MLG FLC DSNDS BELOW ASSIGNED ALT DURING APCH.

Narrative

WE WERE FLYING THE LAST OF 6 SEGMENTS ON DAY 3 OF A 3 DAY SCHEDULE. THIS DAY STARTED WITH A EARLY AM WAKE UP CALL AND ENDED WITH A LNDG ON THE SIXTH LEG AT XX24; A 14 HR AND 59 MIN DUTY DAY. THERE HAD BEEN LONG DELAYS ON EARLIER SEGMENTS DUE TO WX. WE APCHED CHICAGO ON THE HEELS OF A COLD FRONT WITH ASSOCIATED IMC; TSTMS; RAIN CHANGING TO SNOW; WIND AND TURB. WE WERE CLRED TO DSND TO 9000 FT. AT ABOUT THE SAME TIME; MY ATTN WAS DIVERTED TO THE ACARS PANEL WHERE I WAS ENTERING DATA FOR AN ARR TIME ESTIMATE; A RPT 'HIGHLY DESIRED' BY THE COMPANY. WHILE ENTERING THE DATA; THE ALT ALERT SOUNDED; I LOOKED UP AND OBSERVED THAT WE WERE DSNDING THROUGH 8700 FT. I PULLED THE YOKE BACK AND RETURNED TO 9000 FT. NO APPARENT CONFLICT OCCURRED. A FEW MINS LATER; WE WERE CLRED TO 7000 FT. THE FO DSNDED AT 1000 FPM THROUGH 7000 FT; BUT I CAUGHT IT AT 6800 FT AND RETURNED TO 7000 FT. HE MADE A TEXT BOOK LNDG IN A 90 DEG; 26 KT XWIND. PRIOR TO TKOF ON THIS FINAL SEGMENT; I MENTIONED TO MY FO 'WE'RE BOTH TIRED; LET'S WATCH EACH OTHER!' THIS IS A CLASSIC EXAMPLE OF FATIGUE INDUCED ERROR BROUGHT ON BY A 15 HR DUTY DAY FLOWN IN ADVERSE WX ON A 2 MAN COCKPIT IN NIGHT IMC. IT OCCURRED DURING A HIGH WORKLOAD PORTION OF THE FLT WHEN OTHER DUTIES DIVERTED MY ATTN AWAY FROM MONITORING THE FO AS HE FLEW THE APCH. ERRORS WILL OCCUR. I HAVE LISTED SEVERAL CONTRIBUTING FACTORS LEADING TO THIS ONE.