## 2 Theoretical Basis about Risk
### ALARP Risk Evaluation Criteria
In other words, it can be defined as the risk of death to which a single individual is subjected in an unsafe place at a given moment in time. This risk gives an annual probability of death value for a certain position. The social risk, on the other hand, is given by the frequency with which a certain number of people are subjected to a certain level of damage following a specific accidental event. This risk is well illustrated by the F-N curve, which correlates the number of deaths (N) on the horizontal axis with the frequency (F) of one or more deaths on the vertical axis. These curves were developed originally to assess nuclear risks since tolerance thresholds, which reflected the social aversion to more deaths during a single catastrophic event. In these charts, the two thresholds of risk acceptability and tolerability are a function of such parameters as slope and anchor point. A first indication of the development of the social risk curves is given by the historical accident curves in each region, which are important indications of the starting point and the slope to be associated with the limit lines. The former parameter, the anchor point, is the cumulative limit frequency (F) for a certain number of fatalities. The inclination, on the other hand, which is always negative and generally ranges between \(-1\) and \(-2\), is a function of risk aversion towards accidents with a progressively increasing number of fatalities [27; 28; 29]. Figure 3 shows a generic F-N graph, divided into four areas. In the unacceptable region, the risk should be reduced regardless of the investment. It follows that if an investment is unsustainable, exposed people should be turned away. In the intense security  
Figure 2: The ALARP principle. region, the probability of the catastrophic event occurring is very low but must always be kept under control. In the widely acceptable region, no investment is needed to further reduce risk. Finally, in the tolerable region, risk should be further reduced if the ALARP principle is practicable, that is cost-benefit approaches are used to evaluate the convenience of a mitigation option or to compare the various possible interventions. In other terms, the costs of implementing risk reduction measures are compared with the reduced risks assessed in monetary terms, thus assigning an economic value to life. In literature, there are several estimates of the economic value of life in which people are considered as a resource in economic activities. However, the ethical criticisms to this approach are equally relevant. Thus, cost effectiveness analysis is often used to avoid attributing a cost to human life [30]. According to this method, the ratio between the cost of the risk reduction measures and the risk reduction itself is assessed, avoiding giving life an economic value. In this case, indicators such as gross-cost-of-a-fatality (GCAF) and net-cost-of-a-a-fatality (NCAF) are estimated:  
\[\text{GCAF}= \frac{\Delta\text{C}}{\Delta\text{R}}, \tag{1}\] \[\text{NCAF}= \frac{\Delta\text{C}\ -\ \Delta\text{B}}{\Delta\text{R}}, \tag{2}\]  
where \(\Delta\text{C}\) is the cost of the risk mitigation intervention; \(\Delta\text{B}\) is the benefits of implementing the mitigation strategy; \(\Delta\text{R}\) is the risk reduction arising from the planned intervention, in terms of victims or damage avoided. To understand the dynamism and applicability of the ALARP approach, it is increasingly used for land-use planning in the immediate vicinity of industries or dams, for landslide risk management as well as for risk assessment in tunnels [31; 32]. According to [PERSON] [33], the ALARP principle provides a useful framework for establishing risk tolerance criteria. [PERSON] et al. [34] argue that the ALARP principle should be interpreted dynamically. Again, [PERSON] [35] believes that the ALARP criterion  
Figure 3: Societal risk evaluation criteria: example of a risk curve on the F-N plane. can represent \"a general thinking way\".