C560 FLT CREW TAKING OFF ON RWY 17R ON TRISS RNAV SID FROM DFW MAKES INITIAL TURN TO THE RIGHT VICE LEFT TO INTERCEPT THE 153 DEG COURSE IN NAVYE.

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I WAS PIC ON A NON PAX FLT ROM DFW TO BNA. MY COPLT WAS THE PF IN THE L SEAT AND I WAS THE PNF IN THE RIGHT SEAT. WE WERE CLRED TO DEPART RWY 17R FROM DFW ON THE TRISS2 RNAV DEP. BOTH OF US VERIFIED THE PROGRAMMING OF OUR HONEYWELL NZ-2000 FMS. WE HAD RWY 17R AS THE DEP RWY AND THE TRISS2 DEP IN THE BOX. BEFORE SWITCHING TO TWR; GND CTL ASKED US TO VERIFY OUR FMS DEP RWY AND THE FIRST WAYPOINT. WE VERIFIED RWY 17R AND THAT OUR FIRST WAYPOINT WAS NAVYE. GND SAID THAT WAS CORRECT AND TOLD US TO CONTACT TWR. THE PF SAID THAT SHE WOULD SELECT NAV ON THE MODE SELECTOR AND THE FLT DIRECTOR WAS IN THE FMS OR LNAV MODE. AT ABOUT 1100 FT MSL THAT COMMAND BARS COMMANDED A RIGHT TURN AND THE PF FOLLOWED THE COMMAND BARS. AFTER ONLY GOING INTO ABOUT A 5 DEG BANK THE COMMAND BARS TURNED LEFT TO FOLLOW THE 153 DEG COURSE ON THE DEP. 30 MINUTES LATER WHILE ENRTE; CTR GAVE US A PHONE NUMBER FOR THE DFW TWR EAST AND TOLD US TO CALL. ON ARR AT BNA; I CALLED AND TALKED TO A CTLR AND SHE EXPLAINED THAT THE COMPUTER SHOWED OUR SHORT RIGHT TURN AFTER DEP. SHE ALSO STATED THAT THEY HAD HAD OTHER SIMILAR DEVS RECENTLY FROM OTHER ACFT ON THE SAME RWY AND SID. IN CONCLUSION; I KNOW WE HAD OUR FMS PROGRAMMED CORRECTLY AND I KNOW THAT THE FLT DIRECTOR BRIEFLY COMMANDED THE RIGHT TURN. ON RNAV ARRS AND DEPS A PLT RELIES ON THE FMS AND THE FLT DIRECTOR. I THINK THERE IS POSSIBLY A SOFTWARE PROBLEM WITH THE DEP AND TRANSITION. AT NO TIME WAS ANY ACFT SEPARATION COMPROMISED.CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: BOTH RPTRS CONFIRMED THE ACFT WAS LIGHT AND DID REACH THE REQUIRED ALT WHILE STILL OVER THE RWY PROPER. THEY DESCRIBED THE FLT DIRECTOR COMMANDS AS FIRST INDICATING A RIGHT TURN AND ABOUT THE TIME THEY INITIATED THE RESPONSE; THE COMMAND WAS REVERSED TO A LEFT TURN. BOTH FELT THIS WAS LIKELY THE RESULT OF THE FMS PURSUING THE 'COURSE' INBOUND TO TRISS WHICH WAS TO THE RIGHT OF THE ACFT WHEN THEY SATISFIED THE CONDITIONAL FIX ALT REQUIREMENT OF AT OR ABOVE 1080 FT MSL.