Exercise 3

 

1. Consider a 28-4 fractional factorial design.

  1. How many variables does this design have?

  2. How many runs are involved in this design?

  3. How many levels are used for each of the variables?

  4. How many ( independent ) generators are there for this design?

  5. How many words are there in the defining relation ( counting I )?

 

 

2. Repeat problem 1 for a 29-4 fractional factorial design.

 

 

3. Repeat problem 1 for a 26-1 fractional factorial design.

 

 

4. Analyze the following experimental results from a welding study. Do you notice any relationship among Y1, Y2, and Y3?

 

Order of runs

X1

X2

X3

X4

X5

Y1

(V)

Y2

(A)

Y3

(W)

12

-1

-1

-1

-1

1

23.43

141..61

3318

1

1

-1

-1

-1

-1

25.70

161.13

4141

2

-1

1

-1

-1

-1

27.75

136.54

3790

6

1

1

-1

-1

1

31.60

128.52

4061

15

-1

-1

1

-1

-1

23.57

145.55

3431

8

1

-1

1

-1

1

27.68

123.75

3425

7

-1

1

1

-1

1

28.76

121.93

3507

4

1

1

1

-1

-1

31.82

120.37

3765

11

-1

-1

-1

1

-1

27.09

95.24

2580

14

1

-1

-1

1

1

31.28

78.31

2450

3

-1

1

-1

1

1

31.20

74.34

2319

16

1

1

-1

1

-1

33.42

91.76

3067

13

-1

-1

1

1

1

29.51

65.23

1925

10

1

-1

1

1

-1

31.35

78.65

2466

5

-1

1

1

1

-1

31.16

79.76

2485

9

1

1

1

1

1

33.65

72.80

2450

 

 

The variables and their settings were as follows:

 

 

 

 

 

 

 

 

 

 

 

Variable

-1

1

X1

Open-circuit voltage(V)

31

34

X2

Slope

11

6

X3

Electrode melt-off rate (ipm)

162

137

X4

Electrode diameter (in.)

0.045

0.035

X5

Electrode extention (in.)

3/8

5/8

 

 

 

5. A mechanical engineer used the following design:

 

1

2

3

4

5

-

-

-

+

-

+

-

-

-

-

-

+

-

-

+

+

+

-

+

+

-

-

+

-

+

+

-

+

+

+

-

+

+

+

-

+

+

+

-

-

 

 

  1. Write a set of generators for this design.

  2. Is this set unique? If so, explain why. If not, write a different set of generators for this design.