In Class Exercise 2^3 Factorial Design.
Group member 1 name:
Group Member 2 name:
Type your answers in red within each question and then submit this file on Canvas today!
An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle on the life (in hours) of a
machine tool. Two levels of each factor are chosen, and three replicates of a 2 factorial design are run. The results are as
follows:
a)
Estimate the main effect of B .
3
Your answer:
b)
tool?)
Use the analysis of variance to confirm your conclusions for part a). (Do any of the factors affect the life of the
Analysis of Variance
Source
DF
Adj SS
Adj MS
F-Value
P-Value
Model
Linear
A
B
C
2-Way Interactions
A*B
A*C
B*C
3-Way Interactions
A*B*C
Error
7
3
1
1
1
3
1
1
1
1
1
16
1612.67
1051.50
0.67
770.67
280.17
533.00
16.67
468.17
48.17
28.17
28.17
482.67
230.381
350.500
0.667
770.667
280.167
177.667
16.667
468.167
48.167
28.167
28.167
30.167
7.64
11.62
0.02
25.55
9.29
5.89
0.55
15.52
1.60
0.93
0.93
0.000
0.000
0.884
0.000
0.008
0.007
0.468
0.001
0.224
0.348
0.348
Total
23
2095.33
Your answer:
c)
Using the below Effects and Coefficients table, first fill in the Effect of B and calculate the coefficient of B in the
table. Then, write down a REDUCED regression model for predicting tool life (in hours) based on the results of this
experiment.
Coded Coefficients
Term
Effect
Constant
A
B
C
A*B
A*C
B*C
A*B*C
0.33
?
6.83
-1.67
-8.83
-2.83
-2.17
Coef
SE Coef
T-Value
P-Value
40.83
1.12
36.42
0.000
0.17
?
3.42
-0.83
-4.42
-1.42
-1.08
1.12
1.12
1.12
1.12
1.12
1.12
1.12
0.15
5.05
3.05
-0.74
-3.94
-1.26
-0.97
0.884
0.000
0.008
0.468
0.001
0.224
0.348
VIF
1.00
1.00
1.00
1.00
1.00
1.00
1.00
Your answer:
d)
Using the regression function you estimated, predict the life of the cutting tool when cutting speed is low, tool
geometry is low, and cutting angle is high.
Your answer:
e) Based on the analysis of main effects and interaction plots, what levels of A, B, and C would you recommend using to
increase life of this machine tool?
Your answer:
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