ABCDEFGHIJKLMNOPQRSTUVWXYZAAABACADAEAFAGAHAIAJ
1
RunABC
y (lb/day)
Factor A
concentration of coagulant added
Conclusion (ranking):
1. Factor C
2
11%722005Factor B
treatment temperature
2. Factor A
3
22%7220030Factor C
stirring speed
3. Factor B
4
31%1002006
yellow highlighted
low
Fractional factorial is usuable to represent full factorial.
5
42%10020033
non-highlighted
high
6
51%724004
blue highlighted
4 runs for fractional
7
62%724003
8
71%1004005
9
82%1004004
10
11
Significance of Main Effects (full)
12
Factor A
Runs where A is + :
30+33+3+4=70/4
Average =
17.5+
13
Runs where A is - :
5+6+4+5=20/4
Average =
5-
14
total effect of A =
12.5
15
16
Factor B
Runs where B is + :
6+5+33+4=48/4
Average =
12+
17
Runs where B is - :
5+4+30+3=42/4
Average =
10.5-
18
total effect of B =
1.5
19
20
Factor C
Runs where C is + :
4+5+3+4=16/4
Average =
4+
21
Runs where C is - :
5+6+30+33=74/4
Average =
18.5-
22
total effect of C =
-14.5
23
24
Factor C has the most significant effect. Followed by Factor A. Lastly Factor B has the least significant effect.
25
26
27
28
Significance of Main Effects (fractional)
29
Factor A
Runs where A is + :
30+4=34/2
Average =
17+
30
Runs where A is - :
6+4=10/2
Average =
5-
31
total effect of A =
12
32
33
Factor B
Runs where B is + :
6+4=10/2
Average =
5+
34
Runs where B is - :
30+4=34/2
Average =
17-
35
total effect of B =
-12
36
37
Factor C
Runs where C is + :
4+4=8/2
Average =
4+
38
Runs where C is - :
30+6=36/2
Average =
18-
39
total effect of C =
-14
40
41
Factor C has the most significant effect. Followed by Factor A and B has the least significant effect.
42
43
44
45
RunABC
y (lb/day)
Factor A
concentration of coagulant added
Conclusion for full:
AxB has no interaction
46
11%722005Factor B
treatment temperature
AxC has interaction
47
22%7220030Factor C
stirring speed
BxC has no interaction
48
31%1002006
yellow highlighted
low
Conclusion for fractional:
AxB has no interaction
49
42%10020033
non-highlighted
high
AxC has interaction
50
51%724004
blue highlighted
4 runs for fractional
BxC has no interaction
51
62%724003
Fractional factorial is not usable to represent full factorial.
52
71%1004005
53
82%1004004
54
55
Interection effects (full)
56
At low A
57
Runs of low B =
5+4=9/2
Average =
4.5-
58
Runs of high B =
6+5=11/2
Average =
5.5+
59
total effect of B =
1
60
61
At high A
62
Runs of low B =
30+3=33/2
Average =
16.5-
63
Runs of high B =
33+4=37/2
Average =
18.5+
64
total effect of B =
2
65
66
The gradient of both lines are different by a little margine.
67
When A is low, the interaction between A and B is small.
68
When A is high, the interaction between A and B is slightly more.
69
Both lines are parallel, then the interaction is not significant.
70
71
At low A
72
Runs of low C =
5+6=11/2
Average =
5.5-
73
Runs of high C =
4+5=9/2
Average =
4.5+
74
total effect of C =
-1
75
76
At high A
77
Runs of low C =
30+33=63/2
Average =
31.5-
78
Runs of high C =
3+4=7/2
Average =
3.5+
79
total effect of C =
-28
80
81
When A is high, there is a large different in gradient.
82
When A is low, there is little margine different in gradient.
83
The gradient of both lines are negative and different values.
84
Both lines are not parallel
85
Therefore there is a significant interaction between A and C
86
87
At low B
88
Runs of low C =
5+30=35/2
Average =
17.5-
89
Runs of high C =
4+3=7/2
Average =
3.5+
90
total effect of C =
-14
91
92
At high B
93
Runs of low C =
6+3339/2
Average =
19.5-
94
Runs of high C =
5+49/2
Average =
4.5+
95
total effect of C =
-15
96
97
The gradient of both lines are negative and different values.
98
When B is low, there is a interaction between B and C.
99
When B is high, there is a interaction between B and C.
100
Both lines are parallel, then the the interaction is not significant.