Some more info from Boeing explaining the background for the MCAS on the MAX:
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Last week the FAA issued Emergency Airworthiness Directive 2018-23-51 that is applicable to the MAX-8 and MAX-9 aircraft only. This AD is not applicable to the NG. The AD addresses a possible failure mode on the MAX where erroneous Angle of Attack (AoA) signals can cause the stabiliser to drive towards a nose down position. During certification stall testing it was found that due to the larger engine nacelles the MAX tended to pitch up during the stall exasperating the stalled condition. To address this issue Boeing introduced the Manoeuvre Control Augmentation System (MCAS). The MCAS system commands the stabiliser nose down to improve longitudinal stability during manual flight with flaps up at high angles of attack approaching the stall, or during steep turns with high load factors.
The MCAS function becomes active when the airplane Angle of Attack exceeds a threshold based on airspeed and altitude. Stabilizer incremental commands are limited to 2.5 degrees and are provided at a rate of 0.27 degrees per second. The magnitude of the stabilizer input is lower at high Mach number and greater at low Mach numbers. The function is reset once angle of attack falls below the Angle of Attack threshold or if manual stabilizer commands are provided by the flight crew. The AD addresses the case where an erroneous AoA signal on the on-side FCC causes the stabiliser trim to drive nose down during the normal flight regime when in manual flight.
It is of course possible for the NG AoA probes to fail or provide erroneous signals. This may result in continuous or intermittent stick shaker on the affected side only, minimum speed bar (red and black) on the affected side only, inability to engage the autopilot, automatic disengagement of the autopilot, IAS DISAGREE, ALT DISAGREE and illumination of the FEEL DIFF PRESS light. However as the NG does not have MCAS installed the stabiliser will not drive nose down and there should be no increase in nose down control forces
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So Boeing introduced a system designed to stop a stall induced by the pitch-up moment caused by the MAX's larger more powerful engines, but instead when fed erroneous data it actually pitched down without a high AoA and crashed the plane...