Representing Risk:

A risk scenario could be represented in a p,C plot as a dot. As probabilities are numbers between nil and one, hopefully small, but potentially covering five to six orders of magnitude (from 1/1M -1/100’000 to 1) and costs also present wide ranges, it is common practice to use a log-log plot.

As neither the probability p not the consequence C can be known with certainty, one could argue that the dot is actually a surface whose dimensions depicts the uncertainty on p,C, as depicted in figure 1.

Formally; however, it has to be recognized that any given scenario, for example “catastrophic earthquake”, features a full range of probabilities, going from an extremely low value (not to say nil), to a maximum specific to that scenario, and that each one of those probabilities is linked to a specific related value of consequence. Figure 2 displays such a p,C relationship for a regional transportation risk assessment precisely for the scenario “catastrophic earthquake”.

In most studies, there are no data available to allow to derive a complete p,C relationship, thus risk is represented by the so called “risk bubble” which can be understood as an approximate image of the right central part of the full distribution, thus displays a slope towards the higher consequences values.

The risk bubble, as applied in simplified Risk Assessments allows a range of values to be defined by estimating the optimistic and pessimistic values for the cost of consequences and also for the range in likely estimates of the probability of occurrence. The graphical representation even allows displaying possible image/public reaction damages as an extension of the physical damages incurred for a given scenario as depicted in figure 3. As we will see the p-C plot even allows a rational representation of risk tolerability or acceptability as exemplified in the next two pictures taken from a real life example.

In the next two pictures, figure 4 and figure 5 are drawn for a real case study; the risk bubbles are compared with the position of a yellow band which depicts, as explained in detail in client’s tolerability. Anything below and left of the yellow band is tolerable, what is within the yellow band is in an “uncertainty area”, whereas what lies in the red zone is intolerable (for that clients, facility etc.). Interestingly the hazard scenarios compared in these two pictures, drawn from the same case study, i.e. a luxury watch maker in Switzerland is quite varied in nature, going from a gastro-enteric epidemic (ever seen a watchmaker mounting a delicate watch movement meanwhile running to the toilets every ten minutes? ), to the loss of heating fuel, to criminal activities (for outside, or within the company), arson, traffic accidents etc.

The case of a gastro-enteric epidemics hitting a factory or an entire community is not so uncommon as one could think, even in the western industrialized countries: it has happened in Switzerland in several occasions in mountainous regions (water sources possibly contaminated by cows), in Italy, and even more seriously in Quebec, Canada, in recent years. Interested readers can search the web for information on this and other types of diseases capable of hitting an entire production facility.

As it has become apparent with these examples, the bubble is generally displayed with a right downward slope. The reason for this is easily understood with an example. Let us suppose that the risk scenario under consideration is a traffic accident of a light vehicle. The probability of a fender-bender will be relatively high, with a low cost of consequences, when compared to a total destruction of the vehicle, with a low probability and high cost of consequence.

The formal representation of risk including public reaction “costs” is represented in figure 6 where some p,C points on the full distribution have been linked with their potential public reaction costs. Figure 7 shows a common representation of risks along a linear facility.