CHAPTER10a - CHAPTER Duxbury Thomson Learning Making Hard...

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• A. J. Clark School of Engineering •Department of Civil and Environmental Engineering Third Edition CHAPTER 10 Making Hard Decision Duxbury Thomson Learning ENCE 627 – Decision Analysis for Engineering Department of Civil and Environmental Engineering University of Maryland, College Park Using Data FALL 2003 By Dr . Ibrahim. Assakkaf CHAPTER 10. USING DATA Slide No. 1 ENCE 627 ©Assakkaf Introduction Source for information about probabilities and historical data
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CHAPTER 10. USING DATA Slide No. 2 ENCE 627 ©Assakkaf Introduction So far we have seen two ways to calculate probability for decision models. – Subjective probabilities (chapter 8) – Theoretical probability models (chapter 9) In chapter 9, given a particular probability model, we had just assumed certain parameter values for the any particular distribution. CHAPTER 10. USING DATA Slide No. 3 ENCE 627 ©Assakkaf Introduction Example: – Poisson model for tornadoes occur in a particular area an average of two times a year. In this case, λ = 2/year. – The parameters u n and α n in the example of the Extreme Value Distribution, Type I for maximum wind velocity V n were assumed as ( ) 9157 . 57 17055 . 0 5772 . 0 3 . 61 α γ μ and 17055 . 0 7.52 6 σ 6 α 2 2 2 2 = = = = = = n X n X n n n u π π
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CHAPTER 10. USING DATA Slide No. 4 ENCE 627 ©Assakkaf Introduction Now we will learn to calibrate models to data finding the best parameters CHAPTER 10. USING DATA Slide No. 5 ENCE 627 ©Assakkaf Using Data to Construct Probability Distributions Imagine that you are in charge of a manufacturing plant, and you are trying to develop a maintenance policy for your machines. You may collect the following data over 260 days: 11 days Two failures 32 days One failure 217 days No failures
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CHAPTER 10. USING DATA Slide No. 6 ENCE 627 ©Assakkaf Using Data to Construct Probability Distributions These data lead to the following relative frequencies, which could be used as estimates in your analysis: Data collected: out of 260 days (= 52 weeks × 5 days/week): 0.042 = 11/260 Two failures 1.000 0.123 = 32/260 One failure 0.835 = 217/260 No failures Basically one year’s worth of working days CHAPTER 10. USING DATA Slide No. 7 ENCE 627 ©Assakkaf Using Data to Construct Probability Distributions The only serious consideration to keep in mind is that you should have enough data to make a reliable estimate of the probabilities.
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CHAPTER 10. USING DATA Slide No. 8 ENCE 627 ©Assakkaf Using Data to Construct Probability Distributions Relative frequency histogram for machine failure: 32/260 11/260 1.00 0.75 0.50 0.25 0.00 0 1 2 Machine Failures Relative Frequency 217/260 CHAPTER 10. USING DATA Slide No. 9 ENCE 627 ©Assakkaf Decision-tree Representation of Uncertainty Regarding Machine Failures Note: – The data requirements depend on the particular problem, but the minimum should be approximately five observations in the least likely category. The other categories, of course, will have more observations.
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