CEE 597 – Risk Analysis and Management
Evening Midterm Exam
March 9, 2006
Test is open book and open notes.
You have 90 minutes to complete this 90 point exam.
Show work.
1. (9 points)
Did you see the winter Olympics?
All those crazy athletes. But how dangerous are winter
sports for the American public? You have been commissioned to perform a study of the impact of winter
sports and associated injuries on the American public from recreational
downhill skiing, recreational
crosscounty skiing,
and for comparison
jogging
on roads (weather permitting).
Propose 3 quantitative
criteria
that can be used to compare
different
dimensions of the negative and positive impacts (risks) to
health from these 3 activities, and indicate what aspect of risk each captures.
2. (12 points) Army units search for roadside explosives in Iraqi during the daylight hours. When they
find a very suspicious situation (VSS), they call in a special explosives unit.
(a) Why is a Poisson process likely to be a reasonable model for the identification of VSSs? In what
cases might it NOT be a good model?
Recently in the Baghdad area they have been finding a VSS about ever 2 hours during the day.
(b) If that is so, what are the chances an entire 8hour shift passes without a VSS being found?
(c) One special operations soldier asserts that during the last three hours of her shift, exactly 2
suspicious situations will be reported. What is the probability she is right?
(d) An operations analyst has been requesting special reports from teams responding to daylight
VSSs for a study being conducted for the commander. To have a good sample, he would like to collect
another 45 reports. What is the mean and standard deviation of the number of days (12 daylight hours
per day) that it will take for the officer to obtain those 45 reports.
3. (20 points) Consider the reliability of the system described by the network below:
A
D
G
C
E
I
J
B
F
H
a)
What are ALL the MINIMAL cut sets with 3 or fewer components?
b)
What are ALL the MINIMAL paths with 4 or fewer components?
c)
If all elements are 90% reliable, what
approximately
is the failure probability of the entire system?
d)
What two components are most critical to the reliability of the system?
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4. (8 points) For the system below
(a) evaluate the reliability of the system if the failure probability for B is 0.02, for C is 0.03,
for D is 0.1, and for E is 0.4.
(b) Please draw a network diagram for this system.
System
E
5) (9 points) Let f(t) be the
hazard rate or failure rate function
for a system, and suppose that it has a “classic”
bathtub
shape. (a) What does that tell us about when such systems likely fail? (b) Why do many real
systems have a bathtub failure rate function? (c) What is it that a hazard rate function tells us that makes
it useful? [Please, at most one equation.] (d) If a system has a constant failure rate function f(t) =
!
for all
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 Spring '07
 Stedinger
 Failure rate, Risk Analysis and Management, ra te function, hazard ra te, failure ra te

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