Index
A
additive models 219–221
advanced model forms 241–247
A-Efficiency 206
aerosol formulations 5
analysis, strategy for response surface methodology 186–187
analysis of variance (ANOVA) 67, 146
Anderson, V.L. 124, 171–172, 244
ANOVA (analysis of variance) 67, 146
A-Optimality criterion 162
available theory 34
Average Variance of Prediction 206
B
bare minimum design size 145
Becker, N.G. 243
bias variation 28–29
blending model 161–162
blocking 28–29
blocking formulation experiments 209–213
Box, G.E.P. 205, 225, 230, 262
Box-Cox family 83
Bread experiment 226
C
candidate subgroup 172
case studies
formulations 10–19
plastic part formulation 187–188, 190–195
screening formulations 159–161
sustained release tablet development 129–135, 150–155
characterization phase 35
checkpoints 47
Chick, L.A. 195, 201, 250
cocktails 6
Cody, R. 23
coefficients, interpretation of 60–65
Columns dialog box 63
component constraints 33–34
component effects
calculating 165–166
estimation of 163–168
component effects plot 104, 107
component ratios 23
components 33
computer-aided design, using for experiments 205–207
concrete 6
confidence limits 111–112
CONstrained SIMplex (CONSIM) algorithm 149
constrained systems
about 119
components of 120–121
components with lower bounds 121–122
computation of extreme vertices 124–127
construction of extreme vertices designs for quadratic formulation models 143–146
designs for formulation systems with multicomponent constraints 147–150
four-component flare experiment 135–140
graphical display of four-component mixture space 140–143
identification of clusters of vertices 143–144
midpoints of long edges 127–129
response surface modeling with 185–213
screening 157–180
sustained release tablet development 129–135
sustained release tablet formulation case study 150–155
three-component example 123–124
constraint plane centroid 137–138
contour plots 62–63, 108
CONVERT algorithm 149
Cornell, J.A. 47, 51–52, 62, 219, 224, 231, 234, 242, 257–258, 261
Cox, D.R. 111, 165
Cox axes 193–194, 198
Cox effect direction 163–164
Cox model 105, 111
curvilinear effect 167
D
data, high-quality 23–32
data "pedigree" 57–58
D-Efficiency 206
Derringer, G.L. 252–254
Design Ease 149
designs
considerations for 161–162
considerations for quadratic blending model 188–190
creating for quadratic models using XVERT algorithm 201–204
D-optimal 260–261
extreme vertices 121, 124–127, 143–146, 161, 171–179
for formulation systems with multicomponent constraints 147–150
for formulations with process variables 221–225
response surface 51–53
saturated 145, 162
screening 48–51, 99–107, 113–114
simplex 45–48, 99–113
simplex-centroid 47, 54, 57
simplex-lattice 53
strategy for response surface methodology 186–187
D-Optimal algorithm 162, 189, 190, 193, 260–261
Draper, N.R. 205, 210, 243, 246, 247, 262
dyes 6
E
Elfving, G. 169
end effect blends 99
environmental variables 28
experimental designs, for formulations 43–54
experimental environment
diagnosis of the 33–34
evolution of the 34–37
geometry of the 44–45
experimental error 29
experimental variation, estimation of the 114–115
experiments
administration of 29
basics of 21–39
blocking formulation 209–213
Bread 226
Fish patty 221, 231–235
formulations 6–10
fundamentals of good 22–32
involving formulation and process variables 217–236
screening 94–95
strategy for 34–37
using computer-aided design for 205–207
extreme vertices designs
about 121, 161
computation of 124–127
construction of for quadratic formulation models 143–146
XVERT algorithm for computing subsets of 171–179
F
face-centered-cube design (FCCD) 201
factors 23
FCCD (face-centered-cube design) 201
Fish patty experiment 221, 231–235
Fit Curve 228
Fit Model platform 63, 70
food 5, 11–13
formulation models
basic 60–65
multicollinearity in 255–263
formulation variables, experiments involving 217–236
formulations
See also screening formulations
aerosol 5
case studies 10–19
designs for formulations with process variables 221–225
development of 3–19
displaying compositions using trilinear coordinates 8–10
examples of 4–6
experimental designs for 43–54
experiments 6–10, 37–38, 209–213
number to test 32
robustness of 168–171
four-component flare experiment 135–140
four-component mixture space 140–143
G
gasoline blends 5
G-Efficiency 206–207
glass formulation optimization example 195–201
Goos, P. 162, 190
Graph Builder 78
graphical analysis
of four-component mixture space 140–143
of simplex screening designs 107–113
H
H1 models 243
Hackler, W.C. 242
Hare, L.B. 11
Heinsman, J.A. 253–254
Hirata, M. 129
histogram 76–77
Hoerl, R.W. 56, 66, 68, 255
Huisman, R. 13
I
integration 35
interactive models 219–221
I-Optimality Criterion 162, 189
J
JMP 149, 207–209
Jones, B. 162, 190
K
Kennard, R.W. 255
Kurotori, I.S. 100
L
lack of fit
assessing 145–146
F-ratio 146
test for 81
lattice 51
Leesawat, P. 250
Lenth's method 232
Lewis, G.A. 150
Li, W. 254
linear additive model 219
long edges
midpoints of 127–129
regions with 138–139
lower bounds, components with 121–122
lubricants 15–17
Lucas, J.M. 207
lurking variables 23
M
Marquardt, D.W. 49–50, 161, 175, 202, 258
Martinello, T. 17
McLean, R.A. 124, 171–172, 244
metal alloys 5
Microcel effect 167
midpoints, of long edges 127–129
Minitab 149
MIXSOFT algorithm 149
Model Effects dialog box 62
models
about 55
additive 219–221
advanced forms 241–247
blending 161–162
building process for 56–59
Cox 105, 111
evaluating and criticizing 65–69
formulation 60–65, 255–263
linear additive 219
with more than three components 86–90
non-linear 225–228
quadratic 143–146, 201–204
slack variable 62, 238, 240
specifications for 238–241
Montgomery, D.C. 66, 67, 69, 146, 162, 190, 225, 228, 231, 253–254, 257–258
multicollinearity
about 255–257
addressing 260–263
in formulation models 255–263
impact of 259–260
quantifying 257–259
multicomponent constraints, designs for formulation systems with 147–150
multiple responses, handling 250–254
multiplicative model 220
Myers, R.H. 86, 87
N
non-linear blending 45
non-linear models 225–228
normal probability plot 74–75
O
objectives, well-defined 23
optimization phase 37
Optimum Design Algorithm 162
P
paints 5
pharmaceutical tablets 4, 13–15, 17–19
Piepel, G.F. 62, 104, 149, 164, 165, 166, 193, 195, 201, 250
Piepel effect direction 164–165
Plackett-Burman designs 172, 176, 181–183, 202
plastic part formulation example and case study 187–188, 190–195
plots, basic 59–60
prediction 34
Prediction Profiler 89
Prescott, P. 219
process variables
about 218
designs for formulations with 221–225
experiments involving 217–236
proportions 23
pseudo replicates 143
pure error 146
Q
quadratic blending model, design considerations for 188–190
quadratic models
construction of extreme vertices designs for 143–146
creating designs for using XVERT algorithm 201–204
R
randomization 24–28
Rayner, A.A. 257–258
reference blend 163
regions, with long edges 138–139
replication 31–32, 145–146
residual analysis 69–82
response optimization 247–250
response surface designs 51–53
response surface methodology
basics of 21–39
with constrained systems 185–213
Richter scale 82–83
ridge regression 262
RMSE (root mean square error) 67, 200, 232
rocket propellants 5
root mean square error (RMSE) 67, 200, 232
rubber 6
run chart 77
S
saturated design 145, 162
Scheffé models 60–61, 78, 83–84, 239, 242, 243, 244, 249, 254
screening designs
about 48–51
post- 113–114
simplex 99–107
screening experiments 94–95
screening formulations
case study 159–161
components of 93–115
concepts for 95–99
constrained systems 157–180
purpose of screening experiments 94–95
strategy for 158–159
screening phase 36
simplex 10
simplex designs 45–48, 99–113
simplex in terms of pseudo-components 121–122
simplex-centroid designs 47, 54
simplex-lattice designs 53
slack variable model 62, 238, 240
Snee, R.D. 49–50, 56, 62, 66, 68, 69, 104, 120, 143, 161, 164–166, 175, 193, 202, 224, 228, 229, 231, 242–243, 257–258
soxhlet leaching weight loss 196
"special" cubic model 64
Specialized Modeling platform 228
spinel phase yield 196
St. John, R.C. 243, 246, 247, 262
standard error of the average of y 31–32
strategies, recommended 229–230
subsets, of extreme vertices 171–179
Suich, R. 252–254
summary statistics 59–60
sustained release tablet development and case study 129–135, 150–155
T
temperature viscosity 196
textile fiber blends 6
T-Optimality Criterion 162
trace components 33
transformation, of variables 82–86
trilinear coordinates, displaying formulation compositions using 8–10
23 factorial design 221
U
unconstrained components 33–34
V
variables
environmental 28
lurking 23
process 217–236
transformation of 82–86
variance inflation factors (VIFs) 257
variation 29–31
vertices
See also extreme vertices designs
computation of 135–136
identification of clusters of 143–144
VIFs (variance inflation factors) 257
X
XONAEV algorithm 149
XVERT algorithm
about 159, 162, 189
for computing subsets of extreme vertices 171–179
creating designs for quadratic models using 201–204