B737 CREW DID NOT COMPLY WITH AN ATC ISSUED XING RESTR.

Narrative

WHILE FLYING SW ALONG J-174 APCHING ZIZZI INTXN AT FL260; WE WERE DIRECTED BY ZDC TO DSND AND CROSS THE ZIZZI INTXN AT FL180. WE ACKNOWLEDGED THE CLRNC; SET FL180 IN THE MCP AND I; AS THE PF; PROGRAMMED THE FMC TO CROSS ZIZZI INTXN AT FL180. SINCE WE WEREN'T YET AT THE COMPUTED TOP OF DSCNT POINT; I ELECTED TO CAPTURE THE PROGRAMMED DSCNT PROFILE AND THE ACFT STARTED AT 1000 FPM DSCNT. I CHKED THE PROGRAMMED DSCNT; VERIFIED VNAV AND LNAV CAPTURED ON THE MODE ANNUNCIATOR PANEL; AND ASSUMED THE FMC WOULD FLY THE ACFT TO REACH ZIZZI INTXN AT FL180. APPROX 3 MINS LATER; THE CAPT SAW THAT THE FMC DID NOT INCREASE RATE OF DSCNT AT THE TOP OF DSCNT POINT. WE RETARDED THE THROTTLES TO FLT IDLE AND DEPLOYED THE SPD BRAKE WHILE NOTIFYING ATC THAT WE MIGHT NOT MAKE ZIZZI AT FL180. NEITHER OF US KNOW WHY THE FMC DID NOT DSND PROPERLY AS IT WAS PROGRAMMED AND CONFIRMED BY BOTH PLTS. WE REACHED FL180 APPROX 2 NM SW OF ZIZZI WITHOUT TFC CONFLICT. I'M TRYING TO GET AN ANSWER FROM THE TRAINING DEPT AS TO WHY THE FMC DID NOT FOLLOW THE PROGRAMMED DSCNT.