Problem $2(55)$

Given: You are tasked with evaluating three possible foundation design alternatives for a new

bridge considering extreme flood limit state, possible damage, and repair cost, and a $75-$year

design service life. The occurrence of an Extreme Flood Event is best estimated by the Poisson

distribution and the AASHTO standards require that foundations are designed for an extreme

flood event with a $500-$year recurrence $($Hint: annual occurrence is $\mathrm{.}002/$year$).$ Associated costs

and conditional probabilities are listed in the following table.

Find: Using Decision$-$Tree Analysis Method provide the following:

a$.)$ Construct the decision tree model representing each alternative decision and all possible

outcomes $(10)$

b$.)$ Determine expected value $($cost$)$ for each foundation type and the preferred decision

based on the minimum expected cost criteria. $(10)$

c$.)$ Determine the expected value of perfect information $($EVPI$).(5)$

d$.)$ Develop a cumulative risk profile for each foundation decision. $(10)$

e$.)$ Which strategy is preferred based on total risk? Explain $(5)$

f$.)$ Assume that a flood study can be performed at the proposed bridge location. The firm

you plan to hire has conducted several flood studies in that region, and $15\%$ of those

studies resulted in reports that forecasted significant flood events. Further, the actual

occurrence of significant flood events in the region was $95\%$ accurate compared to the

firm's reports. What is the expected value of this firm's flood study $($EVSI$)?$ Should you

hire them? Explain? $(15)$