Applied Statistics and Probability for Engineers

540 CHAPTER 14 DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS

• 141.1

1

6

10

30

20

60

70

80

90

96

• 64.5 12.1 88.8 165.4 242.0 318.6

99

Normal probability

D

A

AD

Effect

Low (0.80 cm)

200

400

600

800

1400

Etch rate

Å/min

A (Gap)

1000

1200

0

High (1.20 cm)

D(Power)low = 275 w

D(Power)high = 325 w

Figure 14-21 Normal probability plot of effects

from the plasma etch experiment.

Figure 14-22 AD(Gap-Power) interaction from the

plasma etch experiment.

For example, when both Aand Dare at the low level, the predicted value is

and the four residuals at this treatment combination are

The residuals at the other three treatment combinations (Ahigh, Dlow), (Alow, Dhigh), and

(Ahigh, Dhigh) are obtained similarly. A normal probability plot of the residuals is shown in

Fig. 14-23. The plot is satisfactory.

e 3  633  597  36 e 4  601  597  4

e 1  550  597  47 e 2  604  597  7

 597

yˆ776.0625a

101.625

2

b 1  12 a

306.125

2

b 1  12 a

153.625

2

b 1  121  12

Table 14-21 Analysis of Variance for the Plasma Etch Experiment

Source of Degrees of

Variation Sum of Squares Freedom Mean Square f 0 P-Value

A 41,310.563 1 41,310.563 20.28 0.0064

B 10.563 1 10.563  1 —

C 217.563 1 217.563  1 —

D 374,850.063 1 374,850.063 183.99 0.0000

AB 248.063 1 248.063  1 —

AC 2,475.063 1 2,475.063 1.21 0.3206

AD 94,402.563 1 94,402.563 46.34 0.0010

BC 7,700.063 1 7,700.063 3.78 0.1095

BD 1.563 1 1.563  1 —

CD 18.063 1 18.063  1 —

Error 10,186.813 5 2,037.363

Total 531,420.938 15

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