CAPT OF A BRITISH JETSTREAM BA41 OVERSHOT ASSIGNED ALT ON CLB.

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ON DEP CLB OUT OF STL ENRTE TO SUX; ISSUED CLB TO MAINTAIN 12000 FT. AT 1000 FT BELOW ASSIGNED ALT I ADVISED THE CAPT (PF) OF '1000 FT TO GO' AND RECEIVED CONFIRMATION REPLY FROM THE CAPT. AT 100 FT BELOW ALT I SIGNALED (SINGLE 'LITTLE FINGER') 100 FT TO GO AND THOUGHT I OBSERVED CONFIRMATION FROM THE CAPT. ANTICIPATING NORMAL AUTOPLT CAPTURE; I (PNF) BECAME BUSY WITH CHART ORGANIZATION. AT 12300 FT WE RECEIVED AN ALT ALERT HORN; OBSERVED THE DEV AND THE CAPT BEGAN THE ALT CORRECTION. AT APPROX 12200 FT ATC RPTED THE AREA ALTIMETER SETTING AND ADVISED US TO MAINTAIN 12000 FT. THE FLT THEN PROCEEDED UNEVENTFULLY. FACTORS AFFECTING THE DEV: THIS WAS THE LAST ROUND TRIP FLT OF A 4 DAY TRIP. WE WERE ALL WELL RESTED; HOWEVER; THE CAPT HAD BEEN PREPARING FOR A MAJOR AIRLINE INTERVIEW THE ENTIRE TRIP AND WAS EXPECTING THE INTERVIEW THE FOLLOWING DAY. I HAD OBSERVED SOME INCREASING PREOCCUPATION AND DISTR IN HIM ALL DAY. I FEEL THAT THIS WAS THE PRIMARY CAUSE OF THE DEV. ALSO; THIS WAS A CAPT THAT HAD TRANSITIONED TO THE ARPT RECENTLY FROM AN ACFT WITH ANALOG INSTRUMENTATION. WHETHER THERE WAS A CONFUSION ON HIS PART IN REGARD TO PROGRAMMING THE EFIS DISPLAYS OR CONFIRMING AUTOPLT ALT CAPTURE; I CANNOT POSITIVELY SAY. MY RELAXED VIGILANCE AFTER I HAD OBSERVED DISTR IN THE PF RESULTED IN THE BREAKDOWN IN 2-PLT XCHKING PROCS. HAD I NOT ASSUMED A 'NO BRAINER' ACTIVITY AND REMAINED ATTENTIVE I COULD HAVE INTERJECTED BEFORE THE HORN. PRIMARY LESSON -- PLT VIGILANCE.