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CEE 5970
–
Risk Analysis and Management
Evening Midterm Exam
March 11, 2010 r
Test is open book and open notes.
You have 90 minutes to complete this 90 point exam.
Please show readable work.
1. (7 pts) The sinking of the Titanic has received tremendous attention. Describe 3
aspects of the loss of the Titanic that made it such an unprecedented and significant
catastrophe in 1912. What were the 3 most critical factors that resulted in so few
passengers making it into lifeboats (and thus to safety)?
<Remember Prof. Stedinger’s remarks about essays.>
2. (9 pts) Recently food poisoning was identified as an important health threat in the
United States affecting one in four American’s
every year
causing 5,000 deaths (AP 19
Feb. 2010). Propose 3 quantitative criteria that would be useful for comparing
different
aspects of the risk of food poisoning, automobile accidents and smoking in modern
urban life. Specify what each of your 3 criterion emphasizes.
3. (4 pts) Over the last 100 years, the population of the United States has increased from
76 million in 1900, to 280 million in 2000. But if one looks at the number of cancer
deaths, we have gone from 50,000 deaths per year, to 600,000 in 2000. This is an
alarming increase. Explain how we should understand this explosion in the number of
US cancer deaths.
4. (12 pts) Prof. Stedinger is distressed by the number of emails he receives that attempt
to get him to reveal confidential information
(passwords, birth date, SS#). He averages
3 serious attempts to get him to divulge critical personal information every week (one
week = 7 days).
Imagine that such attempts can be described as a
Poisson process
over
the 168 hours in a 7day week.
a) What is the mean and variance of the number of
days
that will pass until 25 of these
attempts occur?
b) What is the probability of having exactly 3 such attempts in the next 72 hours?
What is the mean and variance of the number of attempts in a 72 hour period?
c) Why might a Poisson process be a reasonable model for the arrival of these attempts?
5. (8 pts) Consider the fault tree below.
F
G
System
Failure
A
B
a) If all components have a 1% failure probability, what is the system’s reliability.
b) If you could decrease the failure probability of two components to 0.3%,
which two should you pick to most improve system reliability?
c)
DRAW a network diagram that represents the operation of this system.
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Risk Analysis and Management – Midterm 2010
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6. (12 pts) Consider the reliability of the system described by the network below:
G
C
D
B
F
A
E
H
K
a) What are ALL the minimal cut sets with 3 or fewer components?
b)
If K has a failure probability of 0.5%, and all other components fail with a
probability of 5.0%, what
approximately
is the reliability of entire system?
c) If you can decrease the failure probability of 1 component [not K] from 5% to 1%,
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 Spring '07
 Stedinger

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