Date: 202011
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: Takeoff / Launch; Taxi
ATC / advisory: Tower ZZZ
Reporter organization: Air Carrier
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Human factors: Situational Awareness; Distraction; Communication Breakdown; Confusion
Second reporter function: Pilot Not Flying; First Officer
Anomaly: Deviation / Discrepancy - Procedural Clearance; Ground Incursion Runway
Detector: Person Air Traffic Control
When detected: In-flight; Taxi
Result: Air Traffic Control Issued Advisory / Alert; Flight Crew Returned To Clearance
Contributing factors: Procedure; Human Factors; Environment - Non Weather Related
Primary problem: Human Factors

Narrative: The FO told me upon our initial meeting at the gate that she had been off for the past 7 months; that she flew for the first time 'yesterday' (a ZZZ1 turn); and that this was her second day back after 7 months off. While pre-flighting and briefing on the flight deck; at Gate X; Runway XXL auto-populated for departure when the FO loaded the FMC; as it usually does for a destination airport to the west (ZZZ2 in this case). I told the FO that; during COVID; we often get east side departure runways (ie; [Runway XXR in this case) when we depart from east side gates. So; I told her; she could change it to XXR now; if she wanted to; or we could leave YYL in the box; wait for our runway assignment; and I would taxi very slowly while she loaded the box if we got the east side. We left YYL in the box. We departed the Ramp from Spot X and Ground assigned XXR; which was a very short taxi from Spot X. I made the Takeoff PA; and; as I said I would; I taxied very slowly while the FO loaded the box with the new data; read the Legs page aloud (from the new runway) as I followed along on the ZZZZZ 3 Dept on my iPad; and briefed the Takeoff Data. As we were in the middle of the pad; northbound on taxiway; still fairly far from the departure end of the runway; Tower asked if we were up. The FO said we were. Tower then asked if we would be ready at the end. The FO and I briefly checked with each other and acknowledged that; yes; we would be ready at the end. In my recollection; I then heard 'RNAV to ZZZZZ1; Cleared for Takeoff; XXR.' I chimed the flight attendants and turned on my two Landing Light switches; which is something I purposefully only do once Cleared for Takeoff. The FO finished the checklist with plenty of time (everything was properly set up before she began it); and prior to crossing the hold short line onto XXR; she said something like; 'I'm pretty sure I heard Cleared for Takeoff; but do you want me to verify with them?' I looked at my Landing Lights; saw that I had moved them to the ON position; which I 'only do' once cleared for Takeoff; and thought I specifically heard 'RNAV to ZZZZZ1; Cleared for Takeoff.' So; I said to her; 'No. I don't need you to verify. I heard Cleared for Takeoff; too. ... But please ... verify if you want to! Do you want to?' She said something like; 'No; I think we're good. We both heard the same thing.' I said something like; 'I specifically remember hearing 'RNAV to ZZZZZ1;' which they never say until they clear us for Takeoff. We're okay.'While on the Takeoff Roll and prior to V1; Tower called; 'Aircraft X?' We did not answer. They called again once we were airborne and told us to fly Runway Heading. I pretty much knew at that point that we either were NOT cleared for Takeoff ... OR we WERE cleared for Takeoff and the Tower Controller forgot that he cleared us. Shortly after that call; the Tower Controller said something like; 'Aircraft X; Possible Pilot Deviation; Advise when ready to copy.' And of course; at this point; I had a very sinking feeling. We copied down the number for Tower. Once clean and on our way; I sincerely apologized to the Tower and told him that; in my recollection; he asked us; while we were still fairly far back in the pad; if we would be ready at the end; we said we would; and then he cleared us 'RNAV to ZZZZZ1; Cleared for Takeoff.' He apologized as well; for any confusion; and we went on our way to ZZZ1. Naturally; I had a sinking feeling that perhaps I was at fault ... but I also thought my memory of it was clear ... and I felt just a little hopeful by the fact that the FO and I both independently thought we were cleared for Takeoff. Once at the gate at destination and off of the aircraft; I called the number for ZZZ East Tower. I spoke with a very professional; very kind gentlemen who said he had listened to the tape 3 times and that we were only cleared to Line Up and Wait. I felt so very disappointed with myself at that point.I see several causal factors in thisevent. The number one Causal Factor in my mind was that I should have immediately said to the FO; when she asked me if I wanted her to clarify while crossing the Hold Short Line; 'Yes! Please clarify. Thank you!' If there's ANY doubt in ANYBODY'S mind; then clarify! There were other Causal Factors as well. Two: the FO was on her second day back from a 7 month leave. She was a good stick and has good general knowledge; but she was very understandably 'slower in hearing' and 'slower in doing' than she otherwise would have been had she been more current. Reduced currency of either party in a two-person cockpit; particularly on the first leg of a trip; often results in a more cumbersome; somewhat disjointed crew coordination experience. And that is how I experienced the beginning of our first leg together -- less coordinated than usual; but understandably so. I say this with no disregard or criticism of the FO; who does very good work; and is clearly a sharp; experienced; very good pilot. Three: this was our first leg together of our first day together. We were just getting used to working together as we pre-flighted and taxied out. Four: For many months now; with fewer operating flights; we are often assigned east side runways when departing from east side gates. This is something that is fairly recent in ZZZ; presumably because of reduced operations during COVID and because of runway construction on the west side. However; particularly when departing from Spots X; Y; or Z; and no other aircraft in sight (as was the case this morning); a runway XXR departure often results in a crunch period while the FO re-loads the FMC and re-verifies the departure LEGS page while I cross-check the chart. Though I did not personally feel rushed; and though the FO said she did not feel rushed; a last-minute runway change is just one more thing to do on a short taxi. Five: I long ago established in my mind that I would not turn on the Landing Lights until Cleared for Takeoff. But today; I clearly; for some reason; turned them on anyway when we were apparently NOT cleared for takeoff ... and then I fairly comfortably relied on the fact that I turned them on as further evidence that we WERE cleared for takeoff. Six: It was fairly unusual in ZZZ to be cleared for Takeoff OR Line Up and Wait; from such a distance from the runway. Today; we were still fine-tuning our crew coordination and were working in a more disjointed way than usual. I was taxiing very slowly; and while time didn't consciously seem to be a factor to me (the FO was done with all duties well before we crossed the Hold Short line and entered the runway); I was aware that the FO was briefing me; checking the box; and starting the checklist; at the time that Tower called us ... AND that we accepted an important clearance in the midst of what was actually a very busy time. It is my guess that the distractions of our work at hand; at that time; interfered with the way we each interpreted the clearance. And we later learned that we interpreted it incorrectly. I have no other explanation for the misunderstanding and am still surprised that both the FO and I jointly misunderstood. I have several suggestions ... mostly for myself ... as to how I will prevent this type of event from occurring in the future. Starting from the beginning; in point of time ... ONE: Over the next few days I am going to give strong consideration to the idea of directing the FO to change the auto-populated runway in the FMC RTE Page AT THE GATE; to match the runway that I'm expecting for departure; or at least to match the runway that is closest to the departure gate. It will be less disruptive to change a runway during taxi out to a runway that is FARTHER AWAY from us; than it is to change a runway during taxi out to a runway that is much closer to us. TWO: As the FO loaded the runway change; briefed the takeoff data; ran the checklist; and answered the Tower's call and clearance; despite the fact that there was plenty of distance and time between us and the runway; and despite the fact that I knew I was in control of how fast I taxied (two factors I considered while all this was going on); it would have been so much wiser to tell the Tower controller to Standby rather than taking on One More Thing while on the taxi out. Perhaps if we were not so busy during that particular time when Tower called; we may have heard the proper clearance exactly as it was issued! THREE: It would have been wise to simply say to the FO; 'Don't worry about time at all. We will plan on stopping short of the runway and taking a close look at all of this together.' Particularly under the circumstances (the FO's lack of currency); that would have been the smart-and-considerate-Captain thing to do. I regret not making that choice. It would have removed all pressure. I will be particularly vigilant with less-current and/or new FO's; but I will also try to be mindful of this option in all circumstances. I fear that I may have rushed the FO. FOUR: It was extraordinarily foolish of me not to take the FO up on her suggestion that we clarify the clearance! She asked me if I wanted her to. I should have simply said 'YES! PLEASE! And THANK YOU!' For this; I am most regretful. The answer; ALWAYS; when there is ANY doubt from ANYBODY is to say; YES; Please Clarify! FIVE: And on that note; I will no longer let my own habits lull me into any false sense of security. I have the habit of turning on the Landing Lights ONLY AFTER I have been Cleared for Takeoff. I turned on the Landing Lights while still taxiing north on taxiway; and then I allowed my own habit to lull me into a sense of security that I HAD BEEN cleared. But that was foolishness. I apparently misheard the clearance while distracted by several other obligations. The fact that I turned the lights on; or participated in any other habit of my own; does not necessarily mean I heard or interpreted anything correctly. I will be more vigilant in the future.


Second narrative: Our flight was cleared to taxi to [Runway] XXR in ZZZ. We were taxiing on a parallel toward the end of XXR. There were no airplanes in line and about 200 yards from the end of runway Tower asked if we were ready at the end. I acknowledged we were. We both believed he then cleared us for takeoff. As we turned the corner toward the runway I questioned myself and asked the Captain if we were indeed cleared for takeoff. The Captain said yes; but also added I could verify if I wanted too. I felt almost sure we were cleared for takeoff; so I felt comfortable not asking tower. On takeoff roll we were told of the deviation.This was my second day of work coming back from a 7 month leave. Although it was a short taxi I felt comfortable and prepared for the takeoff. Just prior to the 'clearance' I was busy; but felt we had caught up with everything when he asked if we were going to be ready at the end. I do not know how both the Captain and myself felt certain we were cleared for takeoff. It was quite shocking to find out we were wrong. Even though I questioned myself; I really thought we were cleared to go.My biggest takeaway is whenever I question myself on a clearance just ask ATC to clarify. That would have been the best option. In the future if I doubt myself I will do this first; if possible. Now that I have had this experience; I will most certainly never accept a -- 'TO clearance' -- so far from the end of a runway without clarifying with Tower before TO.


Synopsis: Air Carrier flight crew reported thinking they were cleared for takeoff; but were only cleared to line up and wait.