520 CHAPTER 14 DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS(a) Is there any indication that either factor affects the amount
of warping? Is there any interaction between the factors?
Use = 0.05.
(b) Analyze the residuals from this experiment.
(c) Plot the average warping at each level of copper content
and compare the levels using Fisher’s LSD method.
Describe the differences in the effects of the different
levels of copper content on warping. If low warping is
desirable, what level of copper content would you
specify?
(d) Suppose that temperature cannot be easily controlled in
the environment in which the copper plates are to be used.
Does this change your answer for part (c)?
14-7. Consider a two-factor factorial experiment. Develop a
formula for finding a 100 (1 )% confidence interval on
the difference between any two means for either a row or
column factor. Apply this formula to find a 95% CI on the dif-
ference in mean warping at the levels of copper content 60 and
80% in Exercise 14-6.
14-8. An article in the Journal of Testing and Evaluation
(Vol. 16, no. 6, 1988, pp. 508–515) investigated the effects of
cyclic loading frequency and environment conditions on fa-
tigue crack growth at a constant 22 MPa stress for a particularEnvironment
Air H 2 O Salt H 2 O
2.29 2.06 1.90
10
2.47 2.05 1.93
2.48 2.23 1.75
2.12 2.03 2.06
2.65 3.20 3.10
Frequency 1
2.68 3.18 3.24
2.06 3.96 3.98
2.38 3.64 3.24
2.24 11.00 9.96
0.1
2.71 11.00 10.01
2.81 9.06 9.36
2.08 11.30 10.40(a) Is there indication that either factor affects crack growth
rate? Is there any indication of interaction? Use 0.05.
(b) Analyze the residuals from this experiment.
(c) Repeat the analysis in part (a) using ln(y) as the response.
Analyze the residuals from this new response variable and
comment on the results.
14-9. An article in the IEEE Transactions on Electron Devices
(November 1986, p. 1754) describes a study on the effects of
two variables—polysilicon doping and anneal conditions (time
and temperature)—on the base current of a bipolar transistor.
The data from this experiment follows below Exercise 14-10.
(a) Is there any evidence to support the claim that either poly-
silicon doping level or anneal conditions affect base
current? Do these variables interact? Use 0.05.
(b) Graphically analyze the interaction.
(c) Analyze the residuals from this experiment.
14-10. Consider the experiment described in Exercise 14-9.
Use Fisher’s LSD method to isolate the effects of anneal con-
ditions on base current, with 0.05.14-5 GENERAL FACTORIAL EXPERIMENTSMany experiments involve more than two factors. In this section we introduce the case where
there are alevels of factor A,blevels of factor B,clevels of factor C, and so on, arranged
in a factorial experiment. In general, there will be abc ntotal observations, if there are
nreplicates of the complete experiment.pCopper Content (%)
(C) 40 60 80 100
50 17, 20 16, 21 24, 22 28, 27
75 12, 9 18, 13 17, 12 27, 31
100 16, 12 18, 21 25, 23 30, 23
125 21, 17 23, 21 23, 22 29, 31TemperatureAnneal (temperature/time)
900/60 900/180 950/60 1000/15 1000/301 1020
4.40 8.30 10.15 10.29 11.01
Polysilicon 4.60 8.90 10.20 10.30 10.58
doping
2 1020 3.20 7.81 9.38 10.19 10.81
3.50 7.75 10.02 10.10 10.60warping of copper plates. The two factors studied were
temperature and the copper content of the plates. The re-
sponse variable is the amount of warping. The data are as
follows:material. The data from the experiment follow. The response
variable is fatigue crack growth rate.c 14 .qxd 5/9/02 7:54 PM Page 520 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH112 FIN L: