5 chapter 10 using data slide no 10 ence 627 assakkaf

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Unformatted text preview: CHAPTER 10. USING DATA Slide No. 10 ENCE 627 ©Assakkaf Decision-tree Representation of Uncertainty Regarding Machine Failures – Keep in mind that your probability estimates are just that - estimates. – Ask yourself whether the probabilities estimated on the basis of the data truly reflect the uncertainty that you face. – If you are not satisfied with the representation based on the data, you may need to model your uncertainty using subjective assessment methods. In particular, this might be the case if you think that the past may not indicate what the future holds. CHAPTER 10. USING DATA Slide No. 11 ENCE 627 ©Assakkaf Using Data to Construct Probability Distributions: Empirical CDFs Notes: – You should have enough data to make the %’s reliable. – Also, you should ask the question whether the data was collected over a period in which it was representative? In some settings one year may In some settings one year may not be enough, in other settings not be enough, in other settings ititmay be ok. may be ok. 6 Slide No. 12 CHAPTER 10. USING DATA ENCE 627 ©Assakkaf Using Data to Construct Probability Distributions: Empirical CDFs Slightly more sophisticated approach – Empirical CDFs • Halfway House Example: – Ease transition from prison life to normal civilian life. – Increase chances to re-integrate into society Slide No. 13 CHAPTER 10. USING DATA ENCE 627 ©Assakkaf Using Data to Construct Probability Distributions: Empirical CDFs Example: Halfway House – Yearly per-bed rental costs (in $), let C be the random variable representing costs; 35 halfway houses randomly sampled. C= 1 2 3 4 5 6 7 52 76 100 136 137 186 196 8 9 10 11 12 13 14 205 250 257 264 280 282 283 15 16 17 18 19 20 21 303 313 317 325 345 373 384 22 23 24 25 26 27 28 400 402 408 417 422 472 480 29 30 31 32 33 34 35 643 693 732 749 750 791 891 18 values ≤ 325 18 values ≥ 325 Relative Relative Cumulative Cumulative Frequency Frequency P(C ≤ 325) = P(C ≤ 326) = …= P(C ≤ 344.99) = 18/35 =0.514 7 Slide No. 14 CHAPTER 10. USING DATA ENCE 627 ©Assakkaf Using Data to Construct Probability Distributions: Empirical CDFs Example (cont’d): Halfway House Question: Which value to be used for the 0.514 fractile? Answer: One way is to take a compromise: (325+345)/2 = 335, do the same things for all points. Slide No. 15 CHAPTER 10. USING DATA ENCE 627 ©Assakkaf Using Data to Construct Probability Distributions: Empirical CDFs Example (cont’d): Halfway House Cumulative Probability ½ way point ½ way point 19/35 = 0.543 18/35 = 0.514 17/35 = 0.486 16/35 = 0.457 15/35 = 0.429 14/35 = 0.400 Yearly Bed-Rental Cost 303 313 317 325 335 345 8 Slide No. 16 CHAPTER 10. USING DATA ENCE 627 ©Assakkaf Using Data to Construct Probability Distributions: Empirical CDFs Example (cont’d): Halfway House Estimated cumulative probabilities for the halfway-house data Obs. No. Cost xm Cumulative Probability Obs. No. Cost xm Cumulative Probability 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 52 76 100 136 137 186 196 205 250 257 264 280 282 283 303 313 317 64.0 88.0 118.0 136.5 161.5 191.0 200.5 2...
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This note was uploaded on 10/24/2012 for the course ESI 6385 taught by Professor Mansoorehmollaghasemi during the Fall '12 term at University of Central Florida.

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