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

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