RISK5002 Chap.5 Risk Maps and F-N Diagrams
Risk Maps and F-N Diagrams
Risk maps show how hazard likelihood, intensity or expected consequence vary across places, which makes them powerful for planning, insurance and emergency services, but also easy to misread. F-N diagrams handle a different question: the frequency of accidents that kill N or more people.
On log-log axes, criterion lines split the plot into intolerable, ALARP and broadly acceptable regions, and the slope expresses aversion to large accidents. This chapter sets out the uses, inputs, outputs, strengths and limitations of both tools, derives a criterion F(N) = aN to the minus b from two anchor points, tests a fuel depot against it, and interprets regions in the style of a past exam figure.
Two Australian cases anchor the interpretation. The NSW parks procedure treats a hazard able to kill more than one hundred people case by case, and the Botany Industrial Park assessment placed its societal risk in the ALARP zone under the HIPAP 4 criteria.
The chapter uses them to show what a planning authority does with each region, and it lists the limitations that make two F-N diagrams hard to rank against each other when one shows frequent small accidents and the other rare catastrophes.
What this chapter covers
- 01
Risk maps: use, inputs and outputs
- 02
Misreading return periods
- 03
F-N axes and criterion lines
- 04
Intolerable, ALARP and acceptable regions
- 05
Solving for a and b
- 06
Societal risk in planning decisions
Worked example · free
Derive an F-N criterion and test a depot against it
- +1Divide the anchors: 0.001 / 0.00001 = 100 = 10 to the power b, so b = 2.
- +1Substitute: 0.001 = a x 10 to the minus 2, so a = 0.1 and F(N) = 0.1 N to the minus 2.
- +1At N = 5 the criterion is 0.004, above the depot's 0.002; at N = 20 it is 0.00025, below the depot's 0.0004.
- +1Part of the curve exceeds the line, so the depot fails and needs measures for accidents near twenty deaths.
Key terms
- Risk map
- A geographic display of how hazard likelihood, intensity or consequence varies across regions.
- Return period
- The average interval between events of a given size, often misread as a schedule.
- Risk aversion parameter
- The exponent b in F(N) = aN to the minus b, setting the criterion slope.
- HIPAP 4
- The NSW planning advisory paper whose criteria are used to judge hazardous industry risk.
Risk Maps and F-N Diagrams FAQ
What do the axes of an F-N diagram show?
The horizontal axis shows the cumulative number of fatalities N and the vertical axis the frequency F of events causing N or more fatalities. Both axes are logarithmic so that rare, large accidents and frequent, small ones fit on one chart.
How do I find a and b for a criterion line?
Write F(N) = aN to the minus b for each of the two given points, divide one equation by the other to eliminate a and solve for b, then substitute b back into either equation to find a.
What are the limitations of risk maps?
They rely on past data that may miss emerging or climate-driven risks, their return periods are easily misinterpreted, static maps oversimplify dynamic hazards, they can raise equity concerns through property values and premiums, and they attract controversy when events prove them wrong.
What does the ALARP region mean for a decision maker?
Risk in the ALARP region is neither intolerable nor broadly acceptable. The operator must reduce it as low as reasonably practicable, which means adopting further measures unless their cost is grossly out of proportion to the benefit. In an answer, name the part of the curve in the band and suggest specific measures for that range of fatalities.
Exam move
Practise solving two-point criterion problems with different exponents until the division step is automatic, and sketch each result on log-log axes to check the slope. For interpretation, describe any F-N figure in four moves: which regions the curve occupies, its maximum N against any cap, how quickly frequency falls, and what action follows. Learn the risk-map limitations as a list of five with one example each.
Keep a short list of the published examples, the England, Netherlands and Czechia slopes and the HIPAP 4 limit, and practise citing one of them whenever a question asks you to compare a curve with a criterion.
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