An engineer has performed an experiment to study the effect of four factors on the surface roughness of a machined part. The factors (and their levels) are A =tool angle (12, 15), B =cutting fluid viscosity (300, 400), C=feed rate (10, 15 in/min), and D =cutting fluid cooler used (no, yes). The data from this experiment (with the factors coded to the usual +1, -1 levels) are shown in Table 13E.5.
(a) Estimate the factor effects. Plot the effect estimates on a normal probability plot and select a tentative model.
TABLE 1 3 E .5
Surface Roughness Experiment for Exercise 13.16
Â
Surface
Run
A
B
C
D
Roughness
1
−
0.00340
2
+
0.00362
3
0.00301
4
0.00182
5
0.00280
6
0.00290
7
0.00252
8
0.00160
9
0.00336
10
0.00344
11
0.00308
12
0.00184
13
0.00269
14
0.00284
15
0.00253
16
0.00163
(b) Fit the model identified in part (a) and analyze the residuals. Is there any indication of model inadequacy?
(c) Repeat the analysis from parts (a) and (b) using 1/y as the response variable. Is there an indication that the transformation has been useful?
(d) Fit the model in terms of the coded variables that you think can be used to provide the best predictions of the surface roughness. Convert this prediction equation into a model in the natural variables.
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