Date:13 Oct 98 02:48:14From:standaert@mail.chem.tamu.edu (Bob Standaert)Organization:Department of Chemistry, Texas A&M UniversityReferences:1 2

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It is hard to conclude much about the relative safety of the A320 and 737 on the basis of statistics alone. We are (most fortunately) comparing frequencies of low probability events, and the number of events and flights is too small to produce a meaningful distinction. What follows is an illustration of the point in my typically longwinded style... I apologize for the length and hope that there is enough substance to make up for it, at least in part. Interpreting the observed frequency of improbable events is something that must be undertaken with caution. I'll add extra caution by saying I am not a statistician, only someone who has occasion to use statistics and tries to be careful with them. Let's suppose we do, in fact, know the "true" probability P that an event will occur. We can use the Poisson distribution to calculate the probability F that we will observe X events in N tries: F = [(NP)^X]*[exp(-NP)]/X! What we will find is that many values of X are reasonably possible. Taking Karl's criterion of the hull loss as the event of interest, let's work from the assumption that both airliners have an identical frequency of events, P = 1.2/Mflight. For the sake of argument, let's also lump all of the 737's together. The probability F of observing X losses in N flights is given in the table below. The "SUM" columns refer to the cumulative probability; for instance, with the 737, the chance that we would observe <70 events is 4.6%, the chance we would observe more than 100 is 4.6% (100 - 95.4), and there is a roughly 90% chance that we would observe between 70 and 100 events. For the A320, the corresponding range is 3-10. | 737 (N = 70.6M) | | A320 (N = 5.2 M) | |______________________| |_______________________| | | | | X F(%) SUM X F(%) SUM ---- ------ ------ ---- ------ ------ <70 4.6 0 0.2 0.2 70 1.2 5.8 1 1.2 1.4 71 1.5 7.2 2 3.8 5.2 72 1.7 9.0 3 7.9 13.1 73 2.0 11.0 4 12.3 25.4 74 2.3 13.2 5 15.4 40.8 75 2.6 15.8 * 6 *** 16.0 *** 56.8 * 76 2.9 18.7 7 14.3 71.0 77 3.2 21.8 8 11.1 82.1 78 3.4 25.3 9 7.7 89.9 79 3.7 29.0 10 4.8 94.7 80 3.9 32.8 11 2.7 97.4 81 4.1 36.9 12 1.4 98.8 82 4.2 41.1 13 0.7 99.5 83 4.3 45.4 14 0.3 99.8 84 4.3 49.8 15 0.1 99.9 * 85 *** 4.3 *** 54.1** 16 0.0 100.0 86 4.3 58.3 17 0.0 100.0 87 4.1 62.5 18 0.0 100.0 88 4.0 66.5 19 0.0 100.0 89 3.8 70.3 20 0.0 100.0 90 3.6 73.9 91 3.3 77.2 92 3.1 80.3 93 2.8 83.0 94 2.5 85.6 95 2.2 87.8 96 2.0 89.8 97 1.7 91.5 98 1.5 93.0 99 1.3 94.3 100 1.1 95.4 >100 100.0 In both cases, the most probable outcome (starred) is that we will observe the average number of events (P*N), but there are many other outcomes that are nearly as likely, or at least reasonably likely. As noted above, 90% of the probability falls between 70-100 events for the 737, and 3-10 for the A320, but there is still a 10% probability that we would observe event numbers outside these ranges due to chance alone! I started with the assumption that both birds have identical "true" event frequencies. We can go one step further and ask the following question: what "true" event frequencies are consistent with the observed number of events? Let's take as our criterion that the observed number of events must be within the middle 90% of the probability distribution for the "true" frequency. With a little hacking around on a spreadsheet, I came up with the following ranges (events/Mflight): 737 A320 --------- --------- 1.00-1.44 0.63-2.02 With the 737, we have a much better idea of where the "true" frequency is because we have many more data. The A320 could be significantly better, significantly worse, or (most likely) about the same. There just isn't enough experience yet to pin it down so well. I find it much more informative to discuss (or at least read while others discuss) the specifics of individual events and what they reveal. Regards, Bob --I don't speak for Texas A&M, Texas A&M doesn't speak for me, and we're both happier for it.