14-7 2kFACTORIAL DESIGNS 539Thus, the effect of increasing the gap between the anode and the cathode from 0.80 to
1.20 centimeters is to decrease the etch rate by 101.625 angstroms per minute.
It is easy to verify (using Minitab, for example) that the complete set of effect estimates isThe normal probability plot of these effects from the plasma etch experiment is shown in
Fig. 14-21. Clearly, the main effects of Aand Dand the ADinteraction are significant, because
they fall far from the line passing through the other points. The analysis of variance summa-
rized in Table 14-21 confirms these findings. Notice that in the analysis of variance we have
pooled the three- and four-factor interactions to form the error mean square. If the normal
probability plot had indicated that any of these interactions were important, they would not
have been included in the error term.
Since A101.625, the effect of increasing the gap between the cathode and anode is
to decrease the etch rate. However, D306.125; thus, applying higher power levels will in-
crease the etch rate. Figure 14-22 is a plot of the ADinteraction. This plot indicates that the
effect of changing the gap width at low power settings is small, but that increasing the gap at
high power settings dramatically reduces the etch rate. High etch rates are obtained at high
power settings and narrow gap widths.
The residuals from the experiment can be obtained from the regression modelyˆ776.0625a101.625
2b x 1 a306.125
2b x 4 a153.625
2b x 1 x 4A 101.625 AD 153.625
B 1.625 BD 0.625
AB 7.875 ABD 4.125
C 7.375 CD 2.125
AC 24.875 ACD 5.625
BC 43.875 BCD 25.375
ABC15.625 ABCD40.125
D 306.125Table 14-20 Contrast Constants for the 2^4 Design
A B AB C AC BC ABC D AD BD ABD CD ACD BCD ABCD
112
a
b
ab
c
ac
bc
abc
d
ad
bd
abd
cd
acd
bcd
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