Societal risk

Societal risk is the relationship between the frequency of harmful events and the number of people harmed in each event, within a given population. The term is used for hazards, such as large fires and explosions, that can harm many people at once. It takes account of the likelihood of multiple casualties, which a single risk value for one person does not show. Individual risk describes the risk to a person at a specified location, whether or not anyone is present there. Societal risk, by contrast, depends on how many people are present and how likely they are to be exposed.

Societal risk is often presented as an F-N curve, a plot of the frequency of exceeding a given number of fatalities against that number, as part of a quantitative risk assessment. Australian building codes have evolved partly in response to loss of life, and their requirements tend to reflect community values about both individual and societal risk. Whether a given societal risk is acceptable remains a value judgement, because a universally acceptable level of fire risk does not exist.

Definition and scope

Barry describes societal risk, sometimes called population risk, as a measure of human risk that takes into account the likelihood of multiple casualties from fires or explosions. The Fire Safety Verification Method handbook of the Australian Building Codes Board defines it as the relationship between frequency and the number of people suffering a specified level of harm in a given population. The harm results from the realisation of specified hazards. In that handbook, the given population is normally the population of the building under study, and of adjacent buildings where appropriate. The specified hazard is a fire within or involving these buildings.

Individual risk and societal risk answer different questions. In the same handbook, individual risk is the frequency at which an individual may be expected to sustain a given level of harm from a fire in the building. Barry notes that individual risk contours show the expected frequency of harm at a location regardless of whether anyone is there to suffer it. A societal risk estimate, in contrast, needs a definition of the population at risk, the likelihood that people are present and the reliability of measures such as evacuation.

The same individual risk contours around a hazard (left and right) with few and with many people present. Individual risk is the same; the risk of multiple casualties is not. Based on Barry (2002), pp. 5-210 to 5-211.

Both measures describe parts of the same underlying fire risk. Watts and Hall define the risk of a building as the full probability distribution of fire events and their consequences. They regard the many published definitions of risk as summary measures taken from that distribution. It follows from these definitions that societal risk keeps the information on the size of each event, which an average value would hide.

Barry's example of an individual risk profile shows how individual risk falls with distance from a source. At the nearest plotted point, about 125 ft (40 m) from the liquefied petroleum gas (LPG) tanks of a plant, the fatality probability is 7.43 × 10⁻⁴ per year. At 650 to 700 ft from the tanks, about 200 m, it has fallen to 7.7 × 10⁻⁶ per year. How much societal risk such a profile implies depends on how many people live or work at each distance, which the profile itself does not show.

Individual risk profile: fatality probability per year against distance north from the LPG tanks of an example plant. Based on Barry (2002), p. 5-210.

F-N curves and risk indices

An F-N curve plots the cumulative frequency $F$ of multiple fatalities against the number $N$ of fatalities. The vertical axis gives the frequency of events that exceed a specified number of fatalities. Barry gives this definition in words. In formula form, in the notation of this article, the curve value at $N$ for a set of possible events is the sum of the frequencies of all events that harm more than $N$ people:

$$F(N)=\sum _{i:N_i>N}{f}_i$$

A logarithmic plot is usually used, because the frequencies of different numbers of fatalities may range over several orders of magnitude. The contributions of different parts of a facility can be shown as separate curves in the same graph. Barry's example shows a total facility curve together with curves for shore-based operations and marine transfer operations. Such curves give insight into the risk of a facility both to the employees on the site and to the community beyond its boundaries.

A second way to summarise societal risk is a single number. Societal risk can be expressed as risk indices, which sum the risks from each accident and give an annual predicted fatality rate. Such an index gives a single number that is easy to understand and useful for comparing design and protection options. In the notation of this article, the annual predicted number of fatalities is:

$$E=\sum _i{f}_i{N}_i$$

Barry lists examples of such indices, including the fatal accident rate, the average rate of death, the equivalent social cost index and the mortality index. A ranking of the events that contribute most to the total risk is also useful, because it directs attention to the most critical failures. It follows from the two formulas that an index such as the annual rate of death treats ten small events like one large event with the same total. The F-N curve keeps them apart.

Symbol	Description	Unit
$F(N)$	frequency of events that harm more than $N$ people	year−1 (or per fire, in a conditional analysis)
$N$	number of people harmed (usually fatalities)	persons
$f_i$	frequency of event $i$	year−1 (or per fire)
$N_i$	number of people harmed in event $i$	persons
$E$	expected number of people harmed (annual predicted fatality rate)	persons per year (or per fire)

Both forms rest on consequence models that translate exposure into harm. Most quantifications of human risk are based on fatalities. Barry stresses that it is uncertain what exactly constitutes a fatal dose of thermal radiation, blast or toxic chemicals, so every assumption must be documented. For people in buildings, exposure models range from simple tenability limits to fractional effective dose models and probit functions.

Societal risk in building fire safety

The Australian handbook requires designers to consider both individual and societal risk. A proposed performance solution must achieve a fire safety level at least equivalent to that of a reference building that complies with the deemed-to-satisfy provisions. The choice of reference building is therefore critical, because it is the basis for quantifying the acceptance criteria for both measures. The reference building indirectly defines the acceptable levels of individual and societal risk, and its choice needs the consensus of the stakeholders. Where appropriate, the surrounding land use is also considered.

The handbook warns that the impact of this choice on societal risk may not be apparent from a superficial review. Its example is an apartment building in which the travel distance from an apartment door to a single fire-isolated stair is extended from 6 m to 12 m. With the same footprint and number of occupants, a deemed-to-satisfy layout would need two stairs. A smaller single-stair reference building with a 6 m travel distance would have half the population. The proposed building would then have twice the population at risk and twice the number of fire starts, with a significant effect on societal risk.

Proposed apartment floor with one stair and 12 m travel distance (left) and an unsuitable smaller reference with half the apartments (right). Based on Australian Building Codes Board (2020b), pp. 46 to 47.

The size and form of a building can also call for more analysis. For high-rise buildings above an effective height of 60 m, the handbook suggests a more extensive analysis of structural behaviour in fire. This addresses the potential increase in societal risk from a catastrophic collapse. For some very large buildings with large populations, a more detailed analysis of the risk of unexpected catastrophic failure may also be appropriate.

Codes can also link requirements directly to the number of people at risk. In New Zealand, C/VM2 (second edition, 2025) contains a design scenario, RC, that tests a design for the failure of key fire safety systems. The scenario applies where such a failure could expose more than 150 people to untenable conditions. Lower thresholds apply to sleeping occupancies, at more than 50 people, and to people who are detained, receiving treatment or care, or in early childhood centres, at more than 20 people.

Care settings show how one fire can harm several people. Beard developed a stochastic model for the number of deaths in a fire and applied it to a fire starting on a bed in a hospital ward. The model gave a likelihood of more than 80% of multiple fatalities once the fire exceeded 50 kW. The model assumed that the fire did not spread beyond the ward.

Worked example

The handbook's comparison of two fire safety systems can be read as a small societal risk calculation. In both designs, nobody is exposed to untenable conditions if the system works, and 2 people are exposed if it fails. The probability of failure per fire is 0.1 for system A, in the reference building, and 0.3 for system B, in the proposed design. Each design therefore has one harmful event per fire, with $N_i=2$.

Per fire, the F-N curve of each design is a single step. Events exceeding one person occur with a frequency of 0.1 for A and 0.3 for B, and no event exceeds two people. The expected number of people exposed per fire follows from the second equation:

$$E_{\mathrm{A}}=0.1\times 2=0.2,E_{\mathrm{B}}=0.3\times 2=0.6$$

Design B carries three times the risk of the reference design, although a deterministic analysis of the same two scenarios would find them equivalent. The apartment example adds a further effect. If a building has twice the fire starts of its reference, and a failure is assumed to expose twice as many people, the step moves from 2 to 4 people and its height doubles. The expected number exposed then rises fourfold, from 0.2 to 0.8 per reference fire, although the fire development is unchanged.

F-N curves per fire for the worked example: reference system A, proposed system B, and system A with twice the fire starts and twice the people exposed. Based on Australian Building Codes Board (2020b), pp. 47 and 118 to 119.

Acceptability and risk aversion

Acceptable risk is a value judgement applied to a chosen scale of risk. It requires a decision on how risk is measured and on whose views of acceptability are used. For an authority, acceptable risk is meant to be acceptable to society in general or to a particular community. In a fire and explosion risk assessment, these limits are set at the start as severity limits, likelihood limits and the risk tolerance of management. Results can also be ranked against other voluntary and involuntary risks. If the risk is unacceptable or uncertain, cost-effective options for reducing it are identified and selected.

Watts and Hall ask whether the recent fire losses of a country represent a level of risk that its citizens accept. If they do not, it is unclear why so little attention is paid to the problem; if they do, it is unclear why every serious fire is followed by a great clamour for change. They distinguish technical, societal, enforcer and managerial value judgements, which can rate the same measure, such as residential sprinklers, quite differently.

People do not judge equal calculated risks equally. Studies of risk perception have found preferences for more certainty over less, for familiar over unfamiliar risks and for voluntary over involuntary risks. They have also found preferences for common or ordinary risks over dramatic or memorable ones. Individuals and organisations are inconsistent in their risk aversion, and the view that the present level of public fire risk must be acceptable is not a fully reliable generalisation.

Zero risk is not an achievable goal. Watts and Hall describe the goal that comes closest to it as risk as low as is technically possible: the residual risk after all identified risk reduction measures have been adopted. Australian safe design practice follows a related test. Under the code of practice of Safe Work Australia, control measures should eliminate risks or, if this is not reasonably practicable, minimise them. Where risk reduction is weighed against its cost, human risk may have to be converted into equivalent monetary terms.

The Netherlands shows the problem of implicit acceptance levels. Dutch building regulations do not state how many deaths or injuries a fire may cause. Their requirements grew partly from consensus and history rather than from quantified goals. Van Rossum notes that the chance of dying in a fire, per hour of stay, is much greater in a residential building than in an assembly building. Yet the requirements for fire detection are stricter for assembly buildings.

Limitations and uncertainty

A societal risk estimate is only as good as its population data. The number of people present, their location over time and the reliability of evacuation all enter the calculation, and each is uncertain. Barry recommends presenting results with an uncertainty bandwidth. This is especially important for rare events with large consequences, whose likelihood may be highly uncertain.

The consequence side adds further uncertainty, because the doses that cause death or injury are themselves uncertain. Comparative methods carry their own risk. A reference building with a different population or number of fire starts can distort the societal risk comparison, without this being apparent at first sight.

Finally, a societal risk estimate does not settle acceptability. The acceptable level depends on the problem context, on the alternatives and on the person or group that judges it. The reference-building approach defines acceptable levels only indirectly, by comparison with a building that complies with the regulations. In the Netherlands, Van Rossum observes that fire safety engineering has no risk-based limit values at all.

See also

• Event tree analysis
• Fire risk assessment
• Fire statistics
• Uncertainty analysis

References

• Australian Building Codes Board. (2020b). Handbook: Fire Safety Verification Method (Print version 1.1).
• Barry, T. F. (2002). Quantitative risk assessment in chemical process industries. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 5-176–5-213). National Fire Protection Association; Society of Fire Protection Engineers.
• Ministry of Business, Innovation and Employment. (2025b). Verification Method C/VM2: Framework for fire safety design (2nd ed.).
• Ramachandran, G. (2002c). Stochastic models of fire growth. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-381–3-401). National Fire Protection Association; Society of Fire Protection Engineers.
• Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.
• Watts, J. M., Jr., & Hall, J. R., Jr. (2002). Introduction to fire risk analysis. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 5-1–5-7). National Fire Protection Association; Society of Fire Protection Engineers.