Date: 201407
Location: ZZZ.Airport, US
Aircraft: B737-500
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Flight phase: Landing
ATC / advisory: Tower ZZZ
Aircraft component: Powerplant Fuel Valve
Component problem: Improperly Operated
Reporter organization: Air Carrier
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Human-Machine Interface; Distraction; Training / Qualification; Situational Awareness; Communication Breakdown
Second reporter function: Pilot Not Flying; First Officer
Anomaly: ATC Issue All Types; Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Event / Encounter Other / Unknown
Detector: Person Ground Personnel
When detected: Aircraft In Service At Gate
Contributing factors: Aircraft; Human Factors; Procedure
Primary problem: Human Factors

Narrative: Upon main gear touchdown and thrust reverser deployment; Tower asked us which gate we were going to. The First Officer hesitated a moment as the radio call during that phase of flight is highly unusual and distracting. It surprised both of us. He responded 'Gate X'; Tower said to use Taxiway N and said something about whether to contact Ground or not. When we cleared at N; I asked the First Officer if we were supposed to contact Ground or stay with Tower. This is where I normally start the clock to monitor engine cooling time; this also serves as a double check that the engine is still running. We were told to contact Ground. I was watching the construction area to our right as the First Officer contacted Ground and followed the circuitous route to Gate; a pretty short taxi. I entered the safety zone thinking I had shut down the right engine; stopped the aircraft; shut down the Number 1 Engine; and got the chocks in signal. No Ramp Personnel entered the safety zone; and they contacted me to let me know that the Number 2 Engine was still running. I secured the engine and completed the Parking Checklist. I must visually verify the position of each start lever and assume nothing. The system worked in that the ramp personnel did not enter the safety zone with the engine running except to install the chocks. The Marshaller does not have the optimum position to see if the Number 2 Engine is running. If ATC wants us to use a certain taxiway; tell us on final; not as soon as the tires touch the runway! This distraction added to a dynamic phase of flight; a short taxi and making sure we were clear of a construction area. We got out of our flow and this distraction helped set in motion a chain of events that could have ended quite differently. Our Ramp personnel; by following proper procedures; stopped the chain of errors that posed a threat. They are to be commended for this. Verifying the status of a given aircraft system is essential to prevent this from happening again.


Second narrative: ...due to Company Project work; I had not flown in two months and [had already] noticed I was not performing my flows routinely......I; as pilot not flying; failed. Checklists are there for a reason. I should have caught that the start lever was not in correct position when reading the [Shutdown] Checklist.


Synopsis: Distracted by an inappropriate ATC communication as they touched down and a circuitous routing to the nearby gate due to construction; the flight crew of a B737-500 failed to shut down the right engine during the taxi-in as planned and then failed to note it was still running after gate arrival until advised by ramp personnel.