CIV 360/548: Risk Assessment and Management
Prof. Erik VanMarcke
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 distances are as follows:
(If your browser does not show the picture, just draw a rough map of the area, and indicate on it the points of departure and destination of the stage-coach, and the three way-stations.)
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 CIV 548 registrants (optional for CIV 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.