Date: 201705
Local time of day: 0001-0600
Location: S56.TRACON, UT
Light: Night
Aircraft: Large Transport
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Descent
Airspace: Class B SLC
ATC / advisory: TRACON S56
Second aircraft: Large Transport
Reporter organization: Government
Reporter function: Approach
Reporter qualification: Air Traffic Control Fully Certified
Human factors: Workload; Situational Awareness; Communication Breakdown; Confusion
Anomaly: ATC Issue All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Detector: Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Air Traffic Control Issued Advisory / Alert
Contributing factors: Weather; Company Policy; Human Factors; Procedure; Airspace Structure
Primary problem: Human Factors

Narrative: I was working during an arrival bank. The bank was much busier than normal because of numerous diversions due to weather earlier during the Cargo Bank. I had strong winds out of the south; a handoff that was training at the time; and offloads. Aircraft X checked in on the arrival and I descended the aircraft to 13;000 feet; which he read back. I had aircraft Y on the arrival that I was sequencing in front of aircraft X. I descended aircraft Y to 14;000 feet; then slowed aircraft X to 230 knots. I then went back to aircraft Y and descended him to 11;000 feet.Aircraft X took aircraft Y's instructions and descended to 11;000 feet. I did not hear the incorrect read back at the time; likely hearing only '[the similar flight number]' and incorrectly interpreting that this was aircraft Y. Aircraft X was around 12;000 feet when I noticed that the aircraft had descended below the 12;700 foot Minimum Vectoring Altitude (MVA). I advised aircraft Y to maintain 13;000 feet; then went back and told aircraft X to stop his descent; and advised the aircraft later to maintain 12;000 feet. I realized that aircraft X had taken aircraft Y's instructions when aircraft Y was still level at 14;000 feet; and expedited the aircraft to 11;000 feet again.Aircraft X was given a brasher warning for a pilot deviation; but I missed the readback when I should not have. I was extremely busy at the time with complex traffic and numerous vectors instead of RNAV's; but I still feel that I missed it at a bad time. At the time of this mix-up; my handoffs were on the line with another sector and Traffic Management Unit (TMU); unable to hear the readback from the aircraft. At the same time of this arrival bank; numerous aircraft were departing a satellite airport right into my downwind sequence. I very well may have been talking to my handoff at the time of the missed readback as well; but I do not know for sure. This event definitely hit my psyche as my last 3 arrivals in sequence were not to my normal standard of work; and one offload was high in the downwind to bear.First of all; I should have listened better to the readback and caught it. I pride myself on catching incorrect readbacks and have caught numerous in the past. I can't explain why or how I missed this one and I am extremely disappointed for my failure to do so. I believe that specifically the traffic volume; complexity; and the fact that I had training on handoff could have contributed to this event. Ultimately; my responsibility as a controller is to catch the pilot's error to prevent this from occurring.One thing I most certainly would have changed was the releases off of the satellite airport. This was a particularly busy arrival bank with lots of sequence calls to be made with the arrivals from ZLC. Offloads were called for my sector simply to facilitate the release of traffic underneath my arrival downwind into SLC. I easily could have missed aircraft below if they didn't get handed off or check in immediately; especially when these departures were on a 110 heading towards the mountains with 11;800 and 12;700 foot MVAs. I had to vector these aircraft not on the SID and control their speeds to blend them into a sequence that I made without these aircraft 20 miles prior to the satellite departures tagging on my scope.As a controller; my job is definitely to handle the volume; but I feel that sector overload could easily have been prevented by holding these departures on the ground for literally no more than 5 minutes to provide a safe and efficient traffic flow instead of stacking the downwind multiple times and introducing undue risk in the system. My handoffs were both on the line at the time of the missed readback directly because of offloads being called. TMU called after things had already been coordinated for a sequence and interrupted the handoff when they otherwise would have been involved in the sector. Ultimately; I missed the readback and take responsibility; but sector overload; traffic management; weather; and complexity played a direct role in this event.




Synopsis: Controller reported that during a busy arrival session he missed the wrong aircraft acknowledging a descent clearance. The aircraft descended below the minimum vectoring altitude.