Farmer’s diagram, or F-N curve – Represent society’s degree of catastrophe aversion.
Overview
An F-N diagram, also called a Farmer diagram after the name of the first author to have used this representation, is a graphical representation of the level of societal risk generated by a technology, activity or a project. The vertical scale (�F) shows the frequency of the events represented, and the horizontal scale represents the consequences (typically the number of deaths, �N). A point (�,�)(F,N) on the curve represents the cumulative frequency of experiencing �N or more fatalities due to the activity represented.
A few comments concerning this graphical representation:
- a lower curve represents a safer situation (the frequency of the negative events is lower);
- F-N diagrams are drawn using a logarithmic scale on both axes, to allow the range of values for both F and N to span many orders of magnitude;
- by construction, an F-N curve is always decreasing (falling or flat) from left to right;
- obtaining all the estimates needed to plot a full F-N curve is a very resource-intensive exercise, because data is needed concerning the whole range of accident severities, from relatively frequently occurring events for which data is often easy to obtain, to very infrequent events for which little (generally no) operating experience is available, and where estimates are produced using risk analysis techniques.
Alongside information concerning the total number of fatalities generated by an activity (represented by the area under the curve, even if this is difficult to assess graphically due to the logarithmic scales), the F-N diagram provides information on the “scale” of accidents (whether deaths are clustered together). Clustered deaths (high-fatality accidents) are typically more socially sensitive and receive more attention from the media than the same number of deaths “spread out” over a large number of small accidents.
Applications
There are three main applications for a Farmer diagram:
- Representing the historical record of accidents associated with an activity;
- Representing the results of a quantitative risk analysis (QRA);
- Specifying criteria for assessing the tolerability of risk.
These are discussed in the following sections:
Historical information on accidents
The following figure, used in a research report funded by the UK HSE, compares the frequencies and severities of fatal railway accidents with those of road and air transport. It is based on accident data from the period 1967-2001.
High-fatality accidents, represented on the left-hand side of the F-N curve, are infrequent compared with accidents that individually kill fewer people. This is not the result of a mathematical law concerning safety, but rather because large accidents generate considerable distress and attention from society, and a lot of effort is therefore put in place to prevent them. This is not necessarily a very rational way for societies to think about safety and accident prevention. As an illustration, one of the activity areas which leads to the largest number of preventable deaths in most industrialized countries is healthcare. Doctors kill (accidentally) large numbers of patients, but almost always only one person at a time, so relatively little attention is paid to preventing these avoidable deaths (for example, there is little safety regulation in healthcare (see the discussion below). There is therefore more uncertainty on the left-hand side of the plot than on the right-hand side, where many more observations are available.
Results of a quantitative risk analysis
An F-N diagram can be used to present in a summarized graphical form the results of a quantitative risk analysis, for example in arguments presented to a safety authority in favour of the building or continued operation of a system or facility. The safety authority will check that the estimated F-N curve is within or below the “ALARP” band.
Social tolerability of a hazardous activity
An early use of F-N diagrams was to estimate the social tolerability of a new hazardous activity. Society must decide what level of risk imposed by a system or technology is tolerable, given its benefits to society.See our slides on Risk acceptability and tolerability for more background information on this topic.
One method of doing this is to compare the risk associated with the new system against the risk of similar systems. If the new system is in an area similar to, or below existing systems, then the risk is likely to be acceptable.
