B737-500 FLC FAILS TO MAKE AN ALT XING. ADVISED ZSE CTLR AND RECEIVED SOME VERBAL ADMONITION. FLT SWITCHED TO SEA APCH; CTLR GAVE A NEW ALT ASSIGNMENT. RPTRS CITE A LATE START OF DSCNT BY THE FMS.

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THE AUTOPLT DID NOT START THE DSCNT TO CROSS TAWBN INTXN AT 16000 FT ON TIME OR AS PROGRAMMED. ATC INSTRUCTED US TO CROSS JAWBN AT 16000 FT. I DID NOT XCHK THE DSCNT COMPUTER IN MY HEAD TO INSURE ITS CALCULATIONS WERE CORRECT. ABOUT 15 MI FROM JAWBN; WE REALIZED THAT WE WERE NOT GOING TO MAKE JAWBN AT 16000 FT; AND TOLD ATC OF THIS SO SHE COULD VECTOR US OR HOLD US AS NECESSARY. SHE JUST SAID SOMETHING TO THE EFFECT OF 'DON'T TELL US YOU CAN MAKE THE ALT THEN FIND OUT YOU CAN'T -- CONTACT SEA APCH ON XXX.XX.' APCH THEN GAVE US A NEW ALT TO DSND TO. NOTHING MORE WAS SAID. AS I SEE IT; THE MAIN PROB WAS I RELIED TOO MUCH ON THE ONBOARD COMPUTER WITHOUT WORKING THROUGH THE CALCULATIONS IN MY HEAD. ALSO THE COMMENT AND TONE OF THE AIR TFC CTLR WAS NOT NECESSARY SINCE WE GAVE HER 15 MI NOTICE TO OUR SIT. SUPPLEMENTAL INFO FROM ACN 373210: AUTOPLT; THROUGH PMS; WAS SET FOR THIS ALT. DURING BRIEFING WE NOTICED THAT THE ACFT HAD STARTED DSCNT LATE AND WE WOULD NOT MAKE THE XING RESTR. ONCE AGAIN THIS SHOWS THAT PLT VIGILANCE OVER ALL ASPECTS OF ACFT SHOULD BE MAINTAINED AND THAT RELIANCE ON AUTOMATION CAN GET YOU IN TROUBLE IF YOU'RE NOT BACKING IT UP USING YOUR OWN EXPERIENCE.