ACR MLG INBOUND DESCENDED BELOW THE TCA.

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WHILE ON APCH TO RWY 14L AT IAH; EARLY ON THE MORNING OF 7/XX/88; I WAS BOTH PIC AND PF. WE DIPPED BELOW THE FLOOR OF THE IAH TCA BTWN 18 AND 15 DME ON THE 320 DEG R. THE FLOOR OF THE TCA IN THIS SECTOR FROM 20 DME TO 15 DME IS 4000' MSL; THEN IT DROPS TO 1800' MSL AT 15 DME. AS MY MEMORY SERVES ME; OUTSIDE OF THE TCA WE WERE CLRED TO DSND TO 4000' ON AN ASSIGNED HDG TO INTERCEPT THE RWY 14L LOC AND A VISUAL APCH. AT THE TIME THE IAH VORTAC WAS OTS. THE VORTAC IS USED TO IDENT ALL TCA BOUNDARIES BY DISTANCE AND RADIAL. THE LOC AND G/S BECAME ALIVE AND WE HAD THE RWY IN SIGHT FOR A VISUAL; SO I CONTINUED MY DSCNT BELOW 4000' WITH BOTH VISUAL REF AND G/S GUIDANCE. THE NAV RADIOS WERE BOTH TUNED TO THE LOC AND NO DME INFO WAS DISPLAYED IN THE COCKPIT. WHILE DSNDING AND SLOWING THROUGH 3700'; APCH CTL ADVISED THAT WE HAD DIPPED BELOW THE TCA FLOOR. AT THAT TIME PWR WAS ADDED; THE AUTOPLT DISCONNECTED AND A CLB BACK TO 4000' WAS INITIATED. OUR DSCNT CONTINUED TO A LOW OF 3500' BEFORE THE ACFT BEGAN CLBING. REACHING 4000' THE CTLR ADVISED US THAT WE WERE INSIDE THE 15 DME SECTOR AND CLRED TO 2000' FOR THE VISUAL. THE FLT CONCLUDED A FEW MINS LATER WITH AN UNEVENTFUL LNDG. AT NO TIME WAS EVASIVE ACTION REQUIRED TO AVOID ANY OTHER ACFT. I BELIEVE THE CONTRIBUTING FACTORS TO THE INCURSION ARE PRIMARILY 1) THE CREW WAS COMPLETING A DUTY PERIOD THAT BEGAN THE PREVIOUS EVENING AT XX30 PM MDT AND HAD BEEN UP ALL NIGHT FLYING IN EXCESS OF 7 HRS. SECONDARILY; 2) THE NONOPERATION OF THE IAH VORTAC PROVIDED NO AZIMUTH OR DME INFO FOR TCA BOUNDARY IDENT. I DON'T KNOW WHAT TO SUGGEST BEYOND NORMALLY INCREASED VIGILANCE DURING APCH OPS TO AVOID FURTHER RECURRENCE OF THIS TYPE OF ERROR; ESPECIALLY WHEN BOTH CREW MEMBERS ARE EXHAUSTED AND EXTREMELY FATIGUED FROM FLYING ALL NIGHT WITH ONLY 1 OR 2 HRS IN RESTFUL SLEEP IN THE PREVIOUS 24 HRS. IT IS DIFFICULT TO GET ANY RESTFUL SLEEP THE AFTERNOON BEFORE THE TRIP IN ORDER TO REMAIN FRESH AND ALERT ALL NIGHT.