CALCULATING PROBABILITY
The simplest description of the calculation comes from
Richard Profit's book:
Profit, R. (1995) Systematic Safety Management in the Air Traffic Services, Euromoney
Publications, London. Great book  go get it if you are serious about system
safety.
Risk is defined as the probability and the expected consequences of a hazard arising. Probability is measured on a scale between zero and unity. Unity represents absolute certainty that something will happen. Zero represents impossibility. Thus, the probability that one day I shall die regardless of my lifestyle = 1. The probability that I shall become an archbishop = 0, especially if they found out about my 40th birthday party. The probability that a coin will come down heads = 0.5. The empirical probability of an event can be expressed as:
Probability (p) = Total number of occurrences of the event
Total number of trials
For example, if records show that the loss of surveillance radar at an airport had occurred twice in the past six years (approximately 52560 hours), it may be assumed that the probability (p) of losing that radar is: p = 2/52560 = 0.000038 per operational hour. The number 0.000038 is normally expressed as 3.8 x 10^{5}, or more conveniently, as 3.8E^{5}. Note the important bit  per operational hour. It is not just "probability" but "probability per hour/year/flights/engine hours/1000 pax"
A couple of tables can help here with the calculations:
HOURS PER PERIOD  full time operation 

day 
week 
month 
year 

1 
24 
168 
730 
8,760 
2 
48 
336 
1,460 
17,520 
5 
120 
840 
3,650 
43,800 
6 
144 
1,008 
4,380 
52,560 
10 
240 
1,680 
7,300 
87,600 
12 
288 
2,016 
8,760 
105,120 
13 
312 
2,184 
9,490 
113,880 
25 
600 
4,200 
18,250 
219,000 
50 
1,200 
8,400 
36,500 
438,000 
100 
2,400 
16,800 
73,000 
876,000 
A runway is closed for 28 hours a year for repairs. That's 28 hours per 8760 hours, which is a rate of 0.0032 per operational hour. In scientific notion, it is expressed as 3.2 x 10^{3}
HOURS PER PERIOD  12 hrs/day operation 

day 
week 
month 
year 

1 
12 
84 
365 
4,380 
2 
24 
168 
730 
8,760 
5 
60 
420 
1,825 
21,900 
6 
72 
504 
2,190 
26,280 
10 
120 
840 
3,650 
43,800 
12 
144 
1,008 
4,380 
52,560 
13 
156 
1,092 
4,745 
56,940 
25 
300 
2,100 
9,125 
109,500 
50 
600 
4,200 
18,250 
219,000 
100 
1,200 
8,400 
36,500 
438,000 
The runway lights break every month. That's 12 nights a year. Assume they work/break 12 hours a day. So 12*12=144 hours per year, and operations are night only of course which is 4380 hours. The rate is 0.033 per operational hour. In scientific notion, it is expressed as 3.3 x 10^{2}. It can also be seen that, for this example only, the runway is an order of magnitude more reliable than the runway lights.
Last updated 20 May 2004