Six Sigma - An engineer is interested in the effects of cutting speed ( A ), too
ID: 3219180 • Letter: S
Question
Six Sigma - 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. Two levels of each factor are chosen, and three replicates of a 23 factorial design are run. The results follow:
Treatment
Replicate
A
B
C
Combination
I
II
III
-
-
-
(1)
22
31
25
+
-
-
a
32
43
29
-
+
-
b
35
34
50
+
+
-
ab
55
47
46
-
-
+
c
44
45
38
+
-
+
ac
40
37
36
-
+
+
bc
60
50
54
+
+
+
abc
39
41
47
(a) Estimate the factor effects. Which effects appear to be large?
Treatment
Replicate
A
B
C
Combination
I
II
III
-
-
-
(1)
22
31
25
+
-
-
a
32
43
29
-
+
-
b
35
34
50
+
+
-
ab
55
47
46
-
-
+
c
44
45
38
+
-
+
ac
40
37
36
-
+
+
bc
60
50
54
+
+
+
abc
39
41
47
Explanation / Answer
We use the R software to obtain the factor with largest effect.
> tt <- read.csv("clipboard",sep=" ",stringsAsFactors=TRUE)
> head(tt)
Cutting Geometry Angle Life
1 No No No 22
2 No No No 31
3 No No No 25
4 Yes No No 32
5 Yes No No 43
6 Yes No No 29
> sapply(tt,class)
Cutting Geometry Angle Life
"factor" "factor" "factor" "integer"
> summary(aov(Life~Cutting*Geometry*Angle,tt))
Df Sum Sq Mean Sq F value Pr(>F)
Cutting 1 0.7 0.7 0.022 0.883680
Geometry 1 770.7 770.7 25.547 0.000117 ***
Angle 1 280.2 280.2 9.287 0.007679 **
Cutting:Geometry 1 16.7 16.7 0.552 0.468078
Cutting:Angle 1 468.2 468.2 15.519 0.001172 **
Geometry:Angle 1 48.2 48.2 1.597 0.224475
Cutting:Geometry:Angle 1 28.2 28.2 0.934 0.348282
Residuals 16 482.7 30.2
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
We can thus wee that the Geometry is having the highest influence/effect.