An engineer suspects that the surface finish of a metal part is influenced by the feed rate and the depth of cut. He selects three feed rates and four depths of cut. He then conducts a factorial experiment and obtains the following data: Feed Rate (in/min) | Depth of Cut (in) --- | 0.15 | 0.18 | 0.20 | 0.25 0.20 | 74, 64, 60 | 79, 68, 73 | 82, 88, 92 | 99, 104, 96 0.25 | 92, 86, 88 | 98, 104, 88 | 99, 108, 95 | 104, 110, 99 0.30 | 99, 98, 102 | 104, 99, 95 | 108, 110, 99 | 114, 111, 107 1.Manually find the interaction effect of Feed Rate and Depth of Cut. 2.Plot the data in the interaction plot. Does it appear that interaction effects are present? Does it appear that factor Feed Rate and factor Depth of Cut main effects are present? 3.Manually obtain the ANOVA table
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Step 1: Calculate the interaction effect of Feed Rate and Depth of Cut by multiplying the values of each combination and then summing them up. Show more…
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Problem 1: An engineer suspects that the surface finish of a metal part is influenced by the feed rate and the depth of cut. He selects three feed rates and four depths of cut. He then conducts a factorial experiment and obtains the following data: Feed Rate (in/min) | Depth of Cut (in) --- | --- | --- | --- | --- | 0.15 | 0.18 | 0.20 | 0.25 0.20 | 74, 64, 60 | 79, 68, 73 | 82, 88, 92 | 99, 104, 96 0.25 | 92, 86, 88 | 98, 104, 88 | 99, 108, 95 | 104, 110, 99 0.30 | 99, 98, 102 | 104, 99, 95 | 108, 110, 99 | 114, 111, 107 1. Plot the data in the interaction plot. Does it appear that interaction effects are present? Does it appear that factor Feed Rate and factor Depth of Cut main effects are present? Discuss. (15 points) 2. Manually obtain the ANOVA table (15 points) 3. Manually find the main effects of Feed Rate and Depth of Cut. (15 points) 4. Manually find the interaction effect of Feed Rate and Depth of Cut. (15 points) 5. Compute a 95 percent confidence interval estimate (Tukey's test) of the mean difference in response for feed rates of 0.20 and 0.25 in/min. (10 points) 6. Perform above analyses using Minitab and compare it with the results that you obtained manually. (30 points)
Ameer S.
An engineer suspects that the surface finish of a metal part is influenced by the feed rate and the depth of cut. She selects three feed rates and four depths of cut. She then conducts a factorial experiment and obtains the following data: Feed Rate (in/min) | Depth of Cut (in) 0.15 | 0.18 | 0.20 | 0.25 0.20 | 74 (5), 64 (11), 60 (29) | 79 (20), 68 (22), 73 (36) | 82 (28), 88 (7), 92 (18) | 99 (13), 104 (6), 96 (24) 0.25 | 92 (33), 86 (2), 88 (16) | 98 (15), 104 (8), 88 (35) | 99 (32), 108 (23), 95 (3) | 104 (17), 110 (27), 99 (10) 0.30 | 99 (12), 98 (21), 102 (4) | 104 (34), 99 (1), 95 (19) | 108 (26), 110 (31), 99 (9) | 114 (14), 111 (25), 107 (30) a) Analyze the data and draw conclusions. Use α = 0.05. b) Draw the main effect and interactions plot. c) Check the adequacy of the model. Note that the number between parentheses is the order of the run within the 36 runs.
Sri K.
An engineer suspects that the surface finish of a metal part is influenced by the feed rate and the depth of cut. He selects three feed rates and four depths of cut. He then conducts a factorial experiment and obtains the following data: Feed Rate (in/min) Depth of Cut (in) 0.15 0.18 0.20 0.25 0.20 74 79 82 99 64 68 88 104 60 73 92 96 0.25 92 98 99 104 86 104 108 110 88 88 95 99 0.30 99 104 108 114 98 99 110 111 102 95 99 107 a) Analyze the data and draw conclusions. Use α = 0.05. b) Prepare appropriate residuals plots and comment on the model's adequacy.
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