Federal officials have told Southwest Airlines to fix the way it calculates the weight of luggage loaded on flights after finding frequent mistakes during a yearlong investigation.

Southwest said today that it has made improvements in its methods for calculating the weight and balance of loads, and that it isn’t facing enforcement action.

The airline said that it voluntarily reported the issue to the Federal Aviation Administration last year.

The FAA investigation was first reported by the Wall Street Journal.

The newspaper said internal FAA documents showed that the airline made frequent mistakes in calculations and luggage-loading practices that could cause errors when pilots compute their plane’s takeoff weight.

Southwest crews count bags they load and use an average weight to calculate the load. The FAA found cases in which the bag load was more than 1,000 pounds heavier than paperwork indicated, the newspaper reported. FAA inspectors believed pilots might respond incorrectly to an engine emergency if they had inaccurate information about the distribution of weight between front and rear cargo bays.

An FAA spokesman told the Associated Press that the agency opened an investigation in February 2018. Since then, he said, the FAA directed the airline to develop a comprehensive fix to the methods and processes it uses to determine baggage weight.

Southwest, based in Dallas, asked the agency to close the investigation. The FAA said the agency won’t do so until regulators are satisfied that Southwest’s corrections are being applied consistently.

Southwest sought to downplay the investigation, saying that a so-called open letter of investigation is a common way for the FAA to discuss safety issues with an airline.

Since the investigation started, the airline’s publicity department said in a statement, “Southwest has implemented controls and enhanced procedures to address our weight and balance program concerns, and we’ve shared those measures with the FAA.”

Southwest believes that changes it made throughout last year “have enhanced our weight and balance program and resolved the issues that we originally reported to the FAA.”

Southwest, which carries more passengers within the United States than any airline, disputed an estimate that one-third of its flights took off after faulty calculations of the weight of checked bags, but it declined to give a figure.

No passenger had died in an accident on Southwest until last April when a piece from a broken engine smashed into a window on the plane and a passenger was partially pulled through it. The accident led to stepped-up inspection of fan blades on certain engines used by Southwest and other carriers.

The airline, however, has been fined for safety violations. Notably, Southwest agreed in 2009 to pay $7.5 million to settle FAA allegations that it operated 46 planes without performing required inspections for possible cracks in the planes’ aluminum skin.