B737-800
Flight Crew Air Transport Pilot (ATP)
Fatigue; Distraction
Deviation / Discrepancy - Procedural Published Material / Policy; Flight Deck / Cabin / Aircraft Event Other / Unknown; Ground Event / Encounter Other / Unknown
Flight Crew Overcame Equipment Problem
Human Factors; Procedure
This was the second flight of the day for the crew. We were delayed due to winds and a runway change pushing our flying time past 8 hours for the day. After a challenging arrival and approach we taxied to Gate X which is a short taxi and requires engine cool down prior to shutdown. I hacked the clock clearing the runway. As we stopped at the gate I thought I had set the parking brake but was also concerned about the cool down period and after a short discussion; mentioned to FO then we had a few more seconds to go as I referenced the clock. I did not visually confirm the parking brake light was on at this time. After a few more seconds I turned off the fasten belts sign and checked the APU was on the buses. When the cool down time expired I called for the engines to be shut down and the parking checklist.Before we could start the checklist the ground crew flashed a light at the FO to get his attention and he recognized we were moving backwards. He called it out and we both pushed the brake pedals to stop the plane. I looked down to see the parking brake light was not on and the parking brake was not properly set. The ground crew hooked up a tug and towed us back to position. The passengers deplaned normally and the flight attendants reported no injuries. The ground crew came to the cockpit and confirmed no injuries to ground personnel or damage to the plane. The longer than normal flight day combined with challenging approach procedures with difficult weather conditions added a level of fatigue that probably contributed to this incident.Additionally I allowed the non-standard shutdown procedure to interfere with the normal parking flow and did not prioritize confirming that I had properly completed checklist items prior to worrying about the cool down clock. Staying focused and prioritizing what is most important especially as you get tired. Slow down enough to confirm each step and follow the checklist first; then take care of non-standard things. Don't allow distractions to break the flow or habit patterns. For this particular airport; anytime you land on runway X there will be a cool down period so it could be briefed ahead of time to alleviate any discussion or confusion at the gate. For me personally; perhaps verbalizing the first items of the checklist as they are completed will keep the focus where it needs to be.  If a first officer gets used to hearing me mention each item out loud then on one leg doesn't hear an item that may be enough to catch an error.
[Report narrative contained no additional information.]
B737-800 flight crew reported neglecting to set the parking brake after arriving at the gate due to fatigue and distraction.