ALT UNDERSHOT AND CONFUSED FLT CREW OF A C560 ON FREQ WITH N90 ON A VECTORED APCH TO TEB; NJ.

Narrative

THE INCIDENT OCCURRED ON A FLT FROM E HAMPTON; NY (HTO) TO TETERBORO; NJ (TEB); AS WE WERE DSNDING FROM 4000 FT TO 3000 FT MSL WHILE BEING VECTORED TO THE ARPT AT TEB. WE HAD DEVELOPED SOME PLT FATIGUE INDUCED CONFUSION AS TO WHAT ALT WE WERE ASSIGNED DURING OUR DSCNT INTO TEB. AS WE WERE CONDUCTING OUR DSCNT AND APCH CHKLISTS; AND RECEIVING ATIS WE WERE GIVEN INSTRUCTION TO DSND FROM 4000 FT TO 3000 FT. NEITHER ONE OF US SET THE ALT PRE-SELECT; THINKING THAT THE OTHER ONE HAD DONE SO. A FEW MOMENTS LATER WE NOTICED THAT WE WERE PASSING APPROX 2800 FT AND WERE CONFUSED AS TO WHY THE AUTOPLT HAD NOT CAPTURED THE ALT. WE THEN LOOKED AT THE ALT PRE-SELECT AND NOTICED THAT IT WAS SHOWING 4000 FT. AT THAT MOMENT I BEGAN A CLB BACK TO 4000 FT (NOT SURE WHAT ALT TO BE AT). AS WE WERE LEVELING OFF AT 4000 FT ATC CALLED AND ASKED US WHAT ALT WE WERE AT. WE SAID 4000 FT. HE THEN SAID THAT WE SHOULD BE AT 3000 FT. WE IMMEDIATELY STARTED A DSCNT BACK DOWN TO 3000 FT; AND CONTINUED THE FLT WITHOUT ANY FURTHER INCIDENT. THIS DUTY DAY STARTED EARLY AM PUTTING US ON DUTY FOR JUST OVER 13 HRS AT THE TIME OF THE INCIDENT. OUR FIRST DAY ON DUTY STARTED EARLY AM ON AUG/MON/01; WITH 9 HRS 20 MINS ON DUTY THAT DAY. SECOND DAY STARTED AT EARLY AM AUG/TUE/01; WITH 14 HRS 30 MINS ON DUTY. THIRD DAY STARTED EARLY AM ALSO ON AUG/WED/01 WITH 14 HRS 20 MINS ON DUTY. AT THIS POINT IN THE WEEK WE WERE BOTH FEELING THE EFFECTS OF FATIGUE. BETTER REST AND DUTY REGS ARE THE ONLY WAY TO FIX THIS PROB.