ACR MLG GOT A FALSE TCASII WARNING ON CLB OUT FROM ORD REPEATED ON DSCNT INTO BOS.

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AT 2200 FT MSL AFTER TKOF FROM ORD WE GOT A TCASII RA 'DSND; DSND NOW' WITH RA TFC SHOWING LEVEL WITH US BUT NOT IN SIGHT VISUALLY. SINCE WE WERE ONLY 1500 FT AGL AND IN A 25-30 DEG L BANK; CLBING OUT OVER A DENSELY POPULATED AREA; I ELECTED TO ATTEMPT TO LEVEL THE ACFT AND CONTINUE THE BANKED TURN BEYOND OUR ASSIGNED HDG OF 140 DEGS TO ABOUT 105 DEGS; INSTEAD OF DSNDING TO AVOID THE TFC. THE TRANSPONDER WAS IN TA/RA WITH MY ASSOCIATED SWITCHES IN 'NORMAL' AND 'ABSOLUTE' ON THE TRANSPONDER HEAD; AND I BELIEVE THE FO'S SWITCHES WERE IN THE SAME POS AS MINE. AFTER THE WARNING STOPPED AND NO TFC WAS SPOTTED VISUALLY; THE CLB WAS ONCE AGAIN STARTED TO 5000 FT MSL ALONG WITH AN IMMEDIATE RETURN TO OUR ASSIGNED HDG OF 140 DEGS. PASSING THROUGH 3500 FT MSL WE RECEIVED A TA WITH THE WORDS; 'TFC; TFC.' ORD RADAR; UPON BEING QUESTIONED; SAID THEY SHOWED NO TFC IN OUR IMMEDIATE VICINITY; AND WE SAW NO TFC VISUALLY AND CONTACTED ARTCC WITH NO FURTHER PROBLEMS UNTIL OUR DSCNT INTO BOSTON- LOGAN ARPT. AT 4200 FT MSL DSNDING TO 2000 FT MSL IN CONTACT WITH BOS APCH; WE RECEIVED A TA TO 'CLB; CLB NOW'; WHICH ONCE AGAIN PROVED TO BE A FALSE WARNING WITH NO TFC RPTED BY APCH AND NONE SEEN VISUALLY. THE TCASII TESTED NORMALLY AT THE GATE PRIOR TO DEP; AND WAS IN TA/RA ON TKOF BEFORE AND AFTER GEAR AND FLAPS WERE UP. I BELIEVE WITH THIS EXPERIENCE (MY FIRST WITH TCASII ON THE LINE) OF HAVING SEVERAL FALSE WARNINGS AT LOW ALTS AND IN TKOF AND LNDG REGIMES (POTENTIALLY CRITICAL PERIODS OF FLT) WE NEED TO REEXAMINE EXACTLY WHEN TO HAVE IT ON OR OFF AND TO ASCERTAIN IF IN FACT THIS TYPE OF WARNING CAN EVER BE TRULY RELIABLE. WHERE DO WE GO FROM HERE WITHOUT FURTHER TESTING ON BOTH THE SOFTWARE AND HARDWARE OF THESE UNITS. CAN I REALLY TRUST TCASII FOR RELIABLE TFC AVOIDANCE INPUTS? FURTHER TESTING IS NEEDED TO 'DE-BUG' THIS SYS BEFORE REGULAR LINE USE ON COMMERCIAL ACRS.