# Probability given an occurrence rate (small airplane fatal accidents)

#### TheBard

##### New Member
Hi All,

I would like to know if the method I’m using to calculate a probability based on an occurrence rate is correct or if there is a better method to use.

Here is some context to give you an idea of what I’m working with: I am looking at determining the probability of a fatal accident occurring in a small airplane within the next 20 years vs number of hours flown. I am using historical data from 1974-2016 (2016 is the latest year available) to project rates into the future using an exponential trend line. I am then adjusting these numbers for a variety of reasons (but that is beside the point).

Here are the projected yearly fatal accidents rates per 100,000 hours for 2020-2039 that I am working with:

0.63
0.62
0.61
0.60
0.59
0.58
0.57
0.56
0.55
0.54
0.53
0.52
0.51
0.50
0.49
0.48
0.48
0.47
0.46
0.45

I am very confident in these yearly numbers, so I don’t need any assistance with them. Here is what I primarily need help with:

Even though these rates are technically from an exponential trend line curve, for simplicity I have been using the average of these which is around 0.54 with a reliability equation P = EXP(- #hrs * 0.54/100000) to get the probability of no fatal accident. In the end, I am turning this probability into a “1 in [1/(1-P)] chance” of a fatal accident occurring within the next 20 years vs hours flown. This all assumes number of hours flown per year remains constant. For 1500 hours flown for example, this equates to about a 1 in 124 chance.

Is this the best method to use to calculate the probability of a fatal accident occurring? I’m wondering if there are multiple methods for calculating this kind of probability instead of the EXP(-# hrs * rate) that may be better.

Anyway, if you can provide feedback or help with me determining the best method for this I would be greatly appreciative!

Thanks