Six Sigma - An engineer is interested in the effects of cutting speed ( A ), too
ID: 3229836 • 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:
* 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
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
number of repilicates,n = 3
total:
(1) = 22+31+25 = 78
a = 104
b = 119
ab = 148
c = 127
ac = 113
bc = 164
abc = 127
factor effects:
A = (1 / 4n) * (-(1) + a - b + ab - c + ac - bc + abc)
A = (1/12)*(-78 + 104 - 119 + 148 - 127 + 113 - 164 + 127)
A = 0.333
B = (1 / 4n) * (-(1) - a + b + ab - c - ac + bc + abc)
B = (1/12)*(-78 - 104 + 119 + 148 - 127 - 113 + 164 + 127)
B = 11.333
C = (1 / 4n) * (-(1) - a - b - ab + c + ac + bc + abc)
C = (1/12)*(-78 - 104 - 119 - 148 + 127 + 113 + 164 + 127)
C = 6.833