ACR X TCASII RA HAD LTSS FROM CPR Y. EVASIVE ACTION TAKEN. SYS ERROR.

Narrative

ACR X TRACKING THE RWY 28L LOC INBOUND AT 4000 FT TO LAND AT PIT ARPT WHEN APCH GAVE US A NORTHERLY VECTOR FOR SPACING. THIS NORTHERLY VECTOR BROUGHT US TO WITHIN ABOUT 10 MI OF A STRONG TSTM. IN LIGHT RAIN; WE BEGAN TO RECEIVE MODERATE TURB WHICH WAS RAPIDLY GETTING ROUGHER. I REQUESTED A VECTOR OUT OF THIS AREA AND ATC GAVE US A L TURN TO A 210 DEG HDG AND A DSCNT TO 3000 FT. AS WE ROLLED OUT ON THE 210 DEG HDG AND LEVELED OFF; WE RECEIVED A TCASII TA. I IMMEDIATELY DECREASED THE TCASII RANGE TO 5 MI TO BETTER FIX THE TFC. THE TCASII THEN GAVE US A DSND RA. SHORTLY AFTER STARTING THE DSCNT THE FO PICKED UP THE TFC VISUALLY AT 12 O'CLOCK. THE TFC WAS A TWIN JET CORPORATE TYPE Y AND WAS IN A R HAND CLBING TURN. AS THE TFC PASSED OFF TO OUR L WE RECEIVED A 'CLR OF CONFLICT' AURAL ADVISORY AND RETURNED TO 3000 FT. I NOTIFIED ATC OF OUR TCASII RA AND THE TFC AND RECEIVED NO REPLY. I THINK THAT THIS INCIDENT WAS CAUSED BY AN OVERBURDENED CTLR MAKING A MISTAKE. A CONTRIBUTING FACTOR WAS THE TSTMS IN THE AREA ADDING TO THE CTLR'S WORKLOAD.