Date: 201809
Local time of day: 1801-2400
Location: ZID.ARTCC, IN
Weather elements / visibility: Thunderstorm; Icing; Turbulence
Light: Dusk
Aircraft: Medium Transport
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Descent
Airspace: Class A ZID
ATC / advisory: Center ZID
Second aircraft: Medium Transport
Reporter organization: Air Carrier
Reporter function: Pilot Flying; First Officer
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Human factors: Confusion; Communication Breakdown
Second reporter function: Pilot Not Flying; Captain
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Automation Air Traffic Control; Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Separated Traffic
Contributing factors: Procedure; Company Policy
Primary problem: Ambiguous

Narrative: High and late for descent into DAY caused by ATC; on the verge of requesting lower; ATC issued an immediate descent; minimum of 2000 feet per minute from FL280 to FL240. Both the Pilot Monitoring (PM) and I heard Air Carrier X; the PM read back the clearance. Then ATC directed Air Carrier X to turn 10 deg left for traffic; almost immediately we received a Traffic alert. Then ATC asked what altitude Air Carrier X was at. The PM replied passing FL260 for FL240 at 2000 ft per min. The ATC controller sounding confused; directed continued left turn for traffic; and asked another aircraft what their descent clearance was? They replied FL280 for FL240 at 2000 ft per min. I believed everyone realized what happened; and ATC admitted that two [company] aircraft with similar sounding flight numbers; answered the same clearance; the read back from both aircraft was blocked; and ATC admitted heard neither; nor notified both aircraft that similar sounding flight numbers are on the same frequency. ATC then stated 'no harm; no foul'!! Both aircraft were going to DAY; and we; landed well ahead of the other aircraft.Similar sounding flight numbers; on the same frequency; in the same proximity; plagues [our company]; again!!! ATC not notifying said aircraft of this hazard. PS. The next controller warned both aircraft of similar sounding flight numbers; the controller at the time of the event did not.It's been said; [our company] was going to change policy to minimize similar sounding flight numbers being dispatched in close proximity in time; and space to minimize this hazard. It seems to be getting worse; I've had multiple situations of similar flight numbers in recent weeks.


Second narrative: While in descent into DAY there was another [company] flight with a similar call sign. They were given descend to FL240 with a minimum of 2000 fpm. Because of the similar call signs I read back the clearance the same time the other aircraft did. The radio transition was blocked but neither airplane heard the block and so we both began to descend. When we were about 1000 feet below altitude ATC asked us our altitude. We told him we were complying with descend to FL240 at 2000 fpm. He said that was for another aircraft so we climbed back to FL280. [The cause was] similar sounding call signs and blocked transmissions. [Company] spacing similar call signs farther apart.


Synopsis: Air carrier flight crew reported an airborne conflict due to similar call signs and a communication breakdown with ATC.