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Math to the Max

May11

How safe is the Boeing 737 MAX series? This emotive question requires us to do some mathematics.

In its current implementation the 737 MAX is no safer than first generation jetliners flying in the late 1950s to early 1960s: types that included the Comet, Caravelle, BAC-111, Trident, VC-10, early 707, 720, DC-8 and Convair 880/890. The 737 MAX is about 75 times as dangerous as the previous 737 NG

The root cause is the installation of the huge LEAP engines on a 50 year old airframe has produced an aircraft that is unstable at higher angles of attack. Avionics – notably MCAS – has been included to restore that stability, but has greatly increased the risk of catastrophic loss of flight control in pitch.

Fatal crash rates per million flights

Aircraft and airline safety is often measured in fatal accident rates per million flights (call this FAR). Third and fourth generation aircraft, including the A320, A330, A340, A380, 737–600/700/800/900 and NG, 747–400, 757, 767 and 777 have a FAR of 0.3 or less. The A320 series is 0.11, the 737 Classic and NG series is 0.13 fatal accidents per million flights (Plane crash rates by model). There is some statistical noise, so these small differences are meaningless, as exemplified by Concorde which went from 0 to 11.36 after one accident, but with only 90,000 flights over its long career.

Because of this statistical noise, a single accident in a new aircraft model is concerning, but not very informative. Two early accidents that appear to have the same design related cause – rather than pilot related – become very concerning.

What is the fatal crash rates per million flights of the 737 MAX?

There have been two accidents, but how many flights? Boeing published the number of flights (41,797) after one year of service ending 21 May 2018 and 130 deliveries (see graphic below)

In that 12 months there wee an average of 65 aircraft in service. Simple math suggests 41,797/(12*65) = 53 flights per aircraft per month. Ten months later there are 370 737 MAXs in service. The average of 370 and 130 is 250 and 250*10 = 2500 aircraft months. 2500*53 = 132,500 flights. Added together 41,797 + 132,500 is about 175,000. To be generous lets say 200,000 flights total – it may be higher.

Two fatal accidents in 200,000 flights is 10 fatal crashes per million flights

Both are attributable mainly to design flaws rather than pilot error. Even pilots in Indonesia and Ethiopia flying older 737s have very low accident rates. 10/0.3 is about 30 times acceptable industry standard and 10/0.13 = 75 times the record for the 737–600/700/800/900 and NG series. The FAR of 0.13 is quite a reliable estimate given 18 fatal accidents and 74 million flights.

The 737 MAX – in its current implementation – is a dangerous aircraft.

Fatal accident rates of 10 per million flights have not been seen since the late 1950s early 1960s and only in first generation aircraft like the Comet, Caravelle, BAC-111, Trident, VC-10, early 707, 720, DC-8 and Convair 880/890. The detailed causes of the crashes will no doubt be a complex interaction of flight regimes, avionics (including MCAS), possible hardware failures, and pilot actions. The LEAP engines have made the 737 MAX unstable at high AOA and been accompanied by avionics changes to correct this. But it is clear that more skilled pilots are required to safely fly the 737 MAX than the 737 NG, and that returns the aircraft to the safety level of first generation airliners of the late 50s early 60s. Read more here.

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