This document discusses experimental design and 3k factorial designs. It begins by outlining the key elements of designing experiments, including conjectures or hypotheses, response variables, factors and their levels, treatments, blocking, tools for measurement, and effect models. It then provides an example of a 3^2 factorial design using a syrup frothing experiment with two factors (sugar concentration and acid concentration) at two levels each. The results of this experiment are analyzed, calculating sums of squares for the factors and their interaction. Finally, the document briefly introduces the general principles of a 3k factorial design.

1. 3k Factorial Design
ARIF RAHMAN
1

2. Experiments
Hypothesis/
Conjecture
Design of
Experiment
Conduct
Experiment
Analysis of
Data
Discussion &
Conclusion
Refine
the Model
2

3. Elements of Design of
Experiments
1. Conjecture or hypothesis
2. Response variable
3. Factors, levels and ranges
4. Treatments of factors
5. Blockings
6. Tools and methods for experiments and
measurements
7. Effect models (independent or interaction factors)
8. Replication, randomization and local factor
3

4. P Diagram
Signal
Factors
(m)
Noise
Factors
(x)
Control
Factors
(z)
Scaling
Factors
(r)
Response
Variables
(y)
F(x,m,z,r)
4
Inputs
Controllable Factors
(x)
Uncontrollable Factors
(z)
Output
(y)
F(x,z)

5. Introduction
5

6. Introduction
6

7. Introduction
7

8. 32 Factorial Design
8

9. 32 Factorial Design
9

10. 32 Factorial Design
10

11. 32 Factorial Design
11

12. 32 Factorial Design
12

13. 33 Factorial Design
13

14. 33 Factorial Design
14

15. an Example: Syrup Frothing
Experiment
15

16. an Example: Syrup Frothing
Experiment
16

17. an Example: Syrup Frothing
Experiment
17

18. an Example: Syrup Frothing
Experiment
18

19. an Example: Syrup Frothing
Experiment
19

20. an Example: Syrup Frothing
Experiment
20

21. an Example: Syrup Frothing
Experiment
21

22. an Example: Syrup Frothing
Experiment
22

23. an Example: Syrup Frothing
Experiment
23

24. an Example: Syrup Frothing
Experiment
24

25. an Example: Syrup Frothing
Experiment
25
78
.
126
54
165
3
.
2
16
75
74
)
(
2
2
2
2
2
2





 AB
AB
I
I(AB) J(AB)
-198 -106 -155 -222 -79 -158
331 255 377 238 440 285
-59 -74 -206 -144 -40 -155
74 75 16 -128 321 -28
11
.
174
,
6
54
165
3
.
2
)
28
(
321
)
128
(
)
(
2
2
2
2
2
2







 AB
AB
J
89
.
300
,
6
11
.
174
,
6
78
.
126 


AB
SS

26. an Example: Syrup Frothing
Experiment
26

27. an Example: Syrup Frothing
Experiment
27

28. an Example: Syrup Frothing
Experiment
28

29. an Example: Syrup Frothing
Experiment
29

30. an Example: Syrup Frothing
Experiment
30
SSAB = 6,300.89 = 126.78 + 6,174.11
SSABC = 4,628.76 = 3,804.11 + 221.77 + 18.77 + 584.11

31. General 3k Factorial Design
31

32. General 3k Factorial Design
32

33. 33
That’s all
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