Design and analysis of experiments:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley
2009
|
| Ausgabe: | 7. ed., internat. student version |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 656 S. graph. Darst. |
| ISBN: | 9780470398821 0470398825 |
Internformat
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| 245 | 1 | 0 | |a Design and analysis of experiments |c Douglas C. Montgomery |
| 250 | |a 7. ed., internat. student version | ||
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2009 | |
| 300 | |a XVII, 656 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804138600478015488 |
|---|---|
| adam_text | Contents
Preface
v
1
Introduction
to Designed Experiments
1
1.1
Strategy of Experimentation
1
1.2
Some Typical Applications of Experimental Design
8
1.3
Basic Principles
11
1.4
Guidelines for Designing Experiments
14
1.5
A Brief History of Statistical Design
19
1.6
Summary: Using Statistical Techniques in Experimentation
21
1.7
Problems
22
2
Basic Statistical Methods
23
2.1
Introduction
23
2.2
Basic Statistical Concepts
25
2.3
Sampling and Sampling Distributions
28
2.4
Inferences About the Differences in Means, Randomized Designs
34
2.4.1
Hypothesis Testing
34
2.4.2
Choice of Sample Size
41
2.4.3
Confidence Intervals
44
2.4.4
The Case Where
σ{ Φ
<Ą
45
2.4.5
The Case Where
σ
and erf Are Known
45
2.4.6
Comparing a Single Mean to a Specified Value
46
2.4.7
Summary
47
2.5
Inferences About the Differences in Means, Paired Comparison Designs
48
2.5.1
The Paired Comparison Problem
48
2.5.2
Advantages of the Paired Comparison Design
51
XI
XU Contents
2.6
Inferences About the Variances of Normal Distributions
52
2.7
Problems 55
3
Analysis of Variance
àO
3.1
An Example
61
3.2
The Analysis of Variance
63
3.3
Analysis of the Fixed Effects Model
65
3.3.1
Decomposition of the Total Sum of Squares
66
3.3.2
Statistical Analysis
68
3.3.3
Estimation of the Model Parameters
73
3.3.4
Unbalanced Data 74
3.4
Model Adequacy Checking
75
3.4.1
The Normality Assumption
75
3.4.2
Plot of Residuals in Time Sequence
77
3.4.3
Plot of Residuals Versus Fitted Values
78
3.4.4
Plots of Residuals Versus Other Variables
83
3.5
Practical Interpretation of Results
84
3.5.1
A Regression Model
84
3.5.2
Comparisons Among Treatment Means
85
3.5.3
Graphical Comparisons of Means
86
3.5.4
Contrasts
87
3.5.5
Orthogonal Contrasts
89
3.5.6
Scheffé s
Method for Comparing All Contrasts
91
3.5.7
Comparing Pairs of Treatment Means
92
3.5.8
Comparing Treatment Means with a Control
96
3.6
Sample Computer Output
97
3.7
Determining Sample Size
101
3.7.1
Operating Characteristic Curves
101
3.7.2
Specifying a Standard Deviation Increase
103
3.7.3
Confidence Interval Estimation Method
04
3.8
A Real Economy Application of a Designed Experiment
105
3.9
Discovering Dispersion Effects
107
3.10
The Regression Approach to the Analysis of Variance
Ю9
3.10.1
Least Squares Estimation of the Model Parameters
09
3.10.2
The General Regression Significance Test HO
3.11
Nonparametric Methods in the Analysis of Variance
112
3.11.1
The Kruskal-Wallis Test
Π
2
3.11.2
General Comments on the Rank Transformation H4
3.12
Problems
114
Experiments with Blocking Factors
4.1
The Randomized Complete Block Design
121
4.1.1
Statistical Analysis of the RCBD >23
4.1.2
Model Adequacy Checking 1
31
4.1.3
Some Other Aspects of the Randomized Complete Block Design
· 32
4.1.4
Estimating Model Parameters and the General Regression
Significance Test
135
4.2
The Latin Square Design
138
4.3
The Graeco-Latin Square Design
145
Contents
ХНІ
4.4
Balanced Incomplete Block Designs
148
4.4.1
Statistical Analysis of the BIBD
148
4.4.2
Least Squares Estimation of the Parameters
152
4.4.3
Recovery of Interblock Information in the BIBD
154
4.5
Problems
157
5
Factorial Experiments
162
5.1
Basic Definitions and Principles
162
5.2
The Advantage of Factorials
165
5.3
The Two-Factor Factorial Design
166
5.3.1
An Example
166
5.3.2
Statistical Analysis of the Fixed Effects Model
168
5.3.3
Model Adequacy Checking
177
5.3.4
Estimating the Model Parameters
177
5.3.5
Choice of Sample Size
180
5.3.6
The Assumption of No Interaction in a Two-Factor Model
181
5.3.7
One Observation per Cell
182
5.4
The General Factorial Design
185
5.5
Fitting Response Curves and Surfaces
190
5.6
Blocking in a Factorial Design
198
5.7
Problems
202
6
Two-Level Factorial Designs
207
6.1
Introduction
207
6.2
The 22 Design
208
6.3
The 23 Design
215
6.4
The General
2*
Design
227
6.5
A Single Replicate of the
2*
Design
229
6.6
Additional Examples of Unreplicated
2*
Design
243
6.7 2*
Designs are Optimal Designs
252
6.8
The Addition of Center Points to the
2*
Design
257
6.9
Why We Work with Coded Design Variables
261
6.10
Problems
264
7
Blocking and Confounding Systems
for Two-Level Factorials
273
7.1
Introduction
273
7.2
Blocking a Replicated
2*
Factorial Design
274
7.3
Confounding in the
2*
Factorial Design
275
7.4
Confounding the 2k Factorial Design in Two Blocks
275
7.5
Another Illustration of Why Blocking Is Important
281
7.6
Confounding the
2*
Factorial Design in Four Blocks
282
7.7
Confounding the 2k Factorial Design in 21 Blocks
284
7.8
Partial Confounding
285
7.9
Problems
288
XIV Contents
8
Two-Level Fractional Factorial Designs
289
8.1
Introduction
289
8.2
The One-Half Fraction of the
2*
Design
290
8.2.1
Definitions and Basic Principles
290
8.2.2
Design Resolution
292
8.2.3
Construction and Analysis of the One-Half Fraction
293
8.3
The One-Quarter Fraction of the
2*
Design
302
8.4
The General 2k~p Fractional Factorial Design
309
8.4.1
Choosing a Design
309
8.4.2
Analysis of
Ť ~p
Fractional Factorials
312
8.4.3
Blocking Fractional Factorials
313
8.5
Alias Structures in Fractional Factorials and other Designs
318
8.6
Resolution III Designs
320
8.6.1
Constructing Resolution III Designs
320
8.6.2
Fold Over of Resolution III Fractions to Separate Aliased Effects
322
8.6.3
Plackett-Burman Designs
326
8.7
Resolution IV and V Designs
335
8.7.1
Resolution IV Designs
335
8.7.2
Sequential Experimentation with Resolution IV Designs
339
8.7.3
Resolution V Designs
345
8.8
Supersaturated Designs
347
8.9
Summary
348
8.10
Problems
349
Other Topics on Factorial and
Fractional Factorial Designs
360
9.1
The
3*
Factorial Design
360
9.1.1
Notation and Motivation for the
3*
Design
360
9.1.2
The 32 Design
362
9.1.3
The 33 Design
363
9.1.4
The General
3*
Design
368
9.2
Confounding in the
3*
Factorial Design
368
9.2.1
The
3*
Factorial Design in Three Blocks
369
9.2.2
The
3*
Factorial Design in Nine Blocks
372
9.2.3
The
3і
Factorial Design in
У
Blocks
373
9.3
Fractional Replication of the
3*
Factorial Design
374
9.3.1
The One-Third Fraction of the
3*
Factorial Design
374
9.3.2
Other 3k~p Fractional Factorial Designs
376
9.4
Factorials with Mixed Levels
378
9.4.1
Factors at Two and Three Levels
378
9.4.2
Factors at Two and Four Levels
382
9.5
Problems
385
10
Regression Modeling
388
10.1
Introduction
388
10.2
Linear Regression Models
389
Contents
XV
10.3
Estimation
of the
Parameters in Linear Regression Models 390
10.4
Hypothesis Testing
in Multiple Regression 401
10.4.1 Test
for Significance of
Regression 401
10.4.2 Tests
on Individual
Regression
Coefficients and Groups of Coefficients
403
10.5
Confidence Intervals in Multiple Regression
406
10.5.1
Confidence Intervals on the Individual Regression Coefficients
406
10.5.2
Confidence Interval on the Mean Response
407
10.6
Prediction of New Response Observations
407
10.7
Regression Model Diagnostics
409
10.7.1
Scaled Residuals and PRESS
409
10.7.2
Influence Diagnostics
411
10.8
Testing for Lack of Fit
412
10.9
Problems
414
11
Response Surface Methodology
417
11
.
1 Introduction to Response Surface Methodology
4
1
7
11
.2
The Method of Steepest Ascent
4
1
9
11
.3
Analysis of a Second-Order Response Surface
425
11
.3.
1 Location of the Stationary Point
425
11.
3.2
Characterizing the Response Surface
427
11.
3.3
Ridge Systems
434
11.
3.4
Multiple Responses
435
11.
4
Experimental Designs for Fitting Response Surfaces
439
11
.4.
1 Designs for Fitting the First-Order Model
440
11
.4.2
Designs for Fitting the Second-Order Model
440
11
.4.3
Blocking in Response Surface Designs
446
11.
4.4
Computer-Generated (Optimal) Designs
450
11.
5
Experiments with Computer Models
459
11.
6
Mixture Experiments
466
11
.7
Evolutionary Operation
476
11.
8
Problems
480
12
Robust Design
486
1
2.
1 Introduction
486
1
2.2
Crossed Array Designs
488
1
2.3
Analysis of the Crossed Array Design
490
1
2.4
Combined Array Designs and the Response Model Approach
493
1
2.5
Choice of Designs
499
1
2.6
Problems
502
13
Random Effects Models
505
13.
1 The Random Effects Model
506
13.2
The Two-Factor Factorial with Random Factors
5
1
]
13.3
The Two-Factor Mixed Model
515
13.4
Sample Size Determination with Random Effects
520
XVI Contents
13.5
Rules for Expected Mean
Squares 522
13.6
Approximate
F
Tests
5
^
13.7
Some Additional Topics on Estimation of Variance Components
531
13.7.1
Approximate Confidence Intervals on Variance Components
531
13.7.2
The Modified Large-Sample Method
533
13.7.3
Maximum Likelihood Estimation of Variance Components
535
13.8
Problems 538
14
Experiments with Nested Factors
and Hard-to-Change Factors
542
14.1
The Two-Stage Nested Design
542
14.1.1
Statistical Analysis
543
14.1.2
Diagnostic Checking
547
14.1.3
Variance Components
549
14.1.4
Staggered Nested Designs
550
14.2
The General/w-Stage Nested Design
551
14.3
Designs with Both Nested and Factorial Factors
553
14.4
The Split-Plot Design
557
14.5
Other Variations of the Split-Plot Design
562
14.5.1
Split-Plot Designs with More Than Two Factors
562
14.5.2
The Split-Split-Plot Design
567
14.5.3
The Strip-Split-Plot Design
570
14.6
Problems
572
15
Other Topics
577
15.
l
Nonnormal
Responses and Transformations
578
15.1.1
Selecting a Transformation: The
Box
-Сох
Method
578
15.1.2
The Generalized Linear Model
580
15.2
Unbalanced Data in a Factorial Design
587
15.2.1
Proportional Data: An Easy Case
587
15.2.2
Approximate Methods
589
15.2.3
The Exact Method
590
15.3
The Analysis of Covariance
590
15.3.1
Description of the Procedure
591
15.3.2
Computer Solution
599
15.3.3
Development by the General Regression Significance Test
600
15.3.4
Factorial Experiments with Covariates
602
15.4
Repeated Measures
607
15.5
Problems
609
Appendix
611
Table I. Cumulative Standard Normal Distribution °
12
Table II. Percentage Points of the
t
Distribution
614
Table III. Percentage Points of the
χ2
Distribution
615
Table IV. Percentage Points of the
F
Distribution 616
Table V. Operating Characteristic Curves for the Fixed Effects Model
Analysis of Variance
621
Contents
xvii
Table VI. Operating Characteristic Curves for the Random Effects Model
Analysis of Variance
Table
VII.
Percentage Points of the Studentized Range Statistic
Table
VIII.
Critical Values for Dunnett s Test for Comparing Treatments
with a Control
Table IX. Coefficients of Orthogonal Polynomials
Table X. Alias Relationships for 2k~p Fractional Factorial Designs with
к
< 15
and
η
< 64
Bibliography
Index
625
629
631
633
634
647
653
|
| any_adam_object | 1 |
| author | Montgomery, Douglas C. 1943- |
| author_GND | (DE-588)12861448X |
| author_facet | Montgomery, Douglas C. 1943- |
| author_role | aut |
| author_sort | Montgomery, Douglas C. 1943- |
| author_variant | d c m dc dcm |
| building | Verbundindex |
| bvnumber | BV035300415 |
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| classification_tum | MAT 620f |
| ctrlnum | (OCoLC)845551630 (DE-599)BVBBV035300415 |
| dewey-full | 001.434 519.5/7 |
| dewey-hundreds | 000 - Computer science, information, general works 500 - Natural sciences and mathematics |
| dewey-ones | 001 - Knowledge 519 - Probabilities and applied mathematics |
| dewey-raw | 001.434 519.5/7 |
| dewey-search | 001.434 519.5/7 |
| dewey-sort | 11.434 |
| dewey-tens | 000 - Computer science, information, general works 510 - Mathematics |
| discipline | Allgemeines Mathematik Wirtschaftswissenschaften |
| edition | 7. ed., internat. student version |
| format | Book |
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| id | DE-604.BV035300415 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:30:46Z |
| institution | BVB |
| isbn | 9780470398821 0470398825 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017105289 |
| oclc_num | 845551630 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-N2 DE-20 DE-703 DE-634 DE-19 DE-BY-UBM DE-83 DE-473 DE-BY-UBG DE-573 DE-858 DE-91S DE-BY-TUM DE-Aug4 DE-M347 DE-945 DE-1043 |
| owner_facet | DE-91G DE-BY-TUM DE-N2 DE-20 DE-703 DE-634 DE-19 DE-BY-UBM DE-83 DE-473 DE-BY-UBG DE-573 DE-858 DE-91S DE-BY-TUM DE-Aug4 DE-M347 DE-945 DE-1043 |
| physical | XVII, 656 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Wiley |
| record_format | marc |
| spelling | Montgomery, Douglas C. 1943- Verfasser (DE-588)12861448X aut Design and analysis of experiments Douglas C. Montgomery 7. ed., internat. student version Hoboken, NJ Wiley 2009 XVII, 656 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Experimental design Statistische Analyse (DE-588)4116599-8 gnd rswk-swf Produktinnovation (DE-588)4047346-6 gnd rswk-swf Gestaltung (DE-588)4157139-3 gnd rswk-swf Versuchsplanung (DE-588)4078859-3 gnd rswk-swf Experiment (DE-588)4015999-1 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Prozessmanagement (DE-588)4353072-2 gnd rswk-swf Minitab (DE-588)4394834-0 gnd rswk-swf Experimentauswertung (DE-588)4153362-8 gnd rswk-swf Produktinnovation (DE-588)4047346-6 s Versuchsplanung (DE-588)4078859-3 s Prozessmanagement (DE-588)4353072-2 s Minitab (DE-588)4394834-0 s 1\p DE-604 Experiment (DE-588)4015999-1 s Gestaltung (DE-588)4157139-3 s Statistische Analyse (DE-588)4116599-8 s 2\p DE-604 Statistik (DE-588)4056995-0 s Experimentauswertung (DE-588)4153362-8 s 3\p DE-604 4\p DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017105289&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Montgomery, Douglas C. 1943- Design and analysis of experiments Experimental design Statistische Analyse (DE-588)4116599-8 gnd Produktinnovation (DE-588)4047346-6 gnd Gestaltung (DE-588)4157139-3 gnd Versuchsplanung (DE-588)4078859-3 gnd Experiment (DE-588)4015999-1 gnd Statistik (DE-588)4056995-0 gnd Prozessmanagement (DE-588)4353072-2 gnd Minitab (DE-588)4394834-0 gnd Experimentauswertung (DE-588)4153362-8 gnd |
| subject_GND | (DE-588)4116599-8 (DE-588)4047346-6 (DE-588)4157139-3 (DE-588)4078859-3 (DE-588)4015999-1 (DE-588)4056995-0 (DE-588)4353072-2 (DE-588)4394834-0 (DE-588)4153362-8 |
| title | Design and analysis of experiments |
| title_auth | Design and analysis of experiments |
| title_exact_search | Design and analysis of experiments |
| title_full | Design and analysis of experiments Douglas C. Montgomery |
| title_fullStr | Design and analysis of experiments Douglas C. Montgomery |
| title_full_unstemmed | Design and analysis of experiments Douglas C. Montgomery |
| title_short | Design and analysis of experiments |
| title_sort | design and analysis of experiments |
| topic | Experimental design Statistische Analyse (DE-588)4116599-8 gnd Produktinnovation (DE-588)4047346-6 gnd Gestaltung (DE-588)4157139-3 gnd Versuchsplanung (DE-588)4078859-3 gnd Experiment (DE-588)4015999-1 gnd Statistik (DE-588)4056995-0 gnd Prozessmanagement (DE-588)4353072-2 gnd Minitab (DE-588)4394834-0 gnd Experimentauswertung (DE-588)4153362-8 gnd |
| topic_facet | Experimental design Statistische Analyse Produktinnovation Gestaltung Versuchsplanung Experiment Statistik Prozessmanagement Minitab Experimentauswertung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017105289&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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