14-10 RESPONSE SURFACE METHODS AND DESIGNS (CD) 565(a) Test for differences between salts, application levels, and
interactions. Use 0.01.
(b) Draw a graph of the interaction between salt and
application level. What conclusions can you draw from
this graph?
(c) Analyze the residuals from this experiment.
14-44. An article in the IEEE Transactions on Components,
Hybrids, and Manufacturing Technology(Vol. 15, 1992) de-
scribes an experiment for investigating a method for aligning
optical chips onto circuit boards. The method involves placing
solder bumps onto the bottom of the chip. The experiment
used three solder bump sizes and three alignment methods.
The response variable is alignment accuracy (in micrometers).
The data are as follows:for studying a silver automobile basecoat. The response vari-
able is distinctness of image (DOI). The variables used in the
experiment are
APercentage of polyester by weight of polyester/melamine
(low value50%, high value70%)
BPercentage of cellulose acetate butyrate carboxylate (low
value15%, high value30%)
CPercentage of aluminum stearate (low value1%, high
value3%)
DPercentage of acid catalyst (low value0.25%, high
value0.50%)
The responses are (1)63.8, a77.6, b68.8, ab
76.5, c72.5, ac77.2, bc77.7, abc84.5, d60.6,
ad64.9, bd72.7, abd73.3, cd68.0, acd76.3,
bcd76.0, and abcd75.9.
(a) Estimate the factor effects.
(b) From a normal probability plot of the effects, identify a
tentative model for the data from this experiment.
(c) Using the apparently negligible factors as an estimate of
error, test for significance of the factors identified in part
(b). Use 0.05.
(d) What model would you use to describe the process, based
on this experiment? Interpret the model.
(e) Analyze the residuals from the model in part (d) and com-
ment on your findings.
14-47. An article in the Journal of Manufacturing Systems
(Vol. 10, 1991, pp. 32–40) describes an experiment to investi-
gate the effect of four factors Pwaterjet pressure, F
abrasive flow rate, Gabrasive grain size, and Vjet tra-
verse speed on the surface roughness of a waterjet cutter. A 2^4
design follows.(a) Is there any indication that either solder bump size or
alignment method affects the alignment accuracy? Is
there any evidence of interaction between these factors?
Use 0.05.
(b) What recommendations would you make about this
process?
(c) Analyze the residuals from this experiment. Comment on
model adequacy.
14-45. An article in Solid State Technology(Vol. 29, 1984,
pp. 281–284) describes the use of factorial experiments in
photolithography, an important step in the process of manu-
facturing integrated circuits. The variables in this experiment
(all at two levels) are prebake temperature (A), prebake
time (B), and exposure energy (C), and the response variable
is delta line width, the difference between the line on the
mask and the printed line on the device. The data are as fol-
lows: (1)2.30, a9.87, b18.20, ab30.20,
c23.80, ac4.30, bc3.80, and abc14.70.
(a) Estimate the factor effects.
(b) Use a normal probability plot of the effect estimates to
identity factors that may be important.
(c) What model would you recommend for predicting the
delta line width response, based on the results of this exper-
iment?
(d) Analyze the residuals from this experiment, and comment
on model adequacy.
14-46. An article in the Journal of Coatings Technology
(Vol. 60, 1988, pp. 27–32) describes a 2^4 factorial design usedSolder Bump Size Alignment Method
(diameter in m) 1 2 3
4.60 1.55 1.05
75 4.53 1.45 1.00
2.33 1.72 0.82
130 2.44 1.76 0.95
4.95 2.73 2.36
260 4.55 2.60 2.46Factors Surface
VFPGRoughness
Run (in/min) (lb/min) (kpsi) (Mesh No.) ( )
1 6 2.0 38 80 104
2 2 2.0 38 80 98
3 6 2.0 30 80 103
4 2 2.0 30 80 96
5 6 1.0 38 80 137
6 2 1.0 38 80 112
7 6 1.0 30 80 143
8 2 1.0 30 80 129
9 6 2.0 38 170 88
10 2 2.0 38 170 70
11 6 2.0 30 170 110
12 2 2.0 30 170 110
13 6 1.0 38 170 102
14 2 1.0 38 170 76
15 6 1.0 30 170 98
16 2 1.0 30 170 68mc 14 .qxd 5/9/02 7:55 PM Page 565 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH112 FIN L: