Thousands of Southwest Airlines passengers over the next five days will likely be flying on planes that have missed a required safety inspection, ABC News reported.

The Federal Aviation Administration allowed the carrier to operate the aircraft while Southwest catches up on the checks of their backup rudder system.

The Dallas-based airline had initially grounded 128 planes -- about one-fifth of its fleet -- on Tuesday after it discovered the missed inspections, company officials said. About 80 flights had to be canceled as a result. After Southwest informed federal safety regulators of the situation and its efforts to perform the overdue inspections, the FAA agreed to let the carrier resume flying the planes before the checks are complete. The procedure will now likely occur during overnight hours for most of the affected Boeing 737-700 jets.

"The airline voluntarily removed these aircraft from service while the FAA works with Boeing and Southwest to evaluate a proposal that would allow the airline to continue flying the planes until the inspections are completed over the next few days," the FAA said in a statement.

The federal agency described the nature of the check as a "periodic inspection of a backup system," Bloomberg Business noted. 

"The FAA evaluated the risk and agreed that the airline could continue to operate the planes during this short interim," regulators wrote in a statement.

The missed inspections are meant to control standby hydraulic systems, which serve as the final backup to two primary levels of equipment, Bloomberg Business detailed. Each check takes about two hours, according to Southwest.

John Hansman, professor of aeronautics and astronautics at the Massachusetts Institute of Technology, attributed the missed inspections to an unintentional mistake. "These airplanes have complicated inspection schedules," he said. "They go through a series of different progressive checks. It sounds like a tracking error oversight."

Southwest is unlikely to face an enforcement action or penalty for the lapse because the FAA aims to encourage pilots and carriers to come forward with safety errors voluntarily, according to Bloomberg Business.

John Cox, a former 737 pilot who now heads a safety consulting company, said he approved of the approach. "This is the way the system is supposed to work," Cox said. "They discovered an inadvertent oversight and they brought it to the FAA's attention."