Applied Statistics and Probability for Engineers

14-7 2kFACTORIAL DESIGNS 529

–0.392

1

8

10

30

20

60

70

80

90

95

–0.294 –0.197 –0.099

Residual

–0.001 0.096 0.194

99

Normal probability

Figure 14-14 Normal probability plot of residuals for the

epitaxial process experiment.

0.5

0

• 0.5

e

Low High Deposition time, A

Figure 14-15 Plot of residuals versus deposition time.

0.5

0

• 0.5

e

Low High Arsenic flow rate, B

Figure 14-16 Plot of residuals versus arsenic flow

rate.

14-7.2 2kDesign for k3 Factors

The methods presented in the previous section for factorial designs with k2 factors each at

two levels can be easily extended to more than two factors. For example, consider k3 fac-

tors, each at two levels. This design is a 2^3 factorial design, and it has eight runs or treatment

combinations. Geometrically, the design is a cube as shown in Fig. 14-18(a), with the eight

runs forming the corners of the cube. Figure 14-18(b) lists the eight runs in a table, with each

row representing one of the runs are theandsettings indicating the low and high levels

Figure 14-17 The

standard deviation of

epitaxial layer thick-

ness at the four runs in

the 2^2 design.

0.110 A

B

0.055

0.077 0.251

(1) a

bab

+

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