كتاب Design of Experiments in Chemical Engineering - A Practical Guide
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 كتاب Design of Experiments in Chemical Engineering - A Practical Guide

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تاريخ التسجيل : 01/07/2009
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مُساهمةموضوع: كتاب Design of Experiments in Chemical Engineering - A Practical Guide    كتاب Design of Experiments in Chemical Engineering - A Practical Guide  Emptyالأربعاء 27 أكتوبر 2021, 1:26 am

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Design of Experiments in Chemical Engineering - A Practical Guide
Zˇivorad R. Lazic´

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Contents
Preface IX
I Introduction to Statistics for Engineers 1
1.1 The Simplest Discrete and Continuous Distributions 7
1.1.1 Discrete Distributions 10
1.1.2 Continuous Distribution 13
1.1.3 Normal Distributions 16
1.2 Statistical Inference 22
1.2.1 Statistical Hypotheses 23
1.3 Statistical Estimation 30
1.3.1 Point Estimates 31
1.3.2 Interval Estimates 33
1.3.3 Control Charts 42
1.3.4 Control of Type II error-b 44
1.3.5 Sequential Tests 46
1.4 Tests and Estimates on Statistical Variance 52
1.5 Analysis of Variance 63
1.6 Regression analysis 120
1.6.1 Simple Linear Regression 121
1.6.2 Multiple Regression 136
1.6.3 Polynomial Regression 140
1.6.4 Nonlinear Regression 144
1.7 Correlation Analysis 146
1.7.1 Correlation in Linear Regression 148
1.7.2 Correlation in Multiple Linear Regression 152

II Design and Analysis of Experiments 157
2.0 Introduction to Design of Experiments (DOE) 157
2.1 Preliminary Examination of Subject of Research 166
2.1.1 Defining Research Problem 166
2.1.2 Selection of the Responses 170
2.1.3 Selection of Factors, Levels and Basic Level 185
2.1.4 Measuring Errors of Factors and Responses 191
2.2 Screening Experiments 196
2.2.1 Preliminary Ranking of the Factors 196
2.2.2 Active Screening Experiment-Method of Random Balance 203
2.2.3 Active Screening Experiment Plackett-Burman Designs 225
2.2.3 Completely Randomized Block Design 227
2.2.4 Latin Squares 238
2.2.5 Graeco-Latin Square 247
2.2.6 Youdens Squares 252
2.3 Basic Experiment-Mathematical Modeling 262
2.3.1 Full Factorial Experiments and Fractional Factorial Experiments 267
2.3.2 Second-order Rotatable Design (Box-Wilson Design) 323
2.3.3 Orthogonal Second-order Design (Box-Benken Design) 349
2.3.4 D-optimality, Bk-designs and Hartleys Second-order Designs 363
2.3.5 Conclusion after Obtaining Second-order Model 366
2.4 Statistical Analysis 367
2.4.1 Determination of Experimental Error 367
2.4.2 Significance of the Regression Coefficients 374
2.4.3 Lack of Fit of Regression Models 377
2.5 Experimental Optimization of Research Subject 385
2.5.1 Problem of Optimization 385
2.5.2 Gradient Optimization Methods 386
2.5.3 Nongradient Methods of Optimization 414
2.5.4 Simplex Sum Rotatable Design 431
2.6 Canonical Analysis of the Response surface 438
2.7 Examples of Complex Optimizations 443
III Mixture Design “Composition-Property” 465
3.1 Screening Design “Composition-Property” 465
3.1.1 Simplex Lattice Screening Designs 469
3.1.2 Extreme Vertices Screening Designs 473
3.2 Simplex Lattice Design 481
3.3 Scheffe Simplex Lattice Design 484
3.4 Simplex Centroid Design 502
3.5 Extreme Vertices Designs 506
3.6 D-optimal Designs 521
3.7 Draper-Lawrence Design 529
3.8 Factorial Experiments with Mixture 540
3.9 Full Factorial Combined with Mixture Design-Crossed Design 543
Appendix 567
A.1 Answers to Selected Problems 567
A.2 Tables of Statistical Functions 589
Index 607
Index
a
abstract trials 388
adequate 265
adequate linear model 314 adequate, model lackof fit 265 adequate second-order model 366
aliased/confounded effect 273 analysis of variance (ANOVA)
one-way analysis of variance 63 three-way analysis of variance 64 two-way analysis of
variance 63
approximation 266
arithmetic average 4
arithmetic matrix 275
auxiliary tables with several inputs 205 axial points 323
b
balanced incomplete random blocks 234 Barttlet’s test for equality of variances 111 basic
experiment 262, 265
basic level 185
bell-shaped 17
Bernoulli distribution 10
bias 32
biased variance 11
binomial distribution 11
Bk-designs 363
black-box model 167
c
calculated value 110
canonical analysis of the response surface 438
categorical/qualitative factor 189
center points 323
central composite orthogonal design 350 central composite rotatable design 325 central design
324
central limit theorem 34 chi-square distribution 52
classical design of experiments-one factor at a time 162
Cochran’s test for equality of variances 113 coded factor 268
coefficient of determination 147 coefficient of variation 6 combined model 546
compactness 162
completely randomized block design 227 composite design 323
concordance coefficient 197 concordant domain of factor 262 conditional sum of squares 372
confidence coefficient 34
confidence intervals 31
confidence limits 34
confounded effect 273
consistency 31
constant method 236
continuous 171
continuous distributions 7 continuous D-optimality design 363 contour diagram 263
contour graph 170
contrast 80
controlcharts, upper and lower control limits 42
controllable 168
control points 490
core 323
core points 323
correlation analysis 146
crossed-design 542
d
D- and G-optimality 520 data transformation 113
defining contrast 272
defining research problem 166
degrees of freedom 39
dependent variable (response) 120
design of experiments (DOE) 157
design matrix 268, 275
design point 82
design point of experiment-trial 185
design saturation 272
desirability function 176
determination of experimental error
design points-trials 367
experiment error (reproducibility
variance) 367
measurement error (determination error)
367
replicated measurements
(determinations) 367
replicated trials 367
trial error-variance of replicated trials 367
direct methods 234
discrete 171
discrete distributions 7
disturbance variables 168
domain of extreme experiment 190
domain of factors 190, 262
domain of response 171
D-optimal designs 520
D-optimality designs 363
Draper-Lawrence design 528
e
effect is statistically significant 110
efficiency 32
estimation theory 30
expected value
sum of squares of the values 9
weighted average 9
experimental center 168
experimental domain 186
experimental variance-reproducibility
variance 370
experiment error 195
exponential function 121
extrapolation 265
extreme problems 169, 385
extreme vertices designs 506
extreme vertices screening designs 473
f
factor effects 169
factorial experiments with mixture 539
factor interval of variation 185
factor levels 168
factors 185
factor space 262
factor variation level 185
F-distribution 54
fictional factor 269
fractional factorial experiment 205, 267
fractional replica 268
full factorial experiment 205, 267
g
general response 173
generating ratio 172
Gibbs’s triangle 481
gradient optimization methods 386
graeco-latin square 247
h
Harington’s overall desirability function 176
Hartley’s designs 365
Hartley’s second-order designs 363
hexagonal 431
histogram 115
hypergeometrical 13
hypergeometric distribution 13
i
inadequate linear model 318
inadequate second-order model 366
incomplete random blockdesign 234
independent variables (factors) 120
interaction 82
interaction effects 271
interpolation 265
interpolation model 320
irregular replicas 268
irregular simplex 507
k
Kenworthy designs 539
Kono’s designs 363
l
lack of fit 132, 267
lack of fit of regression models, lack of fit
variance 377
reproducibility variance 377
latin squares 238
a-level of significance 23
levels 185
limited 171
linear regression 121
lower levels 189
Index609
m
main effects 271
mathematical model 1, 262, 265
deterministic 1, 2
random 1, 2
stochastic 1, 2
McLean and Anderson’s design 512
mean average 4
mean deviation 5
mean error 372
measurement confidence 192
measurement error 191, 195
measures of variability 5
median array 4
method of least squares 123
method of random balance 203
method of steepest ascentis
efficient 396
inefficient 396
mixture design 465
mixture design x process factor design 542
mode, most probable value 4
model interpretation 311
multiple regression 136
n
nongradient methods of optimization 414
nonlinear regression 144
nonsymmetrical SSRD 435
normal distributions
bell-shaped distribution 16
Gauss’ distribution 16
normal equations 140
normality of data distribution 115
norming 308
null/centerpoints 323
null point 168, 268
o
one-sided sequential testing 47
one-sided test 27
operational matrix 275
optimality 161
optimality design 307
optimization 385
optimization with multiple responses 170
orthogonal 307
orthogonal design 349
orthogonality 308
orthogonal second-order design
(Box-Benken design) 349
outliers 118
overall desirability 181
p
partial desirability 176
partial responses 173
pentagonal 431
Pirson’s criterion 116
Plackett-Burman designs 225
polynomial coefficients 169
polynomial function 121
polynomial models 169
polynomial regression 140
pooled sample variance 40
pooled variance estimates 66
population 3
power of a test 24
power of solving a replica 272
predicted-calculated response value 169
preliminary examination of subject of
research 166
preliminary ranking of the factors 196
probability density function 14
probability model
Bernoulli distribution 8
single events 8
pseudocomponents 507
psychological experiment 196
pure random balance 204
q
qualitative factor 189
quantitative 171
r
random 191
randomization 161
random numbers 7
random variable
continuous 8
discrete random variable 8
random variations 110
range 5
rank curve 197
ranking 171
ranking of the qualitative responses 183
real factor values 268
reduced combined model 546
regression analysis 120, 160
regression coefficients 121, 169
regular replicas 268
regular simplex 415
reproducibility variance 91
research objective 166
response function 169, 262
responses 167, 170
Index610
response surface 169, 262
robust 191
rotatability 308
rotatable 307
rotatable design 323
Rozebum’s triangle 481
s
samples
random sample 3
statistic sample 3
scatter diagram 147, 204
Scheffe simplex lattice design 484
second-order rotatable design
Box-Wilson Design 323
sequential tests 46
simple general response 173
simplex centroid design 502
simplex-centroid-full factorial design 550
simplex-centroid X three process factor full
factorial design 550
simplex circling 420
simplex figure 415
simplex lattice design 481
simplex lattice screening designs 469
simplex-self-directing method 415
simplex sum rotatable design 431
simplex swaying 420
singularity 171
standard deviation 6
standard error 192
standard normal distribution,
standardized variable 18
starlike/axial/star 323
statistic 4
statistical analysis 367
statistical design of experiments 163
statistical estimation, intervalestimate 30
point estimate 30
statistical hypotheses,
alternative hypothesis 23
primary or null hypothesis 23
type I error 23
type II error 23
statistical inference, hypothesis testing 22
statistical estimation 22
statistically effective 171
statistically significant 110
statistical methods, descriptive statistics 3
inferential statistics 3
steepest ascent (Box-Wilson’s method) 388
subject of research with several responses
172
successiveness 161
symmetry 308
systematic 191
systematic variations 110
t
tabular value 110
test statistic 24
trial error 195
two-sided sequential testing 49
two-sided test 28
u
unbalanced incomplete random blocks 234
unbiased estimate of the population variance
11
uncontrollable 168
uniform distribution 14
universality 171
unlimited 171
unsaturated design 320
upper levels 189
v
variance 5
variance of group means 67
y
Yates method 276
youdens squares 252


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