LTT CREW HAD TCASII RA IN PIT CLASS B AIRSPACE.

Narrative

TKOF FROM PIT WAS ON RWY 10C BEHIND A B757 AND DC9 IN THAT ORDER. WHILE CLBING THROUGH APPROX 2800 FT MSL; I RECEIVED A TCASII TA IMMEDIATELY FOLLOWED BY AN RA. FOR THAT PHASE OF FLT WE WERE MONITORING THE 2.5 NM SCALE AND FLYING THE RWY HDG AS ASSIGNED. THE RA INSTRUCTED ME TO 'DSND; DSND NOW' AT A VERT SPD OF AT LEAST 200 FPM DOWN. I WAS CLBING AT 1500-2000 FPM AND IMMEDIATELY LOWERED THE NOSE. THE NOSE OF THE ACFT WAS NO MORE THAN 5 DEGS LOWER IN PITCH WHEN THE RA DISAPPEARED. IN FACT; THE INTRUDER DISAPPEARED COMPLETELY FROM MY MFD. THE INTRUDER HAD APPEARED AT MY 5 O'CLOCK POS AND ALMOST ON TOP OF ME WITHOUT WARNING. NEITHER MYSELF NOR MY CAPT WERE ABLE TO CONFIRM VISUAL CONTACT AND REASONED THAT THE B757 AND DC9 WERE MUCH TOO FAST TO BE THE CULPRIT. AFTER MOMENTARILY FLYING AT A LEVEL PITCH ATTITUDE AND VISUALLY SCANNING THE SKY; WE RESUMED OUR CLB AND TURNED ON COURSE TO TRI. I SUSPECT THE WHOLE INCIDENT WAS DUE TO A TCASII SYS MALFUNCTION OR SOFTWARE GLITCH. UPON ARR AT TRI; I PERFORMED THE TCASII SELF-TEST FUNCTION. THE SYS TESTED PERFECTLY AND STILL LEAVES ME IN DOUBT TO A POINT ABOUT THE VALIDITY OF THE RA GIVEN THE SPONTANEOUS RA AND LACK OF TFC IN THE AREA.