FOREIGN ACR X NON ADHERENCE TO ATC CLRNC WRONG HDG HAD LTSS FROM SMT Y. SYS ERROR. PLTDEV.

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I WAS WORKING THE ARR RADAR POS AND WAS BRIEFED THAT WX CONDITIONS WERE IMPROVING AND VISUAL APCHS COULD BE MADE FROM ALL DIRECTIONS. I WAS WORKING 5 IFR ACFT AND 2 VFR AND ACCEPTED 2 MORE IFR INBOUNDS. THE RWY IN USE WAS 11L. 2 OF THE IFR ACFT WERE: AN ATX LIGHT TWIN AND AN ACR X SCHEDULED ACR. BOTH ACFT WERE NWBOUND; HDG 300 DEGS; THE TWIN AT 7000 FT AND ACR X AT 8000 FT DIRECTLY ABOVE THE TWIN. I TURNED THE TWIN TO THE NE AND DSNDED IT TO 5000; THE MVA; AND ASKED IT TO RPT THE FIELD IN SIGHT. ANOTHER IFR TWIN WAS HDG S AND DSNDING FROM 7000 TO 6000; THROUGH THE ALT OF A VFR SMA ORBITING AT 6500 FT. TFC WAS ISSUED. THE TWIN WAS DSNDED TO 5000 AND TOLD TO RPT THE FIELD IN SIGHT. AN IFR SMT Y ARRIVING FROM THE NW WAS OBSERVED GOING THROUGH THE RWY 11L LOC AND INSTRUCTED TO TURN R AND INTERCEPT THE LOC AND 140 DEG HDG. MY PLAN WAS FOR THE IFR TWIN FROM THE S TO BE FIRST ON A VISUAL APCH; THE IFR TWIN FROM THE N TO BE SECOND; ON A VISUAL APCH; ACR X TO BE THIRD ON A VISUAL STRAIGHT-IN FOLLOWED BY SMT Y. I TURNED ACR X TO A HDG OF 060 DEGS AND DSNDED IT TO 6000. SMT Y WAS AT 6000 FT. THE ACR X MADE A LARGE WIDE TURN AND I REALIZED THAT IT WOULD NOT FIT INSIDE SMT Y. I INSTRUCTED ACR X TO STOP ITS TURN ON A HDG 360. ACR X RESPONDED WITH '360 CONFIRMED.' I CLRED THE FIRST TWIN FOR A VISUAL APCH AND LOOKED AT ACR X FLT PATH; THEN I ASKED ACR X TO VERIFY ITS HDG AND WAS TOLD 060 DEGS. I DSNDED SMT Y TO 5700 MVA AND CLBED ACR X TO 7000; ISSUED A TA AS TFC 12 O'CLOCK 1 MI. ACR X RPTED THE TFC IN SIGHT. SEPARATION WAS LOST; SAME SALT AND .5 MI. THE TAPE REPLAY OF ACR X'S XMISSION '360 CONFIRMED' SOUNDED AS A QUESTION RATHER THAN A STATEMENT AS I TOOK IT TO BE. IF THE ACR X PLT HAD SAID 'VERIFY;' OR 'CONFIRM THAT HDG' OR 'SAY AGAIN.' I WOULD HAVE RESPONDED AS IT WAS THE STATING OF THE HDG OF '360.'