CL65 FLC INTERCEPTS ILS GS 900 FT BELOW PUBLISHED HT.

Narrative

THIS WAS A CONTINUOUS DUTY OVERNIGHT ASSIGNMENT; THE THIRD IN A ROW. THE PREVIOUS NIGHT; I HAD NO SLEEP DUE TO NOISE IN THE HOTEL. I WAS UNABLE TO GET ANY SLEEP THE FOLLOWING DAY EITHER. I ESTIMATE I HAD BEEN WITHOUT SLEEP FOR ABOUT 42 HRS. DUE TO THE SHORT FLT (DTW-CAK) MY FO SUGGESTED; AND I AGREED; TO BRIEF THE ILS RWY 23 APCH TO CAK BEFORE DEPARTING DTW. THE APCH CALLS FOR INTERCEPTING THE GS AT OR ABOVE 3200 FT MSL. ONCE ACQUIRING THE ARPT VISUALLY; WE WERE CLRED FOR A VISUAL APCH TO RWY 23. I MANEUVERED THE ACFT TO INTERCEPT THE LOC OUTSIDE THE FAF AND SET THE GS INTERCEPT ALT TO 2300 FT INSTEAD OF 3200 FT AS I SHOULD HAVE. I THEN DSNDED TO 2300 FT SINCE THE GS INDICATION SEEMED TO AGREE WE WERE SLIGHTLY 'HIGH.' ONCE ESTABLISHED ON THE LOC AT 2300 FT; THE GS INDICATION WAS CORRECTLY INDICATING 'LOW.' AT THIS POINT. I NOTICED THE VASI LIGHTS ALSO INDICATING BELOW GS AND THE FO NOTICED OUR ALT AND SAID WE SHOULD BE AT 3200 FT; NOT 2300 FT. WE CONTINUED UNTIL GS INTERCEPT AND COMPLETED THE APCH. I BELIEVE I TRANSPOSED THE ALT DIGITS DUE TO FATIGUE. ALSO; I WILL NO LONGER BRIEF AN APCH BEFORE TKOF. I WILL BRIEF IT SHORTLY BEFORE THE APCH SO THAT IT IS MORE EASILY RECALLED DURING THE APCH; EVEN IF CLRED FOR A VISUAL APCH.