A PA60 PLT OVERSHOT ASSIGNED ALT DURING CLB OUT WHILE TROUBLESHOOTING A PROB WITH THE PRESSURIZATION. THE CTLR HAD LIMITED THE ACFT AT AN ALT FOR TFC THAT WAS LESS THAN 5 NM AWAY.

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THIS OCCURRED ON A FLT FROM PSP TO LAS IN CLR; HIGH VISIBILITY WX A FEW MI SW OF TNP VOR. WE HAD DEPARTED PSP IN A PA60 WITH 2 CREW -- I WAS THE PLT. WE FILED FOR AND WERE CLRED TO CLB TO CRUISING ALT OF 11000 FT. WE WERE GOING THROUGH ABOUT 8000 FT CLBING ABOUT 1000 FPM WHEN I NOTICED THAT THE CABIN WAS NOT PRESSURIZING. THEN I OBSERVED THE RED WARNING LIGHT AND THOUGHT WE HAD A MALFUNCTION. THE COPLT AND I TEMPORARILY DIRECTED OUR EFFORTS TO REMEDYING THAT SIT. PRIOR TO THIS OCCURRENCE; SOME MINS BEFORE; CTR ADVISED US TO STOP OUR CLB AT 10000 FT BECAUSE OF TFC. I ACKNOWLEDGED AND SET THE ALT ALERT FOR 10000 FT. WHILE WORKING ON THE CABIN PRESSURIZATION PROB; THE PLANE CLBED THROUGH 10000 FT AND KEPT GOING UP. SUDDENLY I GLANCED AT THE ALTIMETER AND NOTICED WE WERE AT 11000 FT WHEREUPON I STOPPED THE CLB AND STARTED A DSCNT -- WE WERE ON AUTOPLT. SIMULTANEOUSLY CTR ASKED OUR ALT AND I REPLIED 11000 FT AND ACKNOWLEDGED WE WERE CLRED TO 10000 FT AND WERE STARTING BACK DOWN. BY THIS TIME WE WERE AT 10500 FT AND DSNDING AND I ASKED 'WHICH ALT SHOULD I HOLD -- 10 OR 11?' I WAS TOLD TO STANDBY; AND AFTER A MIN OR TWO; HEARING NOTHING MORE AND REALIZING MY LAST CLRED ALT WAS 10000 FT; I CONTINUED THE DSCNT TO THAT ALT. IT'S IMPORTANT TO KNOW THAT THE ALT ALERT DEVICE DID NOT 'BEEP' WHEN WE WENT THROUGH 10000 FT ON THE WAY UP (MORE ABOUT THIS LATER). FINALLY ANOTHER CTLR CAME ON AND ADVISED US TO MAINTAIN 10000 FT AND IN A MIN OR SO ASKED ME TO CONTACT BY PHONE WHEN WE GOT TO LAS THE LOS ANGELES AREA MGR; WHICH I PROMPTLY DID UPON ARR. I EXPLAINED THE SIT; AND WAS TOLD NOT TO WORRY. BUT WAS ALSO TOLD THERE WAS ANOTHER ACFT WITHIN 5 MI; WHICH THE COPLT HAD OBSERVED; AND THAT WAS THE PROB. THE REST OF THE FLT PROCEEDED WITHOUT FURTHER INCIDENT. ABOUT THE ALT ALERT DEVICE: I HAD THE DEVICE REMOVED AND TESTED AT AN AVIONICS SHOP ABOUT 2 MONTHS PREVIOUSLY AND REINSTALLED. IT HAD BEEN USED EXTENSIVELY IN MARCH ON A TRIP AND I NOTICED THAT IT SEEMED TO PERFORM ERRATICALLY WHICH WAS THE ORIGINAL REASON I HAD IT TESTED. ON THE BALANCE OF THE TRIP IN QUESTION; IT FAILED TO BEEP SEVERAL TIMES; BUT OTHERWISE PERFORMED IN A NORMAL FASHION. IT OBVIOUSLY NEEDS REPAIR EVEN THOUGH THE SHOP THAT TESTED IT SAID THAT IT TESTED OK.