HDG DEV. ASSIGNED HDG WAS 060 DEGS; BUT PF; FO; THOUGHT THE HDG WAS 100 DEGS; ASKED THE CAPT; PNF; TO CONFIRM THE HDG; AND THE CAPT SET 060 DEGS ON THE HDG BUG. CTLR INTERVENED AND TOLD THEM THE ASSIGNED HDG WAS 100 DEGS AND BECAUSE OF THE HDG DEV; THEY CONFLICTED WITH ANOTHER ACFT. FLC ATTRIBUTES FATIGUE TO THE LACK OF VIGILANCE AND FLC COORD.

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WE DEPARTED MEMPHIS AT XX40 AM FOR A FLT TO BALTIMORE. I WAS THE PNF AND THE COPLT WAS FLYING. PASSING THROUGH 1000 FT; WE WERE GIVEN A CLRNC TO CLB TO 16000 FT AND TURN L TO A HDG. I SELECTED THE ALT AND VERIFIED IT PER COMPANY PROCS WITH THE COPLT. AS THE COPLT BEGAN THE L TURN; HE ASKED ME IF THE HDG ASSIGNED WAS 060 DEGS. I LOOKED AT THE HSI AND NOTICED THAT THE HDG BUG HAD NOT BEEN SET. I SET 060 DEGS BUT WAS NOT ABSOLUTELY SURE THAT IT WAS THE CORRECT HDG. IT WAS AN 'EXPECTED' HDG; HOWEVER; SO I ACCEPTED IT WITHOUT VERIFYING IT WITH ATC. DEP CTL THEN ASKED WHAT HDG WE WERE FLYING. WHEN WE TOLD THEM '060 DEGS;' THEY STATED THAT THE ASSIGNED HDG HAD BEEN 100 DEGS AND THAT WE NEEDED TO TURN L TO 360 DEGS NOW TO AVOID A LIGHT ACFT WHICH WE NOW SAW AT ABOUT 1 O'CLOCK AND AT OUR ALT; APPROX A MI AWAY. I BELIEVE THE PRIMARY CAUSE OF THIS INCIDENT WAS FATIGUE. IT WAS THE THIRD DAY OF ALL-NIGHT FLYING; AND I HADN'T BEEN SLEEPING WELL DURING THE DAY LAYOVERS. I WAS JUST COMING BACK FROM OVER 2 WKS OF TIME OFF. THE COPLT HAD RELAYED TO ME EARLIER THAT HE WAS ALSO TIRED. I CAN THINK OF NO OTHER REASON THAT I DIDN'T VERIFY THE HDG WITH ATC WHEN I WASN'T POSITIVE THAT IT WAS CORRECT. OTHER FACTORS INCLUDE THE FACT THAT 060 DEGS 'SEEMED RIGHT' TO ME BECAUSE OUR OUTBOUND AIRWAY WAS 064 DEGS AND WE NORMALLY WERE ISSUED HDG IN THAT DIRECTION SHORTLY AFTER TKOF. ANOTHER IMPORTANT FACTOR INVOLVES THE FLT DIRECTOR SYS. OUR B727 FLEET IS MIXED AND MANY ACFT HAVE HDG BUGS INDIVIDUALLY SELECTED BY EACH PLT. THIS ACFT HAPPENED TO BE ONE THAT HAS A COMMON HDG BUG SELECTOR AND I HAD NOTICED SOME CONFUSION IN THE PAST AS TO WHOSE RESPONSIBILITY IT WAS TO SET THE BUG. IN THE FUTURE; I WILL MAKE CERTAIN THAT THE PF ALWAYS SELECTS THE ASSIGNED HDG; AND THE PNF VERIFIES IT. I BELIEVE THIS INCIDENT WOULD NEVER HAVE HAPPENED HAD I BEEN BRIEFING AND USING THAT PROC. SUPPLEMENTAL INFO FROM ACN 341877: I NOTICED AN ACFT XING OUR FLT PATH FROM APPROX THE 1-2 O'CLOCK POS; FROM L TO R; ALMOST CO-ALT. I COULD SEE HIS STARBOARD (GREEN) POS LIGHT AND HIS TAIL LIGHT DISTINCTLY. SUPPLEMENTAL INFO FROM ACN 341215: THE CLRNC WAS ISSUED DURING A CRITICAL PHASE OF FLT (CLEANING UP THE ACFT AFTER TKOF). MY CONCENTRATION WAS DIRECTED MAINLY AT FLYING THE AIRPLANE. I HEARD THE CLRNC BUT I CAN HONESTLY SAY THE 100 DEG HDG CLRNC DID NOT REGISTER WITH ME. I MUST HAVE MISTAKENLY INTERPRETED THE ALT CLRNC OF 16000 FT TO A 060 DEG HDG. WHEN I ASKED THE CAPT TO CONFIRM THE 060 DEG HDG HE INDICATED YES AS I ROTATED THE HDG KNOB TO 060 DEGS. CREW COORD BTWN MYSELF AND THE CAPT WAS PROBABLY THE MAJOR FACTOR. THE FLT DIRECTOR ON THIS PARTICULAR ACFT IS ON THE CENTER FORWARD PANEL. ONE HDG CTL KNOB ON THE PANEL CONTROLLED BOTH THE CAPT'S AND FO'S HDG BUG. PRIOR TO TKOF WE SHOULD HAVE COORDINATED WHO WOULD CONTROL BOTH THE HDG CONTROL KNOB AND THE ALT CONTROL KNOB (IE; THE PNF CONTROLS BOTH OR THE PF CONTROLLING THE HDG KNOB). BECAUSE I WAS FLYING THE ACFT I THOUGHT THE CAPT WAS CONTROLLING BOTH KNOBS AND I'M SURE HE THOUGHT I HAD CONTROL OF THE HDG KNOB.