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CEE_597_Final2006r

# CEE_597_Final2006r - CEE 597 Risk Analysis and Management...

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CEE 597 – Risk Analysis and Management Final Exam and Solutions from 2006 Final EXAM Wed. May 17 th , 2006, 9-11:30 am Test is open book & open notes. You have 150 minutes for this 150 point exam. Write clearly and show important steps. 1. (15 pts) In no more than 2 pages in your exam book, which case study in the reading had the most profound lesson for risk management in our society? What was the lesson? What are the implications of that lesson for the management of risk in our society? 2. Consider the network below. (a) (8 pts) Please draw the equivalent fault tree. (b) (8 pts) Please list all of the minimal cut sets. (c) (7 pts) If all elements are 98% reliable, what is the reliability of the system? (d) (7 pts) To save money, you have been asked to identify system components that could be replaced with units that are only 90% reliability, if the substitution would not dramatically degrade the overall reliability of the network. Which components would you suggest for replacement? If you could improve one component, which would you select? A B E F C G D 3. Consider the dynamic reliability of 3 components in series, all of which have exponential times-to-failure distributions, with the mean time-to-failure of each component equal to 100 hrs, 200 hrs and 300 hrs, respectively. (a) (5 pts) What is the probability that the system is still operating after 100 hours? (b) (5 pts) What is the mean time before failure of this 3-component series system? (c) (5 pts) Component #2 has failure rate of 1 per two-hundred hours; so how long (for what t) can I trust this unit to operate if I want to be 99.9% sure it will not fail before time t? (d) (5 pts) Consider the hazard function h(t) shown below for underground storage tanks. What story does it tell about these systems?

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2006 CEE 597 Examination Page 2 of 8 4. (20 pts) Professor Stedinger has served as a Slope Day volunteer. While standing on the slope he was thinking of CEE 597 and risk. There were 9 Emergency Medical Service (EMS) teams on the slope and in other locations to respond to medical emergencies. In general, medical emergencies could be classified as minor (class 1), drunkenness (class 2), serious (class 3), and life-threatening (class 4 and 5). There is a 10% probability that life-threatening emergencies actually require hospitalization (class 5), otherwise such events are class 4. Suppose that when an emergency does occur on Ho Plaza, on the Slope, or at other locations it has the probabilities listed below of being in each class, and that during the day, 8% of the emergencies were on Ho Plaza, 90% on the slope, and 2% in other locations. At the peak time, the arrival rate of emergencies at those locations collectively equaled one every 5 minutes. Please construct and plot a RISK PROFILE describing the frequency of severe emergency calls that were in classes 2 or above, 3 or above, 4 or above, and class 5 (ignore class 1-- not worth considering).
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