CEE597_Midterm_Soln08

CEE597_Midterm_Soln08 - CEE 597 Risk Analysis and...

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CEE 597 – Risk Analysis and Management Evening Midterm Exam March 7, 2008 Test is open book and open notes. You have 90 minutes to complete this 90 point exam. Please show work. 1. (9 points) Exercise is important for health. But many exercise programs bring safety risks: consider jogging on the street, swimming year-round in Ithaca, and working out in a gym. [One would swim indoors in the winter.] Propose 3 quantitative criteria useful for comparing honestly 3 different critical dimensions of the safety risks associated with these exercise programs, relative to their health benefits; indicate what aspect of risk each criteria addresses. 2. (8 points) In no more than 2 pages in your exam book, indicate which case study from Fleddermann had the most profound lesson for risk management in our society? What was the lesson? What are the implications of that lesson for management of risk in our society? 3. (14 points) Infrastructure reliability is a continuing concern. Assume that the occurrence of serious power outages on the Cornell University campus can be modeled as a Poisson process, and that on average there is one such failure every four years. a) What is the probability of having at least one outage in a given year? What is the probability of having exactly two outages in a decade? b) On average, how many years would someone need to spend at Cornell to experience 3 power outages? c) What are the mean and standard deviation of the number of outages that will occur during a four-year undergraduate education at Cornell? d) Why might a Poisson process be a good description for the arrival of power outages? Why might it not be a good description? 4. (16 points) Consider the reliability of the system described by the network below: D G C B F H A E a) What are ALL the MINIMAL cut sets with 4 or fewer components? b) What are ALL the MINIMAL paths with 4 or fewer components?
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CEE 597 – Risk Analysis and Management – PRELIM 2007 Page 2 of 3 c) If all elements are 90% reliable, what approximately is the reliability of the entire system? d) What component is most critical to the reliability of the system? Why? What 2 or 3 components are least critical? Why? 5. (5 pts) For the system in problem 4 above, if A failed, please draw a fault tree to describe the reliability of the remaining network. 6. (a) (5 points) Consider a system with two independent components in series . Assume component failures are independent Poisson processes with arrival rates of 0.003 /day and 0.001/day, respectively. For how long can one be 99.9 percent certain the system will still be operating? (b) (5 points) A single component has reliability function [the probability component is still functioning after t days] equal to R(t) = 120/(t+120) 3 for 0 t. Please derive the hazard function r(t) for this component and compute its value at t = 0. (c) (2 points) A single component has hazard function or failure rate r(t) = 7/t
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This note was uploaded on 03/02/2011 for the course CEE 5970 taught by Professor Stedinger during the Spring '07 term at Cornell.

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CEE597_Midterm_Soln08 - CEE 597 Risk Analysis and...

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