IE 361 EXAM #3 FALL 2013 Show your work: Partial credit can only be given for incorrect answers if there is enough information to clearly see what you were trying to do. There are two additional blank pages on the back of the exam you can use, but please label your work so it is easy to follow. I have neither given nor received unauthorized assistance on this exam. Name Signed Date Name Printed Section I. True/False Questions / 20 Section II. Multiple Choice Questions / 30 Section III. Multi-part Questions / 50 TOTAL / 100

SECTION I. TRUE/FALSE QUESTIONS Below are 10 true/false questions. Each is worth 2 point each. Clearly write either T or F in front of each. F 1. If a calibration study produced a regression analysis with an estimate for the 95% confidence limits for β1 as (0.12 ± 0.15), the bias for this measurement device is constant. T 2. A prediction interval is likely to contain a single additional observation drawn from a stable process. T 3. In a go/no-go experiment, if all the calls for a single operator on a single part are the same, then there is no repeatability variation. F 4. A stable process will never produce a plotted value outside the Shewhart control limits. F 5. If a fitted interaction effect ab 22 = 20, then ab 11 = -20. T 6. The one-way normal model assumes that while means may vary, the standard deviation does not change between different process conditions. F 7. A 2 7-4 fractional factorial experiment will ) only run 1/16 of the combinations of a full factorial experiment. T 8. In a 2 2-1 full factorial experiment, if one teste combination a, then the only sensible second combination to test is combination b. F 9. One can always assume that higher order interaction effects are less important than the main effects of the factors. F 10. Gauge R&R studies are used to assess the accuracy and precision of the gauge.

SECTION II. MULTIPLE CHOICE Answer six (6) of the eight (8) questions in this section (if you answer more than 6 questions, your top-scoring 6 questions will count towards your score). Circle the letter corresponding to the single best response for each of these questions. If extra space is needed, use the extra pages provided (clearly label the work with the problem number). 11. In the data collection scheme below, which of the following variances can you estimate? a) b) and c) and d) and e),!,"#$ %&'(! 12. The potential of an assistive system to boost performance is tested experimentally. In the experiment the system was either on or off (baseline), and the user was in either low or high workload situations. Given the plot below, which of the following conclusions are supported by the data? a) When the system is on, performance is detectably improved in low workload over high workload b) There is no detectable difference (system on vs. off) in performance at low workload c) Use of the system only improves performance (over baseline) at high workload d) Exactly two of the responses (a) through (c) are true e) All of the responses are true.

13. A 2 4 full factorial experiment was conducted (with factors A, B, C, D). It was determined from the data that the set of b 2 = 7, cd 22 = 4, d 2 = 2 represent all detectable fitted effects (where the other effects have been determined to be not detectable). Which statement is most true? a) Factor A has no effect on the response y, either alone or in combination with other effects b) Factor B has no effect on the response y, either alone or in combination with other effects c) Factor C has an effect on the response y that is independent of the effect of other factors d) Factor D has an effect on the response y that is independent of the effect of other factors e) All of the above 14. For the data presented in Question 13, if the goal is to find a combination of levels of the four factors that makes the mean response y as small as possible, what levels of the factors should be used? a) A low, B low, C low, D low b) A low, B low, C high, D low c) A high, B high, C low, D low d) A high, B high, C high, D low e) None of the above 15. For the data presented in Question 13, if. 20, what is? a) 7 b) 19 c) 21 d) 29 e) None of the above 16. A 2 6 2 fractional factorial study was conducted. Two generators were used to choose levels of Factors D and E are shown below. What is the defining relation for this study? a) I ABCDE b) I ABD ABC c) I ABDE ABCF d) I ABDE ABCF CDEF e) None of the above E ABD and F ABC

17. Given the generators in Question 16, when the Factors A and B are at their low levels, and Factors C and D are at their high levels, what levels are the other two factors? a) E low and F low b) E low and F high c) E high and F low d) E high and F high e) Cannot be determined without more information 18. Given the generators in Question 16, which statement about the experimental results is most true? a) The main effect E is confounded only with the ABC three-factor interaction b) The main effect E is not confounded with any 2-factor interaction. c) The main effect E is confounded with only 2 other factorial effects. d) Exactly two of the responses (a) through (c) are true e) None of the above. 2

SECTION III. MULTI-PART QUESTIONS Below are 2 multi-part questions. Each part is worth the points indicated. If extra space is needed, use the extra pages provided (clearly label the work with the problem number). 19. A ball of radius R is placed into a rectangular box of dimensions a x b x c. The quantity 3 = 456 7 4 3 :;< represents the volume of air left inside the box. Suppose that the measured variables a, b, c, and R are in fact random with means and standard deviations given in the table below. Input a b c R = >? 10 cm 25 cm 50 cm 3 cm >?.1 cm.1 cm.1 cm.2 cm a) [10 pts] Calculate the mean and standard deviation with the experimentally determined volume V. b) [5 pts] Which measured variable above is the largest contributor of uncertainty to the Volume V? Explain.

20. A 2 3 factorial experiment is conducted. The table below shows the data collected. setup Factor A Factor B Factor C y )* s 1 - - - 14, 14, 15 14.333 0.577 2 + - - 16 16 3 - + - 7 7 4 + + - 12 12 5 - - + 13, 16, 12 13.667 2.082 6 + - + 15, 15, 13 14.333 1.155 7 - + + 8, 9, 8 8.333 0.577 8 + + + 15 15 a) [5 pts] Compute a single estimate of the standard deviation of the response y for any of the experimental setups. What are the appropriate degrees of freedom for your estimate? S pooled: 1.258 ν: 16-8 =_8 b) [5 pts] Give two-sided 95% confidence limits for the standard deviation of the response y for any fixed experimental setup. c) [5 pts] Calculate the margin of error based on the two-sided 95% confidence limits for the mean response time of the "all low" combination.

d) [10 pts] The quantity @ = 1 A (= B 7 = A ) C 1 A (= D 7 = < ) C 1 A (= E 7 = ) C 1 A (= F 7 = 1 ) is a measure of the effect on the response y due to change in Factor C from low to high. Make a 95% two-sided confidence interval for this quantity. Does Factor C impact the response in a statistically detectable way? Explain. e) [5 pts] Fill in missing values in the Yates algorithm table below to compute the fitted factorial effects corresponding to the all high treatment combinations. Factor A Factor B Factor C Combination )* cycle #1 cycle #2 cycle #3 cycle#3 8 - - - (1) 14.333 30.333 49.333 100.667 12.583 + - - a 16.000 19.000 51.333 14.000 1.750 + - + - b 7.000 28.000 6.667-16.000-2.000 + + - ab 12.000 23.333 7.333 9.333 1.167 - - + c 13.667 1.667-11.333 2.000 0.250 + - + ac 14.333 5.000-4.667 0.667 0.0833 - + + bc 8.333 0.667 3.333 6.667 0.833 + + + abc 15.000 6.667 6.000 2.667 0.333 f) [5 pts] Calculate the margin of error for the factorial effects calculated in the Yeats algorithm above. Which factors are "clearly larger than the background variation"?