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CEE
597

Risk Analysis and Management
Final Exam
May
17,1995
An apology: I hope you learned more than a simple test like this can reveal.
Test
is open book and open notes.
<And too long.>
You have 150 minutes to complete this 150 point exam.
Balance your effort with the points.
Show
important steps.
1.
(12 points)
Terrorist attacks in this country make big news (bombings, airplane
sabotage, poison in water supplies, cyanide in Tylenol capsules, and that sort of
stuff). Assume that attacks within the country killing
2
5
people an expected to
occur on average once ever
4
years, following a Poisson Process.
a) If I started collecting information on attacks now,
what is the mean and variance of the time I would have to wait
to gather information on 10 attacks?
b) What is the probability of more than 2 attacks in the next 10 years?
What is the probability of an attack in the next month?
C)
Why might a Poisson process be a good model of terrorist attacks?
What weaknesses would a Poisson model have
?
2. (20 points) Consider the system described by the network:
a)
What are the minimal cut sets
?
b)
What are the minimal paths if B is not functioning
?
c)
If
all elements are
99.9%
reliable,
what approximately is probability this system will fail
?
d)
Draw the best fault tree you can to describe this network.
Is it a proper fault tree? If not, what is the problem?
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(6 points) Consider a system with two independent components in series.
Assume arrival rates for failures of both components are Poisson processes with
arrival rates of h and 2h, and both components work initially. What value must h
have for the system to be 99.9% reliable after 1,000 hours of operation.
4.
(7
points) It was recently suggested that because airplanes travel faster than cars,
accidents per mile is
an
inappropriate criterion for safety comparisons. Instead, they
suggest "deaths per hour of travel." Do you agree or disagree with this suggestion.
WHY
?
(Be careful to clarify the purpose of the analysis.)
What aspect of the risk
does "deaths per hour of travel" stress?
5. (15 points) A risk analysts is concerned with the likelihood of and possible
magnitude of toxic gas releases from a manufacturing facility. <Here we go!>
Things can go wrong in either process #1, process #2, during loading, or from leaks
from either
1
tank, or from 2 tanks. The frequency of each kind of accident and the
amount of toxic gas that might be released are listed below:
Accident
Type
Fre quencv
Potential toxic gas release
process #I
0.05
/yr
5,000 m3
process
#2
0.04
10,000 m3
during loading
0.03
leaks from
1
tank
0.02
leaks from 2 tanks
0.01
/yr
The potential release will occur unless action is taken. Either the potential toxic gas
release can be stored if empty tanks are available, or it can be neutralized in a
scrubber, or most of it can be partially destroyed by emitting it through a flame
tower. Because Flame tower only destroys 90% of gas, it is used only as a last resort!
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 Spring '07
 Stedinger

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