B767-200
Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Situational Awareness; Training / Qualification; Human-Machine Interface; Distraction
Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Event / Encounter Loss Of Aircraft Control
Flight Crew Regained Aircraft Control
Human Factors; Aircraft
We taxied into the ZZZ ramp via [specified taxi entrance]. Taxi speed was slow due to tight turns on the ramp and equipment in the area. We lined up on our spot and were being marshaled in from there. Approximately the last 20 ft. of the taxi into the blocks was relatively slow trying to keep our momentum going while not letting the grabby brakes of the 767-200 bring us to a stop. The Marshaller began to raise wands from his waist as a signal to us that we were approaching our stopping point. The aircraft came up about 5' short because the brakes grabbed. The Captain added some power to get the airplane rolling again for the last few feet until the Marshaller crossed wands for us to stop. I saw the Captain bring the power back; felt the Captain push in the brake pedals and saw him set the parking brake. From there my attention was on watching the shutdown sequence. The Captain noticed we were creeping forward about 2 seconds later; applied manual braking and reset the parking brake which was now in the off position. With the parking brake set and verified; the shutdown sequence was completed along with the final checklists. I watched the parking brake being set; but could have missed that the action 'didn't take'. I will be more aware of the possibility of this while training Captains. I do not feel we coasted ahead more than a foot or so after initially setting the parking brake. There may have been some confusion with the Rampers on the ground if they saw the airplane initially stop and started moving in to chock the airplane while we were adding power to taxi in the last 5 ft.
Check Airman reported that the Captain set the parking brake at the gate; but the aircraft continued to move forward.