CEE
597

Risk Analysis
and
Management
Final Exam
May 10,1996
An
apology:
I
hope you learned more than a simple test like this can reveal.
*
Test
is
open book and open notes.
You have 150 minutes to complete this 150 point exam.
Show important steps.
1.
(5
points) Of all the case studies (except TMI) we discussed and
in
the reading
(Bhopal, Titianic, DC10, and those in short studies), which was your favorite, and
what important lesson did it teach about the character of system failures?
2.
(10
points) Different criteria can be used to describe different risks. Consider a
comparison of rollerblading and bicycle riding. Injury rates could
be
expressed as (i)
I
injuries per mile, (ii) injuries per hour of activity, or (iii) injuries per participant per
year. What is the key strength of each of these three criteria, and a reasonable risk
management question that each criteria directly addresses?
3.
(20 points) Consider the
complex
system described by the network:
a)
What are all the minimal cut
sets
with
1,
2,
3
or
4
components?
b)
What are the minimal paths?
c)
If
all elements are 99% reliable, what approximately is the probability system fails?
d)
Draw the best fault tree you can describing this network if E is not functioning
?
Is it a proper fault
tree?
If not, what is the problem?
e) If you could upgrade one component in original network (with
E)
to 99.99%
reliability, which would you choose to maximize reliability of the system
?
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(15 points) Major train derailments continue to happen. Consider derailments of
at least 10 cars. Assume that 15 such derailment happened in the last
5
years, and
assume that this rate will continue.
a) What is the probability of
2
or more derailments in one year?
b) What is the mean and variance of the time one would expect to wait to
observe
25
derailments?
C)
If
15 derailments were observed in 5 years, then one can estimate the annual
derailment rate as you have above. What is the standard deviation of that estimate?
d)
Why is a Poisson process a good model of such derailments?
5.
(12 points)
This
problem could
take
TOO
long
if
you
do
not
economize.
This weekend Prof. Stedinger is going backpacking with the Boy Scouts. Suppose
that they take 2 whitegas stoves and using good fuel, each stove has a probability of
1
in 50 of failing (independent failures). There is an 80% chance that a failed stove
can
be
repaired. However if Ken Mudge, who is bringing the white gas, brings bad
fuel for the stoves [prob. of good fuel is 90%, prob. of poor fuel is lo%], the
probability each stove fails increases to
1
in
4
(independent failures), but there is still
a 80% chance each failed stove can be repaired. (The success of repair efforts are
independent.)
Draw
the event tree carefully.
Calculate
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 Spring '07
 Stedinger
 risk averse organization, proper fault tree, good fuel

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