Date: 201505
Local time of day: 1201-1800
Location: ZOB.ARTCC, OH
Flight conditions: VMC
Weather elements / visibility: 10
Light: Daylight
Aircraft: Cessna Citation Sovereign (C680)
Operator: Air Taxi
Operating under: Part 135
Flight plan: IFR
Mission: Passenger
Flight phase: Descent
Airspace: Class E ZOB
ATC / advisory: Center ZOB
Reporter organization: Air Taxi
Reporter function: First Officer; Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Situational Awareness; Communication Breakdown; Human-Machine Interface
Second reporter function: Captain; Pilot Not Flying
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Automation Aircraft RA
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Flight Crew Took Evasive Action
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: We read back a clearance from ATC as 'cross 75 miles west of LRP VOR @ 11;000'. At the time I was the First Officer and the flying pilot. We were level at about 24;000; we set the Altitude Select to 11;000 and used VNAV to make the descent. About 5 minutes later my Captain and non-flying pilot was on COMM 2 getting the weather and ATIS for our destination airport so he was now not listening to ATC that was on COMM 1. We were descending around 18;000 and the TCAS TA; 'TRAFFIC; TRAFFIC' went off and ATC then queried us and stated 'XXX; traffic 10 o'clock;' as I then replied; 'Roger' and I did not say or have the conflicting traffic in sight. I switched the aircraft autopilot from VNAV to Vertical Speed and slowed our rate of descent as a way to satisfy the TA and when I was doing just that; the RA then signaled in our headsets; 'ADJUST VERTICAL RATE;' where I did take control of the aircraft to follow the RA until 'CLEAR OF CONFLICT' was heard. At that moment the Captain went on the radio and asked ATC why we weren't made aware of the traffic where she replied I did point it out and you are supposed to be at level at 17;000 because of the traffic at 16;000. I then was shaking my head to him because I received no such instruction as to level at 17;000. After a couple exchanges more with ATC she gave us a phone number which we took and stated once on the ground we will be giving her a call. We later arrived at our destination without incident; and once the aircraft was put away; the Captain called Cleveland Center. He put it on speaker so I could also join the conversation; and we spoke with 2 supervisors where they told us that the controller at the time of the incident has gone home sick because she was so shaken up by the incident. He then played the tapes and we were able to hear the controller's clearance was cross 75 miles west of LRP VOR at 17;000; and the next voice you hear is the Captain's reply stating; 'Roger; cross 75 miles west of LRP VOR at 11;000.' That was not clearance given; but for some reason that is what the Captain replied with and I also did not catch this mistake. The controller NEVER responded back telling us that we read back the clearance wrong. It seemed as if Cleveland Center was taking full responsibility and apologized for to us for the confusion. The Chief Pilot was also made aware of the above events and also agreed that the responsibility fell on the Controller's shoulders.


Second narrative: [Report Narrative Contained No Additional Information.]


Synopsis: Citation crew read back incorrect descent clearance resulting in an airborne conflict with other traffic.