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This link says that:

fatal accidents occurred once every 200,000 flights in the 50s and 60s. Now, fatal accidents only occur once every two million flights

While many sources, including this one, agree that the average number of commercial flights per day is around 100,000.

If that is the case, then we should see a fatal accident every 20 days or so (2 million flights), but in 2017, there were no fatal incidents on commercial flight at all.

What is the explanation for this? Is it just that the first link is plain wrong?

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    $\begingroup$ The stat cited was "Now, fatal accidents only occur once every two million flights." That quote is not specific about US only, nor about Commercial Flights only. It is possible that there is a fatal incident in all flights, commercial and GA, world-wide, per 2 million flights. $\endgroup$ – abelenky May 3 '18 at 14:45
  • $\begingroup$ The bit about "no fatalities on commercial flights" was for U.S. airlines. It was not only true of 2017, but also 2016, 2015, 2014, 2013, 2012, 2011, 2010, etc. The recent Southwest flight that resulted in 1 passenger death was the first passenger death on a mainline (not regional) U.S.-flagged airliner in scheduled passenger operations since 2001. A few fatal accidents have occurred on the regionals in that time, but not many (IIRC, 3 of them.) $\endgroup$ – reirab May 3 '18 at 20:55
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    $\begingroup$ @abelenky makes a good point. There are fatal aircraft accidents all the time in the US. Just yesterday a C130 crashed in Georgia killing 9 crew members. Surely, this type of fatality is counted in the link, but its not an airline so those 9 fatalities don't count when you talk about airline fatalities. Also, there are at least a couple hundred general aviation fatalities each year that likely factor into the statistic. $\endgroup$ – Devil07 May 3 '18 at 21:00
  • $\begingroup$ @Devil07 Is that military? $\endgroup$ – Cloud May 4 '18 at 9:16
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    $\begingroup$ @Fattie That's why one compares deaths per person-mile. $\endgroup$ – David Richerby May 4 '18 at 12:40
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The passage you're asking about is a paraphrase of something Boeing spokeswoman Julie O'Donnell said. If you follow the citation in the article, you can see exactly what she said, and when she said it.

"During the 1950s and 1960s, fatal accidents occurred about once every 200,000 flights," says Julie O’Donnell, a spokeswoman for Boeing. "Today, the worldwide safety record is more than 10 times better, with fatal accidents occurring less than once in every two million flights." [Emphasis added.]

O'Donnell is being quoted in 2014. According to the latest IATA safety fact sheet (published January 1, 2018), IATA measured a fatal accident rate of about one per 2.36 million flights in 2012, and one per 2.58 million flights in 2013. If I were rounding that down for a reporter in 2014, "less than once in every two million flights" is exactly what I'd say.

IATA counted 15 and 14 fatal accidents in 2012 and 2013, respectively. That's an average of one fatal accident every 25 days or so—just like you estimated. As @fooot pointed out in their answer, we've seen fewer fatal accidents in more recent years: an average of one every 30 days, 90 days, 40 days, and 60 days or so in 2014, 2015, 2016, and 2017, respectively.


Statistical postscript

I agree with your gut feeling that, if fatal aircraft accidents were happening at an average rate of one every 20 days, I'd be very surprised to see no fatal accidents at all last year. If fatal accidents were Poisson distributed in time, with a rate of one per 20 days, your chances of seeing no accidents in a year would be less than one in 80 million!

On the other hand, a year with no fatal large commercial passenger jet accidents is totally plausible, given the accident rate of one per 16 million flights that @fooot quotes. In 2017, that comes out to an average accident rate of less than one every 140 days—maybe a lot less, if large commercial passenger jet flights make up only a small fraction of all flights. If fatal accidents were Poisson distributed, with a rate of 1 per 140 days, your chances of seeing no fatal accidents in a year would be better than one in 14.

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The statistic of 100,000 flights per day is a global one, and globally it is not true that there were no commercial airline fatalities in 2017. Per the Aviation Safety Network, there were 7 fatal incidents of commercial passenger aircraft in 2017. It's true that none of these were in the US, and most of these were smaller aircraft that do not get widely reported. If you only consider "large commercial passenger jets," the average is more like 1 in every 16 million flights. However, 2017 was a bit of an outlier. In 2016 there were 14 incidents, which is closer to the quoted average. In 2018 there have been 4 so far.

Fatal incidents are fairly random and will not exactly follow a certain average rate, not even over the course of a year. And with the total number being relatively low, it's even more prone to large fluctuations. The total trend in the accident rate has also been downwards, so we would expect more recent periods to be below average.

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  • $\begingroup$ There have been 4 large commercial disasters this year? Source? $\endgroup$ – Cloud May 3 '18 at 15:10
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    $\begingroup$ 3 of them Then one more (and that doesn't count the single death in the Southwest flight which otherwise landed safely) $\endgroup$ – abelenky May 3 '18 at 15:10
  • $\begingroup$ @Cloud I wasn't limiting it to large planes but it just so happens that they all qualify, the Axios link plus the Southwest accident. $\endgroup$ – fooot May 3 '18 at 15:12
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    $\begingroup$ Sure... 99 people dying is no big deal. Why should we concern ourselves with that? (Colgan 3407 only had 45 passengers + 4 crew on board, but the result of that altered commercial pilot rules for the entire industry) $\endgroup$ – abelenky May 3 '18 at 15:18
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    $\begingroup$ Consider @abelenky's statement carefully. A single incident involving a small aircraft changed the rules for how large 737s should operate -- some causes affect all sizes of planes. It is unfortunate that we sometimes learn our mistakes only due to hindsight and only after fatalities. Therefore if it's for selfish reasons you should care about the cause of crash for all sizes of planes. It is actually quite rare that accidents are caused by aircraft type or sizes because when they happen you will hear about entire fleets being grounded $\endgroup$ – slebetman May 4 '18 at 0:40
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The link is not wrong but your math is a bit misguided. Just because an accident occurred on average every XXX,XXX flights does not mean that on flight XXX,XXX+1 there will be another accident, thats simply not how statistics work.

This also gets complicated due to the FAA's historical records and how the term accident has been used over the years. As regulations have gotten stricter and reporting has gotten more verbose we now have much greater insight into accident information than we did even 25 years ago. The FAA publishers a massive amount of info on the topic, you can find the real numbers for General Aviation here (for the last decade or so) and all accident reports are available here

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  • $\begingroup$ While the term "accident" can be vague, "fatal" is not. It's pretty straightforward to collect statistics on fatal aviation incidents. $\endgroup$ – J... May 3 '18 at 19:21
  • $\begingroup$ +1 Statistics is usually counterintuitive to begin with. When we try to average and extrapolate over something as rare as "major airline crashes" it gets unreliable as well. $\endgroup$ – Agent_L May 3 '18 at 20:55
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    $\begingroup$ The problem is not so much the use of statistics, but rather misunderstanding what the statistics were describing. For U.S. airlines, the number is way less than 1 in 2,000,000 flights. For 2003-2017, it was around 3 in 146,000,000 for scheduled passenger flights and just plain 0 for mainline airliners in scheduled passenger service. $\endgroup$ – reirab May 3 '18 at 21:04
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One can also review the NTSB records to see what the rates were like for more recent years to date. There is a 55MB file .XML that can be downloaded (and opened with what? I have no MS Office tools that will open it like an Excel spreadsheet or similar for sorting/manipulation). I'm pretty sure it's a big table.

https://www.ntsb.gov/_layouts/ntsb.aviation/index.aspx

Here's a row for example:

ROW PublicationDate="05/02/2018" ReportStatus="Preliminary" BroadPhaseOfFlight="" WeatherCondition="VMC" TotalUninjured="2" TotalMinorInjuries="" TotalSeriousInjuries="" TotalFatalInjuries="" AirCarrier="" PurposeOfFlight="Personal" Schedule="" FARDescription="Part 91: General Aviation" EngineType="" NumberOfEngines="1" AmateurBuilt="Yes" Model="KIS" Make="SENO LOUIS C SR" RegistrationNumber="N66SK" AircraftCategory="Airplane" AircraftDamage="Substantial" InjurySeverity="Non-Fatal" AirportName="EAGLE LAKE" AirportCode="ELA" Longitude="-96.321945" Latitude="29.600556" Country="United States" Location="Eagle Lake, TX" EventDate="04/29/2018" AccidentNumber="GAA18CA242" InvestigationType="Accident" EventId="20180430X21704"

The Table is accessible year by year and month by month here, seems a little easier to digest:

https://www.ntsb.gov/_layouts/ntsb.aviation/month.aspx

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  • $\begingroup$ Hi, I'm a developer and we work with XML files, but you do not open them directly as an end-user. You can, however import the data into excel. Please see: support.office.com/en-ie/article/… $\endgroup$ – Cloud May 4 '18 at 15:26
  • $\begingroup$ Cool, thanks. So, we can sort and see 19 accidents, 21 injuries in 2017 and 20 accidents, 27 injuries (20 in just one accident) in 2016 for big iron, with no fatalities . $\endgroup$ – CrossRoads May 4 '18 at 15:56

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