IPET Report 3 Vol VIII

Probabilistic Risk Model
Risk associated with the hurricane protection system is quantified through a regional
hurricane rate (λ) and the probability P(C > c) with which a consequence measure (C) exceeds
different levels (c). The loss exceedance probability per event is evaluated as
PC ( > c) = ∑∑ Ph ( i) PS ( j | hi) PC ( > c| hi, Sj)
(1)
i j
An annual loss exceedance rate was estimated as follows
λ( C > c) = ∑∑ λP(
hi) P( Sj | hi) × P( C > c| hi, Sj)
(2)
i j
Where P(hi) is the probability of hurricane events of type i, P(Sj|hi) is the probability that the
system is left in state j from the occurrence of hi, and P(C > c | hi, Sj) is the probability that the
consequence C exceeds level c under (hi, Sj). Summation is over all hurricane types i and all
system states j in a suitable discretization. Simulation studies of hurricanes for risk analysis
require the use of representative combinations of hurricane parameters and their respective probabilities.
The outcome of this process is a set of hurricane simulation cases and their respective
conditional rates λP(hi).
Evaluation of the regional hurricane rate λ and the probability P(hi), the conditional probabilities
P(Sj | hi), and the conditional probabilities P(C > c |hi, Sj) is the main objective of the
hurricane model, the system model, and the consequence model, respectively. The probability
P(Sj | hi) covers the states of the components of the HPS, such as closure structure and operations,
precipitation levels, electric power availability, failures modes of levees and floodwalls,
and pumping station reliability. To assess the state of the HPS given a hurricane event requires
an evaluation of the reliability of individual structures, systems and components (e.g., levees,
floodwalls, pump systems) when they are exposed to the loads and effects of the hurricane (e.g.,
the peak surge, wave action) and the relationship of these elements to the overall function of the
system to prevent flooding in protected areas. A detailed description of the risk model is
provided in Appendix 9.
Event Tree
The probability tree of Figure 4 was simplified to determine the rate of flooding levels and
displaying the results as inundation contours within the basins. The processes of transforming
inundation to consequences is simplified by grouping communication, warning decision and
public execution into an exposure factor parameter applied to lives and property at risk, and
grouping power and pumping availability into one event. The resulting event tree appropriately
branched out is shown in Figure 6. The events of the tree are defined in Table 1.
VIII-14 Volume VIII Engineering and Operational Risk and Reliability Analysis
This is a preliminary report subject to revision; it does not contain final conclusions of the United States Army Corps of Engineers.