An FAA review determined that the parts did not pose a safety risk, and the aircraft manufacturer made a similar determination.
Because of that, the FAA has decided that the airline may continue to operate planes that have the unapproved part until they can be replaced. The airline has until Dec. 24 to replace the parts.
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Southwest has replaced the parts on 33 of the 82 planes involved. The airline had faced a Tuesday deadline to replace the parts and had appealed for more time to fix the problem.
There was concern the carrier would be forced to cancel flights and ground planes if the FAA didn't give Southwest more time.
Federal inspectors discovered the parts last week.
On Monday, the airline suspended a contract maintenance firm -- D-Velco -- that got the parts from a subcontractor.
The part in question is called an exhaust gate assembly hinge fitting. It is designed to direct hot air from the engines away from the flaps on the rear of the wing, protecting the flaps from excessive heat.
FAA inspectors questioned the parts after finding they did not come with proper paperwork from the parts supplier, making it difficult to determine if they were built to FAA standards.