B757 FLC BEGAN A LATE DSCNT AFTER ATC QUERIED IF THEY WERE GOING TO MAKE THEIR XING RESTR. THE FMC WAS STILL SHOWING THAT THE ACFT HAD NOT YET REACHED THE TOP OF THE DSCNT POINT. THE FLC DSNDED THE ACFT TO THE XING ALT 2 MI PAST THE RESTR. ALT XING RESTR NOT MET.

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ZLC TOLD US TO CROSS 10 MI S OF DTA VOR AT 31000 FT. THAT CLRNC WAS LOADED INTO THE FMC AND VNAV WAS SELECTED ON THE MCP; AND THE FLT DIRECTOR AND AUTOPLT WERE ENGAGED. A SHORT TIME LATER; CTR CALLED AND ASKED IF WE WERE GOING TO MAKE THE RESTR; WE REPLIED THAT WE WERE AND STARTED OUR DSCNT FROM 37000 FT EVEN THOUGH THE COMPUTER SAID WE HAD NOT YET REACHED OUR TOP OF DSCNT POINT. WITH THE HELP OF THE SPD BRAKES WE REACHED 31000 FT 8 MI S OF DTA. I AM A NEW CAPT ON THE B757 AND WAS RECEIVING MY IOE FROM A LINE CHK AIRMAN WHO WAS IN COMMAND OF THIS FLT. WE HAD FLOWN OVER 8 1/2 HRS HARD TIME AND HAD BEEN ON DUTY OVER 13 1/2 HRS WHEN THIS EXCURSION TOOK PLACE. I DON'T KNOW IF WE PROGRAMMED THE FMC WRONG; OR IF WE HAD A COMPUTER GLITCH; OR IF WE WERE TOO BUSY TO NOTICE OUR POS (RAW DATA). I AM SURE FATIGUE PLAYED A ROLE IN THIS CASE. NO OTHER ACFT WERE IN OUR VICINITY. SUPPLEMENTAL INFO FROM ACN 326760: LOADED IN 13 MI S (FOR EXTRA CUSHION) AT FL310. TOP OF DSCNT FROM COMPUTER GAVE US APPROX 3 MI TO LOSE 6000 FT. HAD TO USE: SPD BRAKES; PWR OFF; AND MAX OPERATING MACH NUMBER SPDS. MISSED BY 1 MI -- HAD FAULTY EQUIP. CALLED ATC UPON ARR. FIRST TIME THIS HAS EVER HAPPENED.