSCNT RATE; AND RAPIDLY DEVIATING FROM PROGRAMMED DSCNT PATH. ATTEMPTED TO REGAIN FLT PATH/SPD CTL BY SELECTING ALTERNATE AUTOPLT PITCH CTL FUNCTIONS (VERT SPD AND LEVEL CHANGE). ACFT DSNDED UNNOTICED THROUGH CLRED ALT (10000 FT) PRIOR TO AUTOPLT DISENGAGEMENT. ATC SUBSEQUENTLY ISSUED A LOWER ALT. OBSERVATIONS: INCIDENT OCCURRED DURING A BUSY TIME AT A CRITICAL POINT ON THE ARR. ATTEMPTING TO TROUBLESHOOT AND CORRECT A COMPLEX SYS MALFUNCTION WHILE MONITORING OTHER AUTOFLT PARAMETERS; RESPONDING TO NUMEROUS RADIO INSTRUCTIONS AND COMPLYING WITH NAV REQUIREMENTS RESULTED IN EXCESSIVE DISTRACTIONS DURING A CRITICAL PHASE OF FLT; NEITHER PLT HEARD/OBSERVED ANY AURAL/VISUAL ALT WARNING (POSSIBLY A RELATED SYS MALFUNCTION). CONCLUSION: THIS PARTICULAR TYPE OF PITCH CTL PROB (STABILIZER); ALTHOUGH INTERMITTENT AND ASSOCIATED WITH AN OTHERWISE RELIABLE SYS; COULD HAVE RESULTED IN SERIOUS AND/OR COMPLICATED CONSEQUENCES. THE AUTOPLT SHOULD HAVE BEEN DISCONNECTED AND THE ACFT HAND-FLOWN AT THE FIRST INDICATION OF SYS TROUBLE. THE RELIANCE ON MODERN AUTOFLT SYS FOR OPERATIONAL EFFICIENCY AND WORKLOAD MGMNT CAN QUICKLY RESULT IN ADDITIONAL AND SOMETIMES EXCESSIVE WORKLOAD; ONCE THESE SYS FAIL OR MALFUNCTION. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE CAPT STATED THAT THE 'STABILIZER OUT OF TRIM' LIGHT HAD COME ON SEVERAL TIMES DURING THE FLT BUT WASN'T CERTAIN THAT THE LIGHT CAME ON DURING THE ALT OVERSHOOT. HE DID NOT WRITE UP THE PROB; A VERBAL RPT WAS GIVEN TO MAINT PERSONNEL AT LAX. HE DOES NOT KNOW WHAT THE FOLLOW UP MAINT WAS BUT WILL CHK IT OUT AND RPT LATER. THE MAIN STABILIZER TRIM WORKING OFF THE CTL WHEEL THUMB SWITCHES WORKED PROPERLY. RPTR AGREED WITH ANALYST ON THE POSSIBILITY OF A JACK SCREW PROB INTERFERING WITH THE OP OF THE SMALLER AUTOPLT TRIM MOTOR.