CEE 360/548: Risk Assessment and Management
Prof. E. VanMarcke
Problem #1
RISKS TO A STAGE-COACH MISSION
There are three way-stations on the route of the Dead Eye stage-coach from Hangman's Hill to Placer Gulch.The distance are as follows:
The maximum distance the stage-coach can travel without a change of horses, which can only be done at the way-stations, is 85 miles. The coaches change horses at every opportunity. However, the way-stations are raided frequently, their livestock driven off by marauding desperados.
In risk assessment of this situation, the event of concern is "mission failure", that is, the stage-coach not reaching its final destination, Placer Gulch. Risk management might involve, say, assigning to sheriff's deputies the duty of protecting the way stations.
The questions fall into three categories:
(a) Event Modeling
Analyze the predicament of the stage-coach by constructing
(i) an event tree
(ii) a fault tree
(iii) a block diagram
Define all relevant events and show where they fit on the event or fault tree, and on the block diagram.
(b) Risk Assessment
Denote by p the chance of finding a particular way-station "raided" (i.e., without horses), the same chance for each station, and assume that events are independent from station to station.
Express the "risk of stage-coach mission failure" in terms of p.
(c) Risk Management
Consider these two ways of using a posse of sheriff's deputies to protect the stage-coach route:
Option 1: Protect just one station, with full effectiveness; the chance of the protected station being raided drops from p to 0.
Option 2: Protect all stations equally, so that the chance of finding any one station raided drops from p to (2/3)p.
Questions:
(i) Under Option 1, which station should be protected? Why?
(ii) Which of the two options can achieve the greatest amount of risk reduction? Does it matter what the value of p is? Explain.
An additional question for CEE 548 registrants (optional for CEE 360 registrants):
How would you solve the risk assessment problem if the distances between consecutive points along the road of the stage-coach were not known exactly, say, if they could be modeled as independent Gaussian (normal) random variables with mean values equal to those given above, and with a coefficient of variation (ratio of standard deviation to mean) of 0.2, the same for each of the four inter-point distances. Just outline your proposed method of analysis.
Problem #2 -- Decision Analysis
Your friend who went to California and into business after high school plans to build a new $2,000,000 home on a site overlooking Silicon Valley. He needs your advice, having become painfully aware of the earthquake hazard he faces: the site is on a steep slope known to be susceptible to landslides during earthquakes. During the period of about 10 years he plans to live in the house, there is a 10% chance of a damaging earthquake that would cause a slide and the loss of the entire ($2-million) investment. If such an earthquake occurs, it will be "moderate" with 80% probability and "severe" ("the Big One") with 20% probability. Your friend considers three possible actions:
Questions:
(a) Draw a decision tree showing possible actions, relevant events, and monetary consequences.
(b) If money is the only consideration and your friend claims to be indifferent to risk (i.e., he makes decisions on an expected-value basis), which of the three alternatives do you recommend? Show why.
(c) Another option is to strengthen the foundation (Action 2) and then take earthquake insurance to cover the potential financial loss during a severe earthquake. At about what level of annual premium does this become a good deal, on the basis of total expected cost?