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Unformatted text preview: CEE 597 - Risk Analysis and Management Final Exam #1 for 1994 Test is open book and open notes. You have 150 minutes to complete this 150 point exam. Some problems are difficult & involved; don't get stuck. Show important steps. 1. (12 points) Automobile crashes causing at least one fatality occur frequently. Assume there are 0.2 fatal crashes occur per day in the state of Maine, and the arrival of fatal crashes can be described by a Poisson process. a) What is the probability that there are no crashes in a given 7-day week ? b) If I started collecting information on crashes in Maine, what are mean and variance of the time I would have to wait to obtain records for 25 crashes ? C) Why might a Poisson process be a good model of accidents resulting in at least one fatality ? What weaknesses would a Poisson model have ? 2. (8 points) Consider the fault tree below. What is the system's reliability if all components have reliability 0.98? System C D 3. (10 points) Consider the diagram below that appears to be a fault tree. What is unusual about this tree that makes the usual rules for computing failure probabilities for fault trees not apply ? Draw a simple network diagram to describe the system this "fault" tree is trying to describe (this may not be immediately clear). 4. (8 points) Consider a system with two independent components in parallel. Assume arrival rates for failures of both components are Poisson processes with common arrival rate h. What value must h have for the system to be 99.99% reliable after 500 hrs of operation, assuming both components are working initially. 5. (15 points) Last week I was at a National Research Committee meeting discussing flood risk for urban comunities. Consider a community protected on two sides by levees. Floods challenging these levees occur primarily in the months of Dec-Mar: M o n t h & , h z F e b M a r Arrival rate of floods 0.01 0.02 0.03 0.02 (floods/month) When a flood occurs, it can vary in size from regular (with probability 85%) to super (with probablity 1%). The table below provides the probability of different size floods and the probability a flood of each magnitude will cause either of the levees to fail. The failure of EITHER levee will result in the flooding of the community. a) Draw an event tree for this problem. b) What is the frequency with which the community is flooded ? Probability Prob. Levee # I Prob. Levee #2 SIZE Flood this size Fails Fails Regular 0.85 0.1 0 Large 0.10 0.3 0.1 Big 0.04 0.9 0.5 Super 0.01 1 .O 1.0 6. (10 points) Air pollution is a major challenge facing our society and those concerned with public health. Consider emissions from a waste-to-energy conversion plant (incenerator) emitting a large volume of high temperature gas (Tgas = 150 OC; Tatmosphere = 20 OC) at a low velocity (9 m/sec) into a stable atmosphere (stability class E; wind speed 3 m/sec) from a tall stack (60 m) with inside diameter of 6 m....
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