ACR RECEIVES DSCNT; SPD RESTRICTION AND HDG CHANGE AT SAME TIME. HDG WOULD TAKE THEM DIRECTLY INTO LINE OF TSTMS. CAPT ASSUMES HDG TO BE 100 DEG MORE THAN ASSIGNED. CTLR CATCHES ERROR AS DOES TCASII.

Narrative

I WAS THE CAPT ON THE FLT AND THE PF. THE FO (PNF) WAS ASSISTING AND 'WORKING' THE RADIOS. WHILE APCHING DAS FROM THE N; THE FO AND I OBSERVED VISUALLY AND ON THE WX RADAR A DEVELOPING LINE OF TSTMS RUNNING IN A LINE SW TO NE IN THE VICINITY OF DAS. THE FLT RECEIVED SEVERAL DIFFERENT HDGS AND ALT ASSIGNMENTS AS THE CLR MERGED US WITH THE OTHER INBOUND FLTS TO IAH. WE PASSED OVER DAS AT 10000 FT AND AT APPROX 5 DME WERE GIVEN INSTRUCTIONS BY APCH CTL TO DSND TO 7000 FT; SLOW TO 210 KTS AND TURN TO A HDG OF 220 DEG. THE FO READ BACK THE CLRNC AS IT WAS GIVEN; RESET THE ALT ON THE FLT DIRECTOR TO 7000 FT AND THEN DIRECTED HIS ATTN BACK TO THE WX RADAR BECAUSE THE 220 DEG HDG WOULD TAKE US TOWARD THE LINE OF TSTMS. I BEGAN TO COMPLY WITH THE APCH CTLS' INSTRUCTIONS EXCEPT THAT I THOUGHT THE CTLR HAD SAID 320 DEG. I DIDN'T QUESTION THE HDG BECAUSE IT WAS TAKING US AWAY FROM THE INTENSE STORMS S OF US AND WITH THE FO'S ATTN DIRECTED AT THE RADAR HE MISSED THAT I WAS TURNING TO THE WRONG HDG. THE PLANE HAD JUST ROLLED OUT ON THE 320 DEG WHEN APCH CTL ASKED WHAT OUR HDG WAS. WE TOLD HIM AND HE ADVISED US THAT THERE WAS DEP TFC N OF US. AT THE SAME INSTANT OUR TCASII ISSUED A TA. THE FO AND I IMMEDIATELY CHKED THE TCASII SCREEN AND LOCATED THE TFC AND THE FO GOT A VISUAL POS ON THE OTHER AIRPLANE. THE CTLR GAVE THE OTHER ACFT A NE HDG AND THEN INSTRUCTED ME TO TURN TO 230 DEG AND EXPEDITE A DSCNT TO 4000 FT AND I IMMEDIATELY COMPLIED. OUR TCASII NEVER GAVE US A RA AND THE FO ESTIMATED THAT OUR CLOSEST PROX TO THE OTHER ACFT WAS ABOUT 1000 FT BELOW AND 2 MI LATERAL SEPARATION. I LEVELED THE ACFT AT 4000 FT AND FROM THAT POINT ON TO LNDG THE FLT WAS UNEVENTFUL.