FLC OF A BEECH; BE02; MODEL 1900 AIRLINER; OVERSHOT ALT ON DSCNT DUE TO ALT ALERTER PROB. THE FLC WAS CORRECTING BACK AS ATC INTERVENED TO REMIND THEM OF THEIR ASSIGNED ALT.

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AFTER DEPARTING PALM BEACH INTL ARPT; THE ALT ALERTER BEGAN SOUNDING SPORADICALLY IN ADDITION TO THE NORMAL 1000 FT TO GO ALERT. THIS HAPPENED CONTINUOUSLY THROUGHOUT THE FLT DURING CLB; ENRTE PHASE AND DSCNT. AS WE APCHED JAX I MADE THE '1000 FT TO GO' CALLOUT AS WE DSNDED THROUGH 8000 FT FOR OUR ASSIGNED ALT OF 7000 FT. I ALSO GAVE COM #1 TO MY FO WHO WAS THE PF AS I WENT TO COM #2 TO GET THE NEW ATIS. AS I CAME BACK TO COM #1; I NOTICED MY FO HAD SLOWED HIS RATE OF DSCNT AS HE APCHED 7000 FT SO I GAVE HIM THE CURRENT ATIS WHILE THE ALT ALERTER CONTINUED ITS ERRATIC CHIMING. ALSO; ABOUT THIS TIME; I WAS POINTING OUT JAX IN THE DISTANCE AS MY FO DID NOT YET SEE THE ARPT. I THEN REALIZED HE HAD DSNDED THROUGH 6800 FT AND NOTIFIED HIM OF THIS. HE STARTED HIS CLB BACK TO OUR ASSIGNED ALT AT 6700 FT. ATC AT THAT POINT REITERATED OUR ASSIGNED ALT AND POINTED OUT TFC AT OUR 10 O'CLOCK POS AND 1000 FT BELOW US WHICH WE CONFIRMED WE ALREADY HAD ON TCASII AND VISUALLY. NEEDLESS TO SAY THE ALT ALERTER WAS WRITTEN UP AS INOP AS SOON AS WE LANDED. OUR DSCNT 300 FT BELOW OUR ASSIGNED ALT WAS BASICALLY ATTRIBUTABLE TO THE FACT THAT AFTER 1 HR 10 MINS OF LISTENING TO THE ALT ALERTER CHIME INCESSANTLY; WE BECAME DISENGAGED FROM ITS USEFULNESS AS A WARNING TOOL. IN THE FUTURE; IF THIS HAPPENS WITH THE ALT ALERTER; I WILL DEFINITELY WAIT UNTIL LEVEL AT THE ASSIGNED ALT BEFORE GETTING ATIS; POINTING OUT ARPTS; ETC.