According to SWAPA, the lawsuit says "that SWAPA pilots agreed to fly the 737 MAX aircraft based on Boeing's representations that it was airworthy and essentially the same as the time-tested 737 aircraft that its pilots have flown for years".
The European Union Aviation Safety Agency (EASA) said on Tuesday it was still assessing proposed changes to Boeing software for the grounded 737 MAX and had yet not found anything that would undermine hopes for a coordinated return to service.
"We have to be able to trust Boeing to truthfully disclose the information we need to safely operate our aircraft", captain Jonathan Weaks, president of the Southwest Airlines Pilots Association (Swapa), said.
"Those representations proved to be false, " the lawsuit says.
Boeing called the lawsuit meritless and has pledged to vigorously defend itself. The airline has more 737 MAX aircraft than any other US airline.
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SWAPA, which represents around 10,000 Southwest pilots, said it filed the lawsuit in the District Court of Dallas County, Texas.
But the lower delivery figures are the latest demonstration of the hit to the company's finances and prospects because of the MAX, which was taken out of service in mid-March following two deadly crashes that killed 346 people. The airline was considering European jets a year ago, however, it eventually had chose to go with larger Boeing 737 family aircraft.
In this file photo taken on March 28, 2019, Southwest Airlines Boeing 737 MAX aircraft are parked on the tarmac after being grounded, at the Southern California Logistics Airport in Victorville, Calif.
Within the third quarter, Boeing delivered 63 jetliners, down from 190 jet shipments a 12 months earlier.
Boeing has trimmed production of the plane and been forced to store hundreds of new aircraft that can not be delivered. Last week, the National Transportation Safety Board said the system didn't allow pilots to easily understand what was happening in a critical situation, and recommended that the federal government require Boeing redesign the Maneuvering Characteristics Augmentation System, or MCAS, so it is more intuitive. Boeing has fought to get the plane back into service but it doesn't look likely until 2020.
Southwest Airlines Co is scheduling without the MAX until at least early January, pending regulatory approval for commercial flight. American Airlines Group and United Airlines have canceled 737 MAX flights through part of December.