(CNN) — Two US airlines fly the 737 MAX 8 -- the type of jet that crashed last year in Indonesia killing 189 people and on Sunday in Ethiopia killing all 157 on board.

American Airlines -- which flies 24 of the new planes -- said in a statement to CNN on Monday that it is monitoring the investigation in Ethiopia and following last year's Federal Aviation Administration directive after the crash in Indonesia of Lion Air Flight 610

The airline "continues to collaborate with the FAA and other regulatory authorities" and it has "full confidence in the aircraft," the statement said.

Southwest -- which includes 34 737 MAX 8s in its fleet -- said in a statement it doesn't plan to change its operational policies or procedures and it remains confident in the safety of its entire fleet. "We have been in contact with Boeing and will continue to stay close to the investigation as it progresses," Southwest said in the statement.

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It's very early in the investigation. Because the flight data recorder and cockpit voice recorder were only recovered Monday, the two crashes have not been directly linked . There are countless reasons a plane can crash -- including birds flying into engines, a problem with weight balance or pilot error.

"This is all so premature," said John Gogila -- former National Transportation Safety Board member. "What I would offer is a word of caution. We need to get the data analyzed first and then decide how to move forward."

Goglia said airlines that fly the 737 MAX 8 should be reviewing their flight training for the aircraft.

'Behind the scenes at airlines'

"You can't underestimate the power of what goes on behind the scenes at airlines," said William Voss, a former FAA deputy director and ex-CEO of the Flight Safety Foundation. "If they think they have a threat, they will step up and respond independently."

Investigators in the Lion Air crash suspect the crash was caused by an angle of attack (AOA) sensor on the outside of the plane which transmitted incorrect data that could have triggered a kind of auto-pilot system called the Maneuvering Characteristics Augmentation System (MCAS) that forced the plane's nose down.

Related content Lion Air crash: Pilots fought automatic safety system before plane plunged

Voss said he thinks airlines that fly the 737 MAX 8 have been "doubling up on inspections of sensors" and making sure all pertinent information about the plane has been communicated to pilots. "And I would be in continuous communications with Boeing," Voss said.

In November Boeing issued an "Operations Manual Bulletin" advising airline operators how to address erroneous cockpit readings. It pointed airlines "to existing flight crew procedures to address circumstances where there is erroneous input from an AOA sensor," a Boeing statement said. The FAA later issued its own emergency airworthiness directive that advised pilots about how to respond to similar problems.

Boeing's bestselling passenger jet is facing increased scrutiny after being involved in two deadly crashes in less than five months, a situation that threatens to tarnish the US plane maker's reputation for safety.

Voss also warned against rampant speculation about the investigation and allowing social media to drive it. "Social media has changed the way we see the world but nothing has changed the reality and physics of human error," he said. "So we can't let social media drive decisions about reality."

United Airlines flies a different version of the 737 MAX -- the 737 MAX 9. It currently has 14 in its fleet. Although there are no reports that MAX 9s have had any trouble with their AOA sensors, the FAA included that type of plane in its November emergency directive

How to know if you're booked on a 737 MAX 8

For passengers, there are three fairly simple ways to know if you're booked to fly on a 737 MAX 8.

1. Check your airline site or app. Clicking on the flight number will show you what type of airplane is assigned to the flight.

2. Check the registration of the airplane on the FAA site. Before you board, note the registration number which is clearly marked on the side of the plane. Plug that number into the Before you board, note the registration number which is clearly marked on the side of the plane. Plug that number into the FAA registration data base here