Air Safety: Nothing But Blue Skies?

Arnold Barnett

We might start out with the question:

How Safe Is It to Fly Now?

Well, how should we measure aviation safety?

An e-mail message:

“My name is L.S. I would like to know if you, as an expert in aviation safety, fly regularly.”

“You see, I stopped flying about a year ago and this has affected my life in a significant matter. Just one last question: what are the odds of me dying in a plane crash?”

Given that a passenger’s greatest fear is of being killed in a plane crash, there is a natural interest in statistics about the likelihood of that outcome.

But which statistics are the most informative?

We restrict our attention here to scheduled passenger jet flights.

“NTSB studies show that, from 1993 through 1996, scheduled US carriers averaged only 0.2 fatal accidents per 100,000 flight hours.

--Wall Street Journal

Two problems with the statistic fatal accidents per 100,000 flight hours as a safety indicator:

The numerator and

the denominator!

• The generic term “fatal accident” blurs the distinction between a crash that kills one passenger out of 300 and another that kills 300 out of 300.

• Measuring activity by “flying hours” misses the point that most accidents occur on landing or takeoff.

What about hull losses per 100,000 departures?

(This is a popular one.)

Consider two hull losses in 2005:

Air France, Airbus 340, Toronto Passengers on board: 291 Passengers killed: 0

Helios Airlines, Boeing 737, near Athens Passengers on Board: 115 Passengers Killed: 115

No difference?

Why not the simple ratio of passengers killed to passengers carried?

There is a reason.

When a Boeing 737 hits a mountain killing all passengers, the implications about safety are the same whether it is full or only 1/3 full. Yet the number of passengers killed is 150 in one case and only 50 in the other. Thus, the “passengers killed” statistic treats the two events very differently, for no good reason.

A crash that kills 28 passengers out of 28 has a very different survival rate than another that kills 28 out of 280. Yet the statistic “number killed” treats the two events the same way, which is unfortunate.

Measure of Safety Performance Over a Past Period:

Death Risk Per Randomly Chosen Flight

Question:

If a person chooses a flight at random from among those of interest (e.g. Brazilian jet flights over the period 1990-99), what is the probability that he will not survive it?

We’ll write out the formula, starting with some definitions:

Let Q be the Death Risk Per (Randomly Chosen) Flight

Also, let N be the number of flights of interest

Let x(i) = the fraction of passengers killed on

flight i (i = 1, 2, …,N)

Then Q is simply the average of the x(i)’s:

Q = ∑ x(i) NWhy? • Chance of selecting flight i is 1/N.• Conditional probability of death given flight i

selected is x(i).• Add up probabilities for N choices because they

are mutually exclusive ways of “losing” the lottery.

This death risk per flight statistic has conceptual advantages compared to the other statistics just discussed.

What Conceptual Advantages?

• Ignores length and duration of flight, which are virtually unrelated to mortality risk

• Weights each crash by the percentage of passengers killed

• Easy to calculate and understand

To get started with actual numbers, what was the death risk

per US jet flight over 2000-08?

Let’s work it out together!

Over 2000-08, scheduled US jets performed a total of 69 million flights.

Among these flights, exactly three crashed in accidents, with no survivors:

• off Los Angeles, 2000

• New York City, 2001

• Lexington, Kentucky 2006

Therefore, someone who chose a US jet flight at random over 2000-08 would sustain an accidental death risk of 3 in 69 million.

That rate works out to 1 in 23 million.

How good is that?

Well, Barack Obama was elected the 44th president of the US 228 years after the first president was chosen.

That works out to one president elected every 5.3 years (228/43).

Moreover, over 2000-07, there were 4.1 million births per year in the United States.

That works out to 4.1 x 5.3 22 million births every 5.3 years in the US , of whom one on average will be elected President.

In other words, an American kid at a US airport today is more likely to grow up to be President than to perish in an accident on her next jet flight.

(1 in 22 million vs. 1 in 23 million)

Furthermore, at a risk of 1 in 23 million per flight:

Someone who took one flight every day would on average go 63,000 years before dying in an air crash. (Pretty good, eh?)

But these calculations leave out 9/11, the worst day ever in the history of commercial aviation.

When 9/11 is included, US death risk per jet flight over 2000-08 increases to 1 in 10 million.

Total Death Risk per US jet flight since start of the jet age:

Period Death Risk per Jet Flight

1960-69 1 in 1 million

1970-79 1 in 3 million

1980-89 1 in 7 million

1990-99 1 in 10 million

2000-08 1 in 10 million

Total Death Risk per First World jet flight Other than US since start of the jet age:

Period Death Risk per Jet Flight1960-69 1 in 500,0001970-79 1 in 2 million1980-89 1 in 4 million1990-99 1 in 10 million2000-08 1 in 20 million

Death Risk per Flight, Developing-World Jet Passenger Services, 1960-2008

Period Death Risk per Flight

1960-69 1 in 100,000

1970-79 1 in 200,000

1980-89 1 in 400,000

1990-99 1 in 500,000

2000-07 1 in 1.5 million

However, on flights between the First and Developing Worlds, the death risk per flight is not lower on First-World jets than Developing-World ones:

(1 in 1.5 million in both categories)

Despite recent suggestions to the contrary, regional jet flights are not less safe in the US than those on larger jets.Death Risk per Flight, US regional jets, 1980-2008:

1 in 35 million

“So what happens now?”

--Evita Peron

Fatal Accidents on First-World Jets Are on the Verge of Extinction

But:

Many a near-extinct species has staged a massive comeback.

Runway Collisions:

Poised To Return?

Maybe not this year, but:

Growth in airport traffic will resume, and it would be expected to increase the risk of runway collisions, perhaps faster than linearly.

Overall, US runway collisions over 2003-2022 could cause 700-800 deaths and 200 serious injuries. (Mid-range figure)

A detailed study in 2000 estimated that:

Moreover, changes in air traffic control in both Europe and the US could bring increased risk of midair collisions.

One might fear that direct routings of aircraft will be inherently more dangerous than the present system of “highways in the sky.”

But potential problems do not have to turn into actual ones.

There is reason to believe that airport collision risk will be tamed in the United States because of technological advances (e.g., ASDE-X, runway status lights) which are projected to reduce risk by as much as 80%.

Also, the revised geometry of direct routings could act to reduce the risk of mid-air collisions.

NOW SOON

But what about the threat of terrorism?

In the US, The 9/11 Commission suggested a certain impatience with recent aviation-security measures when it described them as “fighting the last war.”

(Page 391)

Perhaps this viewpoint makes some sense, but we should note that:

• More US civilians were killed by terrorists during air journeys than during any other activity.

• On a per-hour basis, the terrorism death risk during air journeys was 600 times higher than at other times.

And these statistics are all based on the 35-year period prior to 9/11!

Since 9/11, we have seen:

• The Shoe Bomber’s 2001 attempt to destroy a transAtlantic jet

• The 2002 shootout at LAX that left several dead and injured

• The 2002 firebombing of a Chinese jet

• The simultaneous destruction in 2004 of two Russian jets

• The 2006 plot to destroy ten transAtlantic jets with liquid explosives

• The 2007 firebombing at Glasgow airport.

• The 2008 attempted firebombing of a Chinese jet

The terrorist fascination with aviation, in other words, long preceded 9/11 and has evidently persisted since then. There is perhaps nothing wrong with “fighting the last war” when it resembles to one before that and the one before that, and when we lost the last war disastrously.

Let us turn to one particular security topic: Bombs on airplanes.

Proposals for new measures to prevent airborne explosions are popping up everywhere.

Separating people from their laptops would be painful, although some people could surely use the time to go over reading material, or even revert to pen and paper.

…For now, the surest way to keep dangerous materials out of the cabin is to keep virtually all materials out of the cabin.

The New York Times, 9/10/06

Question by average traveler:

Are they crazy?Son Locos?

Calmer Question:

Can we objectively perform cost-benefit analysis on this crazy proposal?

Well, let’s try, accepting at face value two statistics:• The RAND Corporation has estimated that a

successful terrorist attack against a US aircraft would have a total cost of $15 billion.

• The Research Service of the US Congress has estimated that the monetary equivalent of one minute of passenger delay is 62 cents.

Given a choice, which would you prefer on your next flight?

(1)A ban on laptops or a one-minute arrival delay

(2) A ban on laptops or a four-hour arrival delay?

There is presumably some delay-equivalent X such that you are indifferent between a ban on laptops and an arrival delay

of X minutes.

And the cost of a delay of X minutes is 0.62X, which we could use as your dollar cost estimate of a ban on laptops.

(Pretty crude, eh?)

If the value of X averaged overall US air travelers was 20 minutes, the annual cost of a ban on laptops would be estimated as (20)*(0.62)*600m ≈ $7.5 billion

Comparing $15 billion to $7.5 billion, we reach the rough approximation:

To be cost-effective, a ban on US laptops would have to prevent one successful terrorist attack on aviation every 2 years.

(Can that condition be met?)

Sad Truth:

We cannot adopt any security measure, however expensive, to achieve any increase in security, however small.

Suppose that a jet plane has suddenly plunged from the sky, for reasons unknown.

What should we do, knowing that terrorist acts against transportation often are followed by others within minutes?

Between a terrorist explosion on an airplane and warnings to other pilots in the air, we can expect at least ten minutes to pass.

Major Fatal Terrorist Bombings Against Air/Rail Since 9/11

Year Location Number of Attacks2002 China One2003 Madrid 10 within 3 minutes2004 Moscow One2004 Russia One2004 Russia 2 within 2 minutes2005 London 3 within 1 minute2006 Mumbai 7 within 11 minutes

Tragically, therefore, the “optimal strategy” given the sudden loss of a jet might well be:

Do nothing….except hope.

So, where are we?