CEE 597

Risk Analysis and Management
Final Exam
May 12,1997; 12 noon to 2:30 pm. Hollister 366,368,306,312
My
apology: I hope you kamd more
than
this
simpk
test revealj.
Test is open book and open notes. You have 150 minutes for this 150 point exam.
WRITE CLEARLY
and Show important steps.
1.
(8 points) Different criteria can be used to describe different risks.
Automobile
accidents are a significant source of risk to life and property in our society. What are
four
different
and useful criteria that jointly describe the risk of, and the
frequency and severity of automobile accidents in New York State?
What does
each of your criteria capture?
[A
CEE staff member lost their son in an accident in April.]
2.
(10
points) Consider the fault tree below.
System
Failure
a) If every component has a 5% failure rate, what is reliability of the system?
b) Draw a network diagram for this system like the one in problem 3 below.
3. (15 points) Consider the complex system described by the network:
a)
What are all the minimal cut sets?
b)
If all elements are 96% reliable, except D which is 99% reliable,
what approximately is the probability that the system fails?
c)
Draw a fault tree for the system assuming
E
works for sure.
d) If you could upgrade any component in the original network to 99% reliability,
which would most improve system reliability?
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View Full Document4. (10 points)
Ready for some FUN?
In your position of quality control consultant
for a merchandising company you need to estimate the improvement in the order
error rate (frequency of errors in filling customer orders) for your company next
year. This year on 100,000 orders, 3000 incorporated errors when they were shipped.
40% of the ordererrors were due to errors made by salesman, 1O0/0 in transcribing
salesman's orders, and 50% were made by the warehouse in filling the orders. A
new computerinventory system will reduce warehouse ordererrors by 75%. Efforts
to improve salesman errors through clearer catalogs and better training will
continue: the year before this year salesman made the equivalent of 1500 errors,
versus only 1200 this year (when their were 3000 errors). What do you expect to be
the ordererror rate (in percent) next year?
Briefly justih your choice of models.
5. (10 points)
Consider a system with two independent components in parallel.
Assume arrival rates for failures of both components are independent Poisson
processes with arrival rates of
h
and 31, where
h
=
O.Ol/hr.
(a) What is the reliability of the system after 50 hours of operation.
(b) Is a Poisson process a good model of the arrival of failures for this 2component
system? Why or why not? Would a Poisson process be a better or worse model of
the arrival of system failures if the components were in series
?
6.
(15 points) Risk analysis to some people refers to the science of decision making
under uncertainty.
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 Spring '07
 Stedinger
 Pk, pts

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