CEE_597_Midterm_1998 - CEE 597 Risk Analysis and Management...

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CEE 597 – Risk Analysis and Management Midterm Exam 1998 Test is open book and open notes. You have 50 minutes to complete this 50 point exam. Show important steps. 1. (8 points) Use the lessons provided by the case studies as the basis of a 2-3 paragraph argument in support of, or refuting, the statement that: “Most disasters are a result of a simple linear chain of events.” 3. (8 points) A surveyer is going out on an extended trip in Northern Alaska. She is going to take a special global positioning system (GPS). The critical component on these devices seems to fail randomly in time so she takes 3 [one in the device, and two for backups]. (a) If the components last on average 50 hours before failing, what is the mean and variance of the time until the surveyor can no longer use the GPS? (b) What is the probability the system is still operational after t hours? (c) If the surveyer wanted to be 99% sure the system would still be working after 100 hours, how small would the failure rate of the components have to be? 4. (14 points) Consider the system described by the network : 5. A G F E C B D a) What are all the minimal cut sets? b) What are the minimal paths? c) If all elements are 98% reliable, except A which is 99.5% reliable, what approximately is the probability the system fails? d) If you could upgrade one component to 99.5% reliability, which would you choose to maximize the reliability of the whole system ? e) Draw the best fault tree representation of this system that you can.
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CEE 597 – Risk Analysis and Management Midterm Exam 1998 5. (10 points) Pipelines are reasonably reliable means of shipping gasoline, but occassionally there are failures. Consider pipelines of three sizes: large, medium and small. Assume the frequency of pipline spills for large pipes is one per 2000 days, for medium pipelines is 1 per 500 days, and for small piplines is one per 100 days in the Northeastern US. The probability of different size spills when a pipline breaks are listed below: size of pipe size of spill (gal) probability large 100,000 0.2 50,000 0.3 10,000 0.5 medium 50,000 0.1 10,000 0.4 2,000 0.5 small 10,000 0.2 2,000 0.8 The probabilities of an explosion due to a spill are: Size of spill 2,000 10,000 50,000 100,000 gallons Prob. Explosion 0.001 0.005 0.01 0.1 (a) Draw an event tree for this problem (b) Compute the risk profile for the size of pipeline spills. [No graph needed; table will suffice.]
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CEE_597_Midterm_1998 - CEE 597 Risk Analysis and Management...

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