CEE 597 – Risk Analysis and Management
Evening Midterm Exam
March 8, 2007
Test is open book and open notes.
You have 90 minutes to complete this 90 point exam. Please show work.
1. (9 points) A person concluded that golfing is much more dangerous than sky diving –
look at the statistics: many more people die playing golf (lightning and heart attacks)
than die sky diving (collision with ground and landbased objects). So consider three
summer recreational activities:
biking, sky diving and golf.
Propose 3 quantitative criteria
that can be used to compare honestly 3
different
critical dimensions of the safety risks
associated with these activities; indicate what aspect of risk each criteria addresses.
2. (12 points) Professors Shoemaker and Liu developed a proposal for a Tsunami
warning system (buoys and other sea surface elevation sensing devices). However a
plan should include a testing program. They estimate that on average 1.7 events occur
per year that would generate detectable Tsunami waves.
(a) What is the
mean
and
standard deviation
of the length of time they will have to
wait to have 8 events occur that would test their detection system?
(b) It will take three years to design and deploy the system. During that time, what
is the mean and variance of the number of detectable waves that might occur?
(c) What is the probability of
at least
2 detectable waves in the next 15 months?
3. (18 points) Consider the reliability of the system described by the network below:
D
G
C
J
B
F
H
A
E
K
a)
What are ALL the MINIMAL cut sets with 4 or fewer components?
b)
What are ALL the MINIMAL paths with 4 or fewer components?
c) If all elements are 99% reliable, what
approximately
is the
failure probability of the entire system?
d) What component is most critical to the reliability of the system?
What are the three most critical components and why?
<which includes the MOST critical.>
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4. (5 pts) For the system in problem 3 above, if E and H and G and K all failed, please
draw a fault tree to describe the reliability of the remaining network.
5. (10 points) Consider a system with
two
independent components in
parallel
.
Assume component failures are independent Poisson processes with
arrival rates of
0.02
/day and 0.01/day, respectively.
(a) What is the probability the system operates for at least 30 days?
(b) Provide the Taylor series expansion of the probability the system fails in a short time
period t to illustrate if reliability decreases like t, t
2
or t
3
, as well as the coefficient of
the critical term. Use the Taylor series to compute the time at which the reliability of
the system decreases to 95%.
6. (14 points) Plans for shipping hazardous materials by truck involves 2 routes. The
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 Spring '07
 Stedinger
 Standard Deviation, The Land, Trigraph, Statistical hypothesis testing, type ii error

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