Narrative:

We were at fl 350 preparing to descend via the [arrival] into ZZZ. As we reached top of descent we heard a bang and felt the airplane shudder. I asked the deadheading captain to go see if he could see anything abnormal on the main deck; which he said it was normal. We looked at the load paperwork and determined that it was unlikely a load shift. We spent the rest of the descent talking about what it could have been and working out a plan to manage the plane throughout the approach and landing. I decided we would slow and configure the airplane early to be able to recover if any abnormalities occurred during a configure change. Approach asked us if we wanted the visual or ILS to runway xxl in ZZZ to which I chose the ILS. At this point; we were at 4;000 ft. And were cleared to cross splat at 2;400 ft. On descent from 4;000 ft. To 2;400 ft.; we experienced a series of several bangs and the associated airframe shudders. I [requested priority handling] with approach and turned the autopilot off so I could know sooner if there was any control degradation. At that point; my first officer resumed the radio and answered ATC's standard inquiries after [requesting priority handling].after several bangs had occurred; the captain in the observers seat pointed out abnormal indications of the right engine. It was that point where I figured what we were likely experiencing was compressor stalls on the right engine. I determined the safest action to take since the engine was malfunctioning was to shut it down and secure it and called for the engine severe damage immediate action items. With the additional benefit of having an extra set of eyes in the observers seat verifying the proper actions were being taken; the engine was secured and the bangs and airframe shudders stopped.after we had the engine secured we determined we were far enough out and already configured at flaps 20 for a single engine landing and I decided to go ahead and land rather than continue flying on one engine.I had requested that the airport 'roll the equipment' since we weren't sure something else wasn't going on and to be able to respond immediately if the need would have been necessary. After landing; we rolled down to the end of runway xxl and taxied into the de-ice pad so the emergency personnel could assess the condition of the exterior of the plane. They reported we had a panel open; but everything else looked normal. After they finished their assessment; I determined we could taxi to our gate without any further assistance and released them with my appreciation for a job well done. After the trucks cleared; I called for the after landing flow and we taxied to our gate on the remaining engine.once at the gate; one of the mechanics came up and asked about the RAT (ram air turbine) being deployed. That's when what the emergency responder's statement about a panel being opened made sense. I looked at the switch on the overhead panel and it was in the normal position and safety wired shut so I'm confident its deployment was the result of some other malfunction that triggered it since the normal deployment parameters weren't metthe proficiency and professionalism of my first officer and the deadheading captain (which became a valuable member of my crew) were absolutely exemplary. They made an abnormal situation requiring an engine shutdown very manageable. They; along with the support from ATC and airport rescue significantly contributed to the safe outcome of the flight that morning.

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Original NASA ASRS Text

Title: B767 Captain reported that a compressor stall on approach resulted in a precautionary landing.

Narrative: We were at FL 350 Preparing to descend via the [arrival] into ZZZ. As we reached top of descent we heard a bang and felt the airplane shudder. I asked the deadheading Captain to go see if he could see anything abnormal on the main deck; which he said it was normal. We looked at the load paperwork and determined that it was unlikely a load shift. We spent the rest of the descent talking about what it could have been and working out a plan to manage the plane throughout the approach and landing. I decided we would slow and configure the airplane early to be able to recover if any abnormalities occurred during a configure change. Approach asked us if we wanted the visual or ILS to Runway XXL in ZZZ to which I chose the ILS. At this point; we were at 4;000 ft. and were cleared to cross SPLAT at 2;400 ft. On descent from 4;000 ft. to 2;400 ft.; we experienced a series of several bangs and the associated airframe shudders. I [requested priority handling] with approach and turned the autopilot off so I could know sooner if there was any control degradation. At that point; my First Officer resumed the radio and answered ATC's standard inquiries after [requesting priority handling].After several bangs had occurred; the Captain in the observers seat pointed out abnormal indications of the right engine. It was that point where I figured what we were likely experiencing was compressor stalls on the right engine. I determined the safest action to take since the engine was malfunctioning was to shut it down and secure it and called for the engine severe damage immediate action items. With the additional benefit of having an extra set of eyes in the observers seat verifying the proper actions were being taken; the engine was secured and the bangs and airframe shudders stopped.After we had the engine secured we determined we were far enough out and already configured at flaps 20 for a single engine landing and I decided to go ahead and land rather than continue flying on one engine.I had requested that the airport 'roll the equipment' since we weren't sure something else wasn't going on and to be able to respond immediately if the need would have been necessary. After landing; we rolled down to the end of Runway XXL and taxied into the de-ice pad so the emergency personnel could assess the condition of the exterior of the plane. They reported we had a panel open; but everything else looked normal. After they finished their assessment; I determined we could taxi to our gate without any further assistance and released them with my appreciation for a job well done. After the trucks cleared; I called for the after landing flow and we taxied to our gate on the remaining engine.Once at the gate; one of the mechanics came up and asked about the RAT (Ram Air Turbine) being deployed. That's when what the emergency responder's statement about a panel being opened made sense. I looked at the switch on the overhead panel and it was in the normal position and safety wired shut so I'm confident its deployment was the result of some other malfunction that triggered it since the normal deployment parameters weren't metThe proficiency and professionalism of my First Officer and the deadheading Captain (which became a valuable member of my crew) were absolutely exemplary. They made an abnormal situation requiring an engine shutdown very manageable. They; along with the support from ATC and airport rescue significantly contributed to the safe outcome of the flight that morning.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.