F-N curve

A common form of societal risk measure is an F-N curve, which is normally presented as a cumulative distribution plot of frequency F... 

Figures 12 and 13 illustrate two of the more commonly used methods for displaying societal risk results (1) an F-N curve and (2) a risk profile. The F-N curve plots the cumulative frequencies of events causing N or more impacts, with the number of impacts (N) shown on the horizontal axis. With the F-N curve you can easily see the expected frequency of accidents that could harm greater than a specified number of people. F-N curve plots are almost always presented on logarithmic scales because of...

While the F-N curve is a cumulative illustration, the risk profile shows the expected frequency of accidents of a particular category or level of consequence. The diagonal line is a line of constant risk defined such that the product of expected frequency and consequence is a constant at each point along the line. " As the consequences of accidents go up, the expected frequency should go down in order for the risk to remain constant. As the example illustrates, if a portion of the histogram sticks its head up above the line (i.e., a particular type of accident contributes more than its fair share of the risk), then that risk is inconsistent with the risk presented by other accident types. (Note There is no requirement that you use a line of constant risk other more appropriate risk criteria for your application can be easily defined and displayed on the graph.)... 

The F-N curve, the risk profile, and the risk contour are the three most commonly used methods of graphically presenting risk results. Normally, you will elect to use more than one of these methods when evaluating risk estimates for decision making. 

F-N curve - A cumulative frequency number affected curve. 

Note that most societal F-N curves extend out to hundreds or even thousands of fatalities. Such events involving process plant buildings are extremely unlikely, since few buildings, if any, within process facilities have such large concentrations of people. Aggregate risk curves should reflect site-specific conditions and realistic events. 

On simple inspection, it appears that the risks presented by the cafeteria exceed the company criteria. However, F-N curves are not always the most effective tools for identifying the major contributors to the risk. More detailed analysis, or use of other aggregate risk methodologies, such as determining expected numbers of fatalities per year, may reveal the risk to be more (or less) tolerable than that shown by the F-N curves. 

Section 4.2.2 discussed the use of methods other than F-N curves for determining aggregate risk. An aggregate risk measure can be calculated for Example 10 by multiplying each incident frequency by the expected number of serious injuries or fatalities. This results in a parameter of "fatalities per year."... 

Societal Risk measures the potential for incidents to affect many people. It has historically been applied as a measure of risk to the general public exposed to the same event or events. Societal risk is often presented as a frequency distribution of multiple-casualty events, called an F-N curve, showing the frequency of events F) leading to N or more fatalities. 

As will be shown in Section 4.2, published data are available on the application of societal risk measures, including the development of risk tolerability limits for F-N curves. However, much of this guidance has been developed for characterizing risks to the general public and would not normally be considered as a basis for assessing risks to on-site personnel. It is appropriate, therefore, to suggest another risk measure, similar in concept to societal risk, for on-site applications to process plant buildings ... 

Figures 6.3 and 6.4 show the adjusted F-N curves. With this risk reduction, the company s aggregate risk criteria would be met Therefore, the emergency shutdown system was installed and no further action was required.

FIG. 23-29 Example of a societal risk F-N curve. (AIChE-CCPS, 1989, p. 4.4.)... 

Societal risks are single number measures, tabular sets of numbers, or graphical summaries that estimate risk to a group of people located in the effected zone of an incident. Since major incidents have the potential to affect many people, societal risk is a measure of risk to a group of people. It is most often expressed in terms of the frequency distribution of multiple casualty events, such as the F-N curve shown in Figure 6-5. The calculation of societal risk requires the same frequency and consequence information as individual risk. Additionally,... 

F-N curve—A plot of cumulative frequency verses consequences (often expressed as number of fatalities). A societal risk measure. 

F-N curve A graphical illustration of the cumulative frequency (F) of acci-... 

The data available for determining accurately F, N curves for such binary mixtures over a complete range of concentrations are limited, but the following examples are typical of the general form... 

For comparison is inserted the F, N curve derived on the basis of ideal solution by the equation... 

It will be observed that the F, N curves for such binary mixtures follow the same course—a rapid followed by a more gentle rise of F as iV increases to a well defined maximum followed by a drop and an asymptotic fall in the F value. In the case of alcohol water mixtures F ax. is obtained at about 0 3A. To find an adequate explanation for the complete F, N curve is by no means an easy matter. It is clear that the first portion of the curve may be taken to represent an increasing surface concentration of alcohol and this proceeds to a limiting value—an observation first made by Milner (Phil. Mag. xill. 96, 1907), who showed that for relatively strong solutions of acetic acid the surface tension of the solutions could be expressed as a function of the concentration of the acetic acid in the following form ... 

The large positive shift and the parabolic behaviour of the 5 = f(N) curves in the case of divalent cations was attributed first by Fraissard at al. [2] to the high polarisability of xenon and the distortion of the xenon electron cloud by the strong electric fields created by the 2+ cations. Later, Cheung et al. [5] proposed a model to explain the strong adsorption of xenon in zeolites with 2+ cations (Ca2+, Mg2+, Ba2+). It consists in extending the electron attraction described above to the point where an electron is transferred from the xenon to the cation. This model suggests that a partial bond between the xenon atom and the 2+ cation is formed by donation of a xenon 5p electron to the empty s-orbital of the 2+ cation. 

Fig. 30. Electron emission from metals with differently shaped surface barriers. j—current density in amp/em1, F—field in volts/A. Calculations for cf> = tf>2 = 4.5 ev, tj> j = 5.5 ev width of conduction band = 0.4 ev d = 2.5A. Slopes of F-N curves identical to better than 1%.

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