Date: 201205
Local time of day: 0601-1200
Location: ZFW.ARTCC, TX
Flight conditions: VMC
Weather elements / visibility: Thunderstorm; Turbulence
Aircraft: A319
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Flight phase: Climb
Airspace: Class A ZFW
ATC / advisory: Center ZFW
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Communication Breakdown; Fatigue; Workload
Second reporter function: First Officer; Pilot Not Flying
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Air Traffic Control Separated Traffic
Contributing factors: Human Factors; Procedure; Staffing; Weather
Primary problem: Human Factors

Narrative: While climbing through 15;000 FT to level at 17;000 MSL on an assigned heading vector of 360 degrees and an assigned speed of 250 KTS we received a clearance to 'climb to FL350.' We read back the clearance; confirmed it per SOP; set altitude on the FMC and then continued our climb. However; upon climbing through about FL187; ATC called to 'verify' that we were level at 17;000 FT. [When advised we weren't; he] promptly assigned FL230; and a heading of 320 degrees. After about another ten minutes en route; we received a request to call Center upon landing. After landing I called as requested and was advised that a 'pilot deviation' had occurred. This was explained to me as an ATC separation deviation of 4.5 NM and 600 FT vertical with a CRJ in front of us. At no time was there any doubt of the altitude assignment in the cockpit. Nor did we receive a TCAS alert; or perceive a collision threat. It is now apparent that ATC meant to say 'fly heading 350' not 'flight level 350' by mistake as we were certain of the altitude assignment and did read back the clearance without any correction from the controller. I believe that this mistake occurred due to the high ATC workload caused by the thunderstorms in the area. [A logical solution to events of this type would be to] reduce pilot/ATC workloads; hours of duty; radio congestion; and increase Air Traffic Control training/supervision.


Second narrative: There was quite a bit of thunderstorm activity in the area and our flight had been delayed due to an inability to fuel with the lightning that was upon and around the airport. ATC was extremely busy and the ATC frequencies were congested. There was no confusion in our minds regarding the clearance to climb to FL350. Neither pilot believed we had misheard the clearanceThe Controller said that; during the event; my readback of FL350 had been received. Both pilots felt that it was strange that ATC would receive my readback of an assignment to FL350 but that no correction by ATC was issued if that readback was in error. I believe the Controller miss-phrased the clearance that he intended to give our flight.


Synopsis: Although; while at 16;000 MSL; both pilots of an A320 heard 'cleared to FL350' and had readback FL350 ATC was alarmed to note they were climbing out of FL187 and directed them to stop their climb at FL230 and fly a new heading to avoid traffic with which they were conflicted.