A primer on experiments with mixtures:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Hoboken, N.J.
Wiley
c2011
|
| Schriftenreihe: | Wiley series in probability and statistics
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024781481&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Includes bibliographical references and index |
| Umfang: | xii, 351 p. ill. 25 cm |
| ISBN: | 9780470643389 0470643382 |
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| 245 | 1 | 0 | |a A primer on experiments with mixtures |c John A. Cornell |
| 264 | 1 | |a Hoboken, N.J. |b Wiley |c c2011 | |
| 300 | |a xii, 351 p. |b ill. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a Wiley series in probability and statistics | |
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| 650 | 4 | |a Mixtures |x Experiments | |
| 650 | 4 | |a Solution (Chemistry) |x Experiments | |
| 650 | 4 | |a Powders |x Mixing |x Experiments | |
| 650 | 4 | |a Mixtures |x Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1819250434092564480 |
|---|---|
| adam_text | Contents
Preface
ix
1.
Introduction
1
1.1
The Original Mixture
Problem.
2
1.2
A Pesticide
Example Involving Two
Chemicals,
2
1.3
General
Remarks About Response
Surface
Methods,
9
1.4
An
Historical
Perspective,
ІЗ
References and Recommended Reading,
17
Questions,
17
Appendix I A: Testing for Nonlinear Blending of the Two Chemicals
Vendex and Kelthane While Measuring the Average Percent Mortality
(АРМ)
of Mites,
20
2.
The Original Mixture Problem: Designs and Models for Exploring
the Entire Simplex Factor Space
23
2.1
The Simplex-Lattice Designs,
23
2.2
The Canonical Polynomials,
26
2.3
The Polynomial Coefficients As Functions of the Responses at
the Points of the Lattices,
31
2.4
Estimating The Parameters in the
[q, m
}
Polynomials,
34
2.5
Properties of the Estimate of the Response. v(x),
37
2.6
A Three-Component Yarn Example Using A
{3, 2)
Simplex-Lattice Design.
38
2.7
The Analysis of Variance Table,
42
2.8
Analysis of Variance Calculations of the Yam Elongation Data.
45
2.9
The Plotting of Individual Residuals.
48
2.10
Testing the Degree of the Fitted Model: A Quadratic Model or
Planar Model?.
49
vi
CONTENTS
2.11
Testing Model Lack of Fit Using Extra Points and Replicated
Observations,
55
2.
1
2
The Simplex-Centroid Design and Associated Polynomial
Model,
58
2.13
An Application of a Four-Component Simplex-Centroid Design:
Blending Chemical Pesticides for Control of Mites,
60
2.14
Axial Designs,
62
2.15
Comments on a Comparison Made Between An Augmented
Simplex-Centroid Design and a Full Cubic Lattice for Three
Components Where Each Design Contains Ten Points,
66
2.16
Reparameterizing
Scheffé s
Mixture Models to Contain A
Constant (fo) Term: A Numerical Example,
69
2.17
Questions to Consider at the Planning Stages of a Mixture
Experiment,
77
2.18
Summary,
78
References and Recommended Reading,
78
Questions,
80
Appendix 2A: Least-Squares Estimation Formula for the Polynomial
Coefficients and Their Variances: Matrix Notation,
85
Appendix 2B: Cubic and Quartic Polynomials and Formulas for the
Estimates of the Coefficients,
90
Appendix 2C: The Partitioning of the Sources in the Analysis of
Variance Table When Fitting the
Schelfe
Mixture Models.
91
3.
Multiple Constraints on the Component Proportions
95
3.1
Lower-Bound Restrictions on Some or All of the Component
Proportions,
95
3.2
Introducing ¿-Pseudocomponents,
97
3.3
A Numerical Example of Fitting An L-Pseudocomponent Model,
99
3.4
Upper-Bound Restrictions on Some or All
Component Proportions,
101
3.5
An Example of the Placing of an Upper Bound on a Single
Component: The Formulation of a Tropical Beverage,
103
3.6
Introducing r/Pseudocomponents,
107
3.7
The Placing of Both Upper and Lower Bounds on the
Component Proportions,
112
3.8
Formulas For Enumerating the Number of Extreme Vertices,
Edges, and Two-Dimensional Faces of the Constrained Region,
119
3.9
McLean and Anderson s Algorithm For Calculating the
Coordinates of the Extreme Vertices of a Constrained Region,
123
3.10
Multicomponent Constraints,
128
CONTENTS
vìi
3.11
Some Examples of Designs for Constrained Mixture Regions:
CONVRT and CONAEV Programs,
131
3.12
Multiple Lattices for Major and Minor Component
Classifications,
138
Summary,
154
References and Recommended Reading,
155
Questions,
157
4.
The Analysis of Mixture Data
159
4.1
Techniques Used in the Analysis of Mixture Data,
160
4.2
Test Statistics for Testing the Usefulness of the Terms in the
Scheffé
Polynomials,
163
4.3
Model Reduction,
170
4.4
An Example of Reducing the System from Three to Two
Components,
173
4.5
Screening Components,
175
4.6
Other Techniques Used to Measure Component Effects,
179
4.7
Leverage and the Hat Matrix,
190
4.8
A Three-Component Propellent Example,
192
4.9
Summary,
195
References and Recommended Reading,
196
Questions,
197
5.
Other Mixture Model Forms
201
5.1
The Inclusion of Inverse Terms in the
Scheffé
Polynomials,
201
5.2
Fitting Gasoline Octane Numbers Using Inverse Terms in
the Model,
204
5.3
An Alternative Model Form for Modeling the Additive Blending
Effect of One Component In a Multicomponent System,
205
5.4
A Biological Example on the Linear Effect of a Powder
Pesticide In Combination With Two Liquid Pesticides
Used for Suppressing Mite Population Numbers,
212
5.5
The Use of Ratios of Components,
215
5.6
Cox s Mixture Polynomials: Measuring Component Effects,
219
5.7
An Example Illustrating the Fits of Cox s Model and
Scheffé s
Polynomial,
224
5.8
Fitting A Slack-Variable Model,
229
5.9
A Numerical Example Illustrating The Fits of Different Reduced
Slack-Variable Models: Tint Strength of a House Paint,
233
5.10
Summary,
239
VIU CONTF.NTS
References and Recommended Reading.
240
Questions,
242
6.
The Inclusion of Process Variables in Mixture Experiments
247
6.1
Designs Consisting of Simplex-Lattices and Factorial
Arrangements,
249
6.2
Measuring the Effects of Cooking Temperature and Cooking
Time on the Texture of Patties Made from Two Types of Fish,
251
6.3
Mixture-Amount Experiments,
256
6.4
Determining the Optimal Fertilizer Blend and Rate for Young
Citrus Trees,
262
6.5
A Numerical Example of the Fit of a Combined Model to Data
Collected on Fractions of the Fish Patty Experimental Design,
269
6.6
Questions Raised and Recommendations Made When Fitting a
Combined Model Containing Mixture Components and Other
Variables,
272
6.7
Summary,
277
References and Recommended Reading,
278
Questions,
280
Appendix 6A: Calculating the Estimated Combined Mixture
Component-Process Variable Model of Eq.
(6.10)
Without the
Computer,
282
7.
A Review of Least Squares and the Analysis of Variance
285
7.1
A Review of Least Squares,
285
7.2
The Analysis of Variance,
288
7.3
A Numerical Example: Modeling the Texture of Fish Patties,
289
7.4
The Adjusted Multiple Correlation Coefficient,
293
7.5
The Press Statistic and Studentized Residuals,
293
7.6
Testing Hypotheses About the Form of the Model: Tests of
Significance,
295
References and Recommended Reading,
298
Bibliography
299
Answers to Selected Questions
317
Appendix
337
Index
347
|
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| id | DE-604.BV039923039 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:05:23Z |
| institution | BVB |
| isbn | 9780470643389 0470643382 |
| language | English |
| lccn | 2010030990 |
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| physical | xii, 351 p. ill. 25 cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
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| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spellingShingle | Cornell, John A. 1941- A primer on experiments with mixtures Mathematisches Modell Mixtures Experiments Solution (Chemistry) Experiments Powders Mixing Experiments Mixtures Mathematical models Solution (Chemistry) Mathematical models Powders Mixing Mathematical models Lösung Mathematik (DE-588)4120678-2 gnd Chemie (DE-588)4009816-3 gnd Computermathematik (DE-588)4788218-9 gnd |
| subject_GND | (DE-588)4120678-2 (DE-588)4009816-3 (DE-588)4788218-9 |
| title | A primer on experiments with mixtures |
| title_auth | A primer on experiments with mixtures |
| title_exact_search | A primer on experiments with mixtures |
| title_full | A primer on experiments with mixtures John A. Cornell |
| title_fullStr | A primer on experiments with mixtures John A. Cornell |
| title_full_unstemmed | A primer on experiments with mixtures John A. Cornell |
| title_short | A primer on experiments with mixtures |
| title_sort | a primer on experiments with mixtures |
| topic | Mathematisches Modell Mixtures Experiments Solution (Chemistry) Experiments Powders Mixing Experiments Mixtures Mathematical models Solution (Chemistry) Mathematical models Powders Mixing Mathematical models Lösung Mathematik (DE-588)4120678-2 gnd Chemie (DE-588)4009816-3 gnd Computermathematik (DE-588)4788218-9 gnd |
| topic_facet | Mathematisches Modell Mixtures Experiments Solution (Chemistry) Experiments Powders Mixing Experiments Mixtures Mathematical models Solution (Chemistry) Mathematical models Powders Mixing Mathematical models Lösung Mathematik Chemie Computermathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024781481&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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