"Our team has made 96 flights totaling over 159 hours of air time with this updated software," said Boeing CEO Dennis Muilenburg while speaking Thursday at the George W. Bush Presidential Center in Dallas, Texas. Muilenburg, who went on a 737 Max test flight last week, says the company is making progress developing a plan to fix the aircraft's MCAS flight control software and improve pilot training, two problems that will need to be resolved before regulators certify the plane to fly again.

The test flights are one prong of a broad effort by Boeing to get the Max back in the air. The company is also updating airlines by bringing representatives into flight simulators and showing them how the modified flight control system will feel in the cockpit. Boeing says representatives from two-thirds of the 50 airlines that have the Max in their fleets have tested the new software in a simulator.

"We want everyone to be confident in it and the additional training and educational resources we're developing and deploying," Muilenberg said, adding that the last few weeks have been the most "heartwrenching" of his career.

The company will likely submit its plan to fix the Max, which has been grounded since mid-March, to the Federal Aviation Administration and other regulators within the next two weeks, according to people familiar with the matter. Getting those regulators to approve the plan will likely take several more weeks.

"I expect that the airplane is still several weeks away from getting the final seal of approval to be flown again, not so much that the software fix is a problem, but just from an optics standpoint," said Jeff Guzzetti, former director of the FAA's accident investigation civision. Guzzetti believes the FAA is stinging from criticism its relationship with Boeing was "too cozy" because the FAA designated Boeing engineers to self-certify parts of the 737 Max before the plane was given final approval in 2017.

Boeing has scrambled to restore faith in its 737 Max after the jet's anti-stall software was implicated in two crashes in the last five months that killed 346 people and grounded the planes worldwide. The company said it will cut Max production by 20% as it works on a software fix to get the jets running again. They've been grounded since mid-March.

Investigators suspect that faulty data feeding into the aircraft's MCAS flight system played a major role in the Indonesia and Ethiopia accidents. Investigators and lawmakers have scrutinized Boeing's software system malfunction, from the original design to the training and safety certifications.

When designing the newest Max jets, Boeing allegedly increased the power of the automated system that pushes the plane nose down, making it hard for pilots to regain control of the doomed jets. Changes to the anti-stall system were not fully reviewed by the FAA.

Boeing said Tuesday that deliveries and new orders for all of its 737 jets fell in the first quarter, and earlier in the week, Wall Street analysts downgraded Boeing stock. The company's shares have have fallen nearly 9 percent in the past month.

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