Modelling Under Risk and Uncertainty: An Introduction to Statistical, Phenomenological and Computational Methods

3.1 Phenomenology and Motivation of the Example

Consider a vulnerable installation located on a river bank: housing, industrial facilities or power plant benefiting from the cooling resource and so on. The risk situation can be characterised schematically by the following components:

• hydro:– flood flows q may entail high water levels, potentially flooding the installation if the maximal level z_c occurring during a flood event overflows the crest of the dike (supposedly at level z_d), (see Figure 3.1)
• systems reliability:– conditional on dike overflow (an event defined by s = z_c − z_d > 0), an elementary protection system, comprising plant isolation active or passive devices, exhaust pumps and so on, which may or may not contain the consequences of failure,
• economics:– the final detrimental consequences depend upon the effective vulnerability of the facilities, largely unknown at the time of the hypothetical event. They are encapsulated in an overall cost of damage c_d. It adds up to the more-manageable investment costs c_i resulting from design decisions so as to form the complete cost c_c to be optimised.

Referring back to the generic concepts in Chapter 2, the outputs of interest (vector z) may here include various variables or events according to the decision-making framework and components included in the system model:

• the overflow s,
• the overflow event E_o = {s| s > 0},
• the plant failure event E_p,
• or the total cost c_c.

In fact, the decision-making framework can involve schematically ...