CEE 597 – Risk Analysis and Management
Midterm Exam
1998
Test is open book and open notes.
You have 50 minutes to complete this 50 point exam.
Show
important steps.
1. (8 points) Use the lessons provided by the case studies as the basis of a 23 paragraph argument in
support of, or refuting, the statement that:
“Most disasters are a result of a simple linear chain of events.”
3. (8 points) A surveyer is going out on an extended trip in Northern Alaska. She is going to take a
special global positioning system (GPS). The critical component on these devices seems to fail randomly
in time so she takes 3 [one in the device, and two for backups]. (a) If the components last on average 50
hours before failing, what is the mean and variance of the time until the surveyor can no longer use the
GPS? (b) What is the probability the system is still operational after t hours? (c) If the surveyer wanted
to be 99% sure the system would still be working after 100 hours, how small would the failure rate of the
components have to be?
4.
(14 points) Consider the system described by the
network
:
5.
A
G
F
E
C
B
D
a)
What are all the minimal cut sets?
b)
What are the minimal paths?
c)
If all elements are 98% reliable, except A which is 99.5% reliable,
what approximately is the probability the system fails?
d)
If you could upgrade one component to 99.5% reliability,
which would you choose to maximize the reliability of the whole system ?
e)
Draw the best fault tree representation of this system that you can.
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View Full DocumentCEE 597 – Risk Analysis and Management
Midterm Exam
1998
5. (10 points)
Pipelines are reasonably reliable means of shipping gasoline, but occassionally there are
failures. Consider pipelines of three sizes: large, medium and small. Assume the frequency of pipline
spills for large pipes is one per 2000 days, for medium pipelines is 1 per 500 days, and for small piplines
is one per 100 days in the Northeastern US. The probability of different size spills when a pipline breaks
are listed below:
size of pipe
size of spill (gal)
probability
large
100,000
0.2
50,000
0.3
10,000
0.5
medium
50,000
0.1
10,000
0.4
2,000
0.5
small
10,000
0.2
2,000
0.8
The probabilities of an explosion due to a spill are:
Size of spill 2,000
10,000
50,000
100,000
gallons
Prob. Explosion
0.001
0.005
0.01
0.1
(a) Draw an event tree for this problem
(b) Compute the risk profile for the size of pipeline spills. [No graph needed; table will suffice.]
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 Spring '07
 Stedinger
 Three Mile Island, The Land, Trigraph, Mile Island, Risk Analysis and Management

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