OR3120_Final_2010Solutions

# OR3120_Final_2010Solutions - ORIE 3120 — Final Exam...

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Unformatted text preview: ORIE 3120 — Final Exam Solutions Spring 2010 Professors Peter Jackson and David Ruppert This exam is closed book and closed notes, though there is a list of useful formula at the end of the exam. You may use a hand calculator but you cannot share a calculator with another student. Time yourself carefully. Do the problems first that you find easiest. You do not need to complete all numerical calculations. For example, an answer in the form (0.1)(157) + (0.9)(123) would be just as acceptable as 126.4. You should not leave the exam room until you have finished your exam and handed it to a proctor. Exceptions will be made only when absolutely necessary, and you must ask a proctor for permission to leave the exam room. The point value of each sub-question is in square brackets, for example, [4]. This exam has 9 problems. Make certain that your exam is complete. All solutions should be written on this exam. Good luck. 1. Holt’s forecasting method is being used to forecast weekly demand for a product. After 90 weeks, b a 90 = 61 and b b 90 = 0 . 50. The next week’s demand is x 91 = 63 . 5. (a) If α = 0 . 60, then what is b a 91 ? [6] b a 91 = (1- α )( b a 90 + b b 90 ) + αx 91 = 62 . 7 (b) If b b 91 = 0 . 52, then what is β ? [6] b b 91 = (1- β ) b b 90 + β ( b a 91- b a 90 ) so that . 52 = (1- β )(0 . 50) + β (62 . 7- 61) and therefore β = 0 . 02 / 1 . 2 = 0 . 0167 2. A quality engineer is redesigning a production line to reduce variability. There are five factors (named A – E ) thought to influence variability. These factors were varied using a 2 5- 1 experimental design and the standard deviation of the product (called StdDev ) was measured at each factor-level combination. The engineer used the following R program: lmfit = lm(StdDev~A*B*C*D*E) cbind(A,B,C,D,E,lmfit\$fitted,lmfit\$resid) halfnorm(lmfit\$effects[2:16],labs=names(lmfit\$effects[2:16]),nlab=4) The printed R output was: > cbind(A,B,C,D,E,lmfit\$fitted,lmfit\$resid) A B C D E 1 1 -1 -1 -1 -1 12.774569 0 2-1 1 -1 -1 -1 5.677091 0 3-1 -1 1 -1 -1 8.644590 0 4 1 1 1 -1 -1 13.040916 0 5-1 -1 -1 1 -1 11.422411 0 6 1 1 -1 1 -1 10.717676 0 1 7 1 -1 1 1 -1 15.547299 0 8-1 1 1 1 -1 3.079728 0 9-1 -1 -1 -1 1 11.784997 0 10 1 1 -1 -1 1 11.121262 0 11 1 -1 1 -1 1 15.137416 0 12 -1 1 1 -1 1 2.687788 0 13 1 -1 -1 1 1 12.966592 0 14 -1 1 -1 1 1 5.603903 0 15 -1 -1 1 1 1 9.057290 0 16 1 1 1 1 1 13.313075 0 The plot produced by the R program is: 0.0 0.5 1.0 1.5 2 4 6 8 10 12 Half-normal quantiles Sorted Data C C:D A:B A:C B A (a) Based on the half-normal plot, which effects do you consider significant? [4] The main effects of A and B and the AB and AC two-way interactions. (b) Why was a half-normal plot rather than p-values used to detect significant effects?...
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## This note was uploaded on 03/18/2012 for the course ORIE 3120 taught by Professor Jackson during the Spring '09 term at Cornell.

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OR3120_Final_2010Solutions - ORIE 3120 — Final Exam...

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