RENTON, WA - MARCH 14: Boeing 737 MAX airplanes, including the 737 MAX 9 test plane (L), are seen at Renton Municipal Airport, on March 14, 2019 in Renton, Washington. The 737 MAX, Boeing's newest model, has been been grounded by aviation authorities throughout the world after the crash of an Ethiopian Airlines 737 MAX 8 on March 10.  (Photo by Stephen Brashear/Getty Images)
PHOTO: Stephen Brashear/Getty Images North America/Getty Images
RENTON, WA - MARCH 14: Boeing 737 MAX airplanes, including the 737 MAX 9 test plane (L), are seen at Renton Municipal Airport, on March 14, 2019 in Renton, Washington. The 737 MAX, Boeing's newest model, has been been grounded by aviation authorities throughout the world after the crash of an Ethiopian Airlines 737 MAX 8 on March 10. (Photo by Stephen Brashear/Getty Images)
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(CNN) —  

As the Boeing 737 MAX remains grounded, a new Senate investigation has launched and details of a federal grand jury have emerged, the latest in a series of probes looking into how the plane was certified and the problems that have occurred since.

Whistleblower reports raise questions about whether Federal Aviation Administration inspectors who reviewed the Boeing 737 MAX for certification were properly trained, Senate Commerce Chairman Roger Wicker said in a letter Tuesday to FAA acting Administrator Daniel Elwell informing him that the committee was opening an investigation into the safety inspectors’ training.

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“According to information obtained from whistleblowers and a review of documents obtained by the committee, the FAA may have been notified about these deficiencies as early as August 2018,” the Mississippi Republican wrote. “Furthermore, the committee is led to believe that an FAA investigation into these allegations may have been completed recently.”

Wicker wrote that “such potential lack of training and certification” of FAA inspectors “may have led to an improper evaluation” of the computerized stabilization system that has come under scrutiny following the October Lion Air crash.

That Senate investigation is one of several into the FAA and Boeing following two fatal MAX accidents since October.

The Transportation Department inspector general, Calvin Scovel, last week announced a wide-ranging review of the FAA’s certification of the aircraft, as well as the certification authority the agency delegates to companies like Boeing.

Transportation Secretary Elaine Chao also is forming a commission to review the FAA’s aircraft certification process.

Justice Department prosecutors have issued multiple subpoenas as part of a grand jury criminal investigation, including one to a former Boeing employee requesting all “communications, including drafts, related to the Boeing 737 Max.”

The MAX fleet remains grounded worldwide following October’s Lion Air accident and last month’s Ethiopian Airlines crash. Boeing was expected to submit a software fix for the stabilization system last week, but the FAA announced Monday that the company would need additional weeks of work on the fix.

Asked to comment, FAA spokesman Greg Martin pointed CNN to Elwell’s testimony before a Senate Commerce subcommittee last week: “In our quest for continuous safety improvement, the FAA welcomes external review of our systems, processes, and recommendations.”

The subpoenas stem from a criminal investigation that began after the Lion Air crash, sources said. Criminal investigators in the Justice Department have sought information from Boeing on safety and certification procedures, including training manuals for pilots, along with how the company marketed the new aircraft.

They also requested records from Peter Lemme, who worked for Boeing as a flight controls engineer from 1981 to 1997, long before the MAX was in development. That subpoena was first reported by The Seattle Times.

Lemme wrote a detailed blog post about the Lion Air crash on his website in November.

The subpoena to Lemme, details of which emerged Tuesday, indicates the broad scope of the Justice Department investigation into what caused the two 737 MAX crashes, requesting, “Any and all documents, records, emails, correspondence, audio or video recordings, text messages, voice messages, chats, and/or other communications, including drafts, related to the Boeing 737 Max.”

Lemme told CNN he does not have access to any internal Boeing documents, is “taking it quite seriously” and is “sharing … everything I have.”

It’s not yet clear what laws could be at issue in the probe. Among the areas of focus for criminal investigators are the processes by which Boeing itself certified the plane as safe and the data it presented the FAA about that self-certification, the sources said.

The FBI’s Seattle office and Justice Department’s criminal division in Washington are leading the investigation.

CNN’s Evan Perez, Shimon Prokupecz and Richard Davis contributed to this report.