FLT CREW OF B757-200 EXPERIENCES FAILURE OF AUTOFLT SYS TO MEET XING RESTR AT SLIDR ON ARR TO PHX.

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AT FL360 WE WERE CLRED TO CROSS SLIDR AT FL310. I ENTERED THAT RESTR INTO THE FMC LEGS PAGE AND RESET THE ALT ALERTER TO FL310. BOTH OF THESE WERE CONFIRMED BY THE FO. I ALSO RECHKED THE TARGET DSCNT SPD AND ENTERED THE EXPECTED XING RESTR FOR HOMRR. WE WERE STILL SEVERAL MI AWAY FROM SLIDR AT THIS TIME. AS WE APCHED THE TOP OF DSCNT POINT; I MONITORED THE AUTOPLT AS IT STARTED THE DSCNT TO FL310. EVERYTHING LOOKED FINE; AS IT WAS STABLE IN THE DSCNT WITH IDLE THRUST AND ON VNAV PROFILE; SO I TURNED MY ATTN TO GETTING OUT MY APCH CHARTS. AFTER ABOUT 20 SECONDS; I LOOKED BACK AT THE INSTS AND NOTICED THE AIRPLANE WAS HOLDING ALMOST LEVEL AT FL345; AIRSPD WAS 25 KTS BELOW TARGET AND THE VNAV PATH INDICATOR WAS SHOWING THAT WE WERE BELOW THE PATH; YET WE WERE ALMOST OVER THE SLIDR WAYPOINT. I POINTED OUT THIS DISCREPANCY TO MY FO AND ASKED IF HE HAD ANY IDEA WHY THE AUTOPLT WAS LEVELING. I ALSO QUICKLY CHKED THAT THE FLT DIRECTORS WERE ON; VNAV AND LNAV WERE ENGAGED AND THE AUTOPLT WAS ENGAGED. THE FMC SHOWED THAT THE SLIDR RESTR OF FL310 WAS STILL IN THE DSCNT PAGE AND THE ALT ALERTER ON THE AUTOPLT PANEL WAS PROPERLY SET TO FL310. WITHOUT TAKING MORE TIME TO FIGURE IT ALL OUT; I DISCONNECTED THE AUTOPLT AND AUTOTHROTTLE AND MADE A RAPID DSCNT TO FL310. I ESTIMATE THAT WE CROSSED SLIDR ABOUT FL338 AND WERE LEVEL AT FL310 A FEW MI PAST SLIDR. AFTER LEVELING AT FL310; WE RECHKED EVERYTHING AND COULD NOT FIND ANY REASON FOR THE AUTOPLT TO BEHAVE THE WAY IT DID. THE AIRPLANE PROBABLY BEGAN TO GRADUALLY LEVEL OFF AROUND FL352; ABOUT THE TIME I TURNED MY ATTN AWAY. BECAUSE THE LEVELOFF WAS GRADUAL AND THE AUTOTHROTTLES DID NOT INCREASE; IT WAS NOT NOTICEABLE TO US WHILE WE WERE DOING OTHER THINGS. THE SPD HAD DECREASED BECAUSE THE AUTOTHROTTLES HAD NOT INCREASED WITH THE LEVELOFF; BUT THEY WERE JUST STARTING TO MOVE FORWARD WHEN I DISCONNECTED THEM. IT WAS ALSO STRANGE THAT THE VNAV PATH SHOULD SHOW US BELOW PATH WHEN WE WERE ACTUALLY HIGH. SOMEHOW THE VNAV PATH HAD CHANGED WITHOUT ANY INPUT FROM US. IT WAS AS THOUGH IT DECIDED TO IGNORE THE SLIDR RESTR; BUT THAT RESTR WAS STILL IN THE FMC. AS WE WERE LEVELING AT FL310; ATC ASKED US IF WE HAD BEEN GIVEN SLIDR AT FL310. WE SAID THAT WE HAD RECEIVED THAT RESTR; BUT THAT WE HAD EXPERIENCED AUTOMATION PROBS. THE CTLR SAID IT WAS NO PROB. WE DID NOT GET ANY TCASII AND THERE WAS NO INDICATION THAT ANY OTHER ACFT WAS IN ANY WAY AFFECTED BY OUR ACTIONS. EVEN WHEN WE REVIEWED THE SIT ON THE GND; WE STILL COULD NOT FIGURE OUT WHY THE ACFT STARTED TO DSND JUST FINE BUT THEN ACTED THE WAY IT DID. THIS ACFT HAS THE NEW PEGASUS COMPUTER NAV SYS AND IT MIGHT HAVE SOMETHING TO DO WITH THAT. THIS WAS ONLY MY SECOND FLT WITH THIS NEW SYS. IN THE FUTURE; I WILL TAKE MORE CARE TO MONITOR THE ACFT -- NOT ONLY AT THE START OF DSCNT AND NEAR THE RESTR; BUT ALSO THROUGHOUT THE DSCNT. I THINK I WILL ALSO ENTER A WAYPOINT A FEW MI AHEAD OF THE ACTUAL XING RESTR POINTS TO ALLOW FOR CORRECTION IF THIS PROB SHOWS UP AGAIN. WHEN IT LEVELED OFF THAT CLOSE TO THE WAYPOINT; IT ELIMINATED OUR ABILITY TO CORRECT IN TIME TO MAKE THE RESTR. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR HAD NO FURTHER EXPLANATION FOR THE ANOMALY. HE STATED THE RESTR WAS PROGRAMMED WELL IN ADVANCE OF THE RESULTING TOP OF DSCNT POINT AND THE DSCNT STARTED IN APPROPRIATE SYNCHRONIZATION WITH THE VNAV PATH VISUAL INDICATOR. THE AUTO FLT SYS PERFORMED CORRECTLY AFTER IT WAS RE-ENGAGED AND HE FELT A WRITE-UP WITHOUT A BETTER UNDERSTANDING OF WHAT HAPPENED OR A SUBSEQUENT RECURRENCE WAS OF LIMITED VALUE. HE CLARIFIED THAT HIS SUGGESTION THE PEGASUS SOFTWARE MAY BE AT FAULT WAS MERELY IN RECOGNITION OF THE FACT THAT THE ACFT DIFFERED IN THAT RESPECT FROM THE B757'S IN WHICH HE HAD FLOWN PREVIOUSLY. THERE WAS NO SPECIFIC ANOMALY THAT POINTED DIRECTLY TO THE SOFTWARE.