CEE_597_Final_2000 - CEE 597 Risk Analysis and Management...

CEE 597
-
Risk Analysis and Management
Final Exam
Tuesday
-
May 16,2000
-
noon to 2:30 pm.
Test is open book and open notes. You have 150 minutes for this 150 point exam.
Write clearly and show important steps.
And remember, I hope you learned more than I could include on this exam.
-
JRS
1. (10 pts.) Of all the case studies (except TMI) we discussed or in the reading (Bhopal, Titanic,
DC- 10, Challenger, different short studies
. . .
),
which one was your favorite?
What
im~ortant lessons
did it teach about the character of system failures? (2-3 paragraphs)
2. (15 pts.) Consider the system described by the
network
below.
a)
What are all the minimal cut sets?
b)
If all elements are 99% reliable, except A and B whch are 99.6% reliable,
approximately what is the RELIABILITY of the system?
c)
Draw a fault tree for the system.
d)
If you could upgrade ANY ONE component in the original network to
a reliability of 99.9%, whch would most improve system reliability?
3. (15 pts.) A local internet provider on occasion has trouble providing service because of
viruses, server crashes, power outages, line failures, software problems,
. . .
What a headache!
Looking over the log, the customer service manager notes that there were 8 significant failures
(each lasting more than 4 hours) in the last year. Assuming this average failure rate continues:
a) What is the probability that there are NO failures in the next week?
b) What is the probability of 2 or more failures in the next month?
c) What are the mean and variance of the time until the next 3 failures occur? (specrfi units)
d) The customer service manager computed the hstorical average failure rate. However, that
number is only an estimate of the true rate with which failures were likely to occur, and depends
on how many accidents were experienced. How precise is the hstorical failure rate as an estimate
of the true failure rate that pertained in the last year? (spec~fi units)

4. (25 pts.) Your reliability engineering group needs to analyze the safety of a chemical plant
similar to the Union Carbide facility that created the disaster in Bhopal, India. A runaway
chemical reaction can result from several causes. The frequencies for the most likely causes are:
0.0006 Iyr human error
0.0003 Iyr mechanical failure
0.0001 Iyr unexplained acts of God and Nature
When a runaway reaction occurs, the amount of excess product that must be dealt with is
100,000 gallons with probability 0.70; 200,000 gallons with probability 0.20; and 500,000
gallons with probability 0.10. The product should be stored if possible, and what cannot be
stored should be diverted into the combustion unit for destruction. The available storage capacity
depends on what else is happening. The capacity of the combustion unit depends on how well it
is maintained and operated. If all of the runway product cannot be stored, and the excess exceeds
the capacity of the combustion unit, than an emergency water spray can be directed across the
exhaust of the combustion unit. This spray effectively removes the residual. But the spray unit
only works if properly maintained and operated (by the same folks responsible for the
combustion unit).