It was unclear to what extent the efforts may overlap. But the pursuit of information by federal investigators comes as the FAA and Boeing face growing questions about the way the government and company worked together to certify the airplane involved in crashes in Ethi­o­pia and Indonesia within months of each other.

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The FAA has for years relied heavily on Boeing and the other companies it regulates to do much of the work of certifying safety, prompting critics to warn that the agency’s approach to the industry is too lenient and could be dangerous. The FAA has argued that its processes are “well established and have consistently produced safe aircraft designs.”

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The FAA and Boeing declined to comment on the work of federal investigators. As with all legal matters, “we do not comment even as to whether such matters exist,” a Boeing spokesman said. The company had said earlier that the FAA’s certification requirements for the 737 Max aircraft were “identical” to those that “governed certification of all previous new airplanes and derivatives.”

The FAA did not say if it was looking at an internal investigation of its own, but a spokesman said that “our full focus is on the software upgrade and supporting the accident investigation.”

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The software change is meant to address an automated feature of the Max jets that investigators say contributed to the Oct. 29 crash in Indonesia that killed 189 people. Flawed sensor data feeding into the plane’s anti-stall system helped push the aircraft downward and into the Java Sea, according to a preliminary report.

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A spokesman for the Transportation Department’s Office of Inspector General would not confirm or deny an investigation. The office does, however, have an auditing arm. The spokesman said that while no new audit has been announced into the Max certification, the office is always “evaluating our use of audit resources and considering future audit work in light of emerging issues,” including congressional requests and earlier audits it has performed on the FAA’s airplane certification procedures.

The Wall Street Journal, citing unnamed sources, first reported that a grand jury in Washington had issued a subpoena to at least one person involved in the development of the 737 Max. The Journal also said a second inquiry by the Transportation Department’s inspector general is focused on the Seattle-area office of the FAA charged with certifying aircraft as well as an office that mandates training requirements.

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Meanwhile, data from the flight recorders on the Ethio­pian Airlines jet show “clear similarities” with the October Lion Air flight in Indonesia, investigators in France said Monday, echoing comments from Ethiopian authorities over the weekend.

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“You got two airplanes of the same type that have experienced problems. So of course they are going to go back and look at the certification process. FAA is going to look at that themselves. And it also appears DOT is going to look at it,” said John M. Cox, a former pilot and an airline safety consultant with the Washington-based aviation safety consulting firm Safety Operating Systems. “They are going to look at everything.”

Even as investigators studying the data have found several similarities, Larry Rooney, president of the Coalition of Airline Pilots Associations (CAPA), a trade association for more than 30,000 pilots, said that does necessarily mean a quick resolution.

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“I suspect even though there will be some similarities, [the crashes] won’t be mirror images of each other,” Rooney said. “No two accidents are exactly the same.”

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And then there is the question of when the planes will fly again. In 2013, when the FAA grounded Boeing’s 787 Dreamliner amid concerns about the plane’s lithium ion batteries, it took three months before the aircraft returned to the skies.

“Grounding [the 737 Max jets] was easy; ungrounding it is going to be hard. The question is going to be how much is going to be enough to put the airplane back in the air,” Rooney said.

Rep. Peter A. DeFazio (D-Ore.), chairman of the House Transportation Committee, said last week that he plans to hold one or more hearings on the Boeing crashes.

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On Sunday, Ethiopia Transport Minister Dagmawit Moges said the condition of the data and voice recorders was good and that enough data had been recovered that her ministry’s Accident Investigation Bureau would release a preliminary report in 30 days on what happened to Flight 302.

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Officials with France’s Bureau D’Enquetes et D’Analyses (BEA) confirmed the “clear similarities” Monday, in announcing that the data from the flight recorders had been transferred to the Ethiopian Accident Investigation Bureau.

The BEA, which has extensive experience analyzing crashes in Europe, began work March 15 to retrieve information from the flight data recorder. Its role in the investigation is now complete, as it has handed off the retrieved data to Ethi­o­pia for further analysis.

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Last week investigators found a device known as a jackscrew in the wreckage, which suggests the Ethio­pian flight might have had a problem with the automated system also suspected in the Lion Air crash.

The jackscrew, used to set the device that raises and lowers the plane’s nose, indicates the jet was configured to dive, Cox said.

That was the second piece of information suggesting similarities between the two crashes involving Boeing 737 Max 8 jets.

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FAA officials last week also cited satellite tracking data as a key similarity. The planes in both cases ascended and descended multiple times before crashing, experts said.

Initial flight data as well as subsequent satellite information showed the Ethio­pian Airlines plane in trouble almost immediately and that it had an erratic flight path during the six minutes the plane was in the air before it crashed into a field outside Addis Ababa, killing all 157 aboard.

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Officials from the U.S. National Transportation Safety Board (NTSB), which sent three investigators to France, the FAA, and Boeing also are assisting in the probe.

U.S. investigators will continue to assist in the analysis of the data, an NTSB spokesman said Monday. Any progress report on the investigation will be issued by Ethio­pian authorities, per international protocol.

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Boeing on Sunday said the company was working with the authorities to evaluate new information as it becomes available.

“Safety is our highest priority as we design, build and support our airplanes. As part of our standard practice following any accident, we examine our aircraft design and operation, and when appropriate, institute product updates to further improve safety,” the company said in a statement.

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“While investigators continue to work to establish definitive conclusions, Boeing is finalizing its development of a previously-announced software update and pilot training revision that will address” the way the automated anti-stall feature, known as MCAS, responds to “erroneous sensor inputs. We also continue to provide technical assistance at the request of and under the direction of the National Transportation Safety Board, the U.S. Accredited Representative working with Ethiopian investigators,” the company said.

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In all, more than 300 people have died in the two crashes involving the Max 8 jet.

In November, Boeing issued a bulletin on how to reset the stabilizer if it started to push the plane’s nose down.

Boeing said last week it had stopped delivery of all 737 Max jets. The company said it would continue manufacturing them, however.