Assignment 10 (do not need to hand in)
1. An engineer is interested in the eﬀects of cutting speed (
A
), tool geometry (
B
), and
cutting angle (
C
) on the life (in hours) of a machine tool. Tow levels of each factor are
chosen, and three replicates of a 2
3
factorial design are run. The results follow:
factor
replicate
ABC
I
II
III

2
2
3
1
2
5
+ 3
24
32
9
+3
53
45
0
++  5
54
74
6

+
4
4
4
5
3
8
++4
03
73
6
++6
05
4
+++3
94
14
7
a) Estimate the factorial eﬀects (calculate at least one main eﬀect and one interaction by
hands). Which eﬀects appear to be large (signiﬁcant)?
b) Use analysis of variance to conﬁrm your conclusions for part a).
c) Write down a regression model for predicting tool life (in hours) based on the results of
this experiment.
d) Analyze the residuals. Are there any obvious problems?
e) Generate main eﬀect and interaction plots for signiﬁcant eﬀects. Based on them, what
levels of
A
,
B
and
C
would you recommend using?
f) Generate the contour plot of the regression model. Does it provide information regarding
the desirable operating conditions for the machine tool?
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 Fall '08
 Staff
 Statistics, Normal Distribution, Regression Analysis, Prime number, etch rate

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