Date: 201902
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Aircraft: Commercial Fixed Wing
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Descent
ATC / advisory: TRACON ZZZ
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Not Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument
Human factors: Communication Breakdown; Confusion; Situational Awareness; Fatigue; Human-Machine Interface
Anomaly: Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Detector: Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Contributing factors: Company Policy; Human Factors; Staffing
Primary problem: Company Policy

Narrative: I was pilot not flying on a leg to ZZZ in the early morning; running roughly 3 hours and 30 minutes hours on the second half of a red-eye turn; second night in a row of red-eye flying on our third calendar day of duty. I had never been this tired in an airplane before. We were returning late on the second half of a red-eye turn. We had accepted a two-hour extension to our duty in order to complete the flight. When informed that we were going to soon be out of duty time; it was under some organizational pressure (to paraphrase: 'we need the aircraft back in ZZZ as we've got a lot of aircraft out of service due to maintenance') Like most pilots; I try to be a good soldier and suck it up when needed; and at the time I accepted the two-hour extension; I did feel like I could do it safely and reasonably rested. I was flat out wrong. About 45 minutes away from our destination; with the sun coming up into our eyes; the stress of that night's events and being on the back side of the clock hit me like a ton of bricks. I was very tired and feeling sleepy. I could not shake it despite the highly caffeinated beverage I had been sipping for the last hour. We were being vectored on the downwind for the ILS 35L into ZZZ; my recollection is that we were given instructions to turn left to heading 150; descend to 8;000 feet. I read back the instructions; then saw the Pilot Flying's hand go up to the altitude selector and set 8000 feet; adjusted the vertical speed to start a reasonable descent; then move over to the HDG knob and turn it to what I thought was 150. I then looked out of the windscreens scanning for traffic; trying to keep my eyes open. A few seconds later ATC queried our heading; after a confused moment I replied 090 (we were unexpectedly in a left turn swinging through about 090) and then she issued instructions for a 100 heading which she said would vector us through the course and she'd turn us to intercept from the other side. The pilot flying and I had a brief conversation regarding what heading we each thought we were given and; with no resolution; pressed on to maintain vigilance and SA to complete the vector and get onto the ILS approach course. I don't know if the pilot flying misunderstood the heading assignment and I missed him setting it incorrectly; or if the controller said a heading that I incorrectly read back. Ultimately; the pilot flying and I were not on the same page with respect to what heading we each thought we had been assigned. If he was as tired as I was; and I believe he might have been; it is understandable. I'm still not sure if we made an error or not but based on the tone of the controller's voice; we may have turned to a heading she did not assign or expect. From my vantage point it appeared no separation was lost nor did we receive any TCAS warnings. There was no further commentary from the controller that there had been an issue but she was also busy and may not have had time to discuss an error on our part or issue a phone number to us. The fatigue I was experiencing had unquestionably slowed my anticipation; awareness and sharpness I normally fly with. It was debilitating; and even sitting here writing this report; I have trouble recalling important details of the flight in question. I will never fly tired again. Our company organization is stretched thin and our safety culture is a joke. The reason we were so late that night resulting in our need to extend was a comedy of errors related to our company priding itself in some sick way in not canceling flights when other airlines do. At least that is how it appears to me. We flew into a Class C airspace mountainous airport in the middle of the night during a winter storm and naturally ran into problems with the gate; with the ramp; with Maintenance and with the deice/anti-icing process. All these events are described in a separate report that would identify me so I won't go into detail. But needless to say; it was circus that ultimately ended withthe question: will you extend your duty to complete this operation? I agreed to and; at that moment; I believed I could do it safely and reasonably rested. However I was dead wrong at predicting how I would feel later with the sun coming up in my eyes after being awake and stressed all night. I will never do this again. Crews should never be given the option to extend on red-eyes; even though it is legal it is clearly not safe. If an airline wants to run these half-baked red-eye operations in order to keep their aircraft utilization up; then it should be with tighter restrictions on crew duty as I've described; require an augmented crew or limit a crew to one leg per night. Humans are not nocturnal.




Synopsis: Air carrier Captain reported a heading deviation due to significant fatigue.