Design and Analysis of Experiments 5th Edition

Design and Analysis of Experiments 5th Edition
اسم المؤلف
Douglas C. Montgomery
16 أكتوبر 2017

Design and Analysis of Experiments 5th Edition
Douglas C. Montgomery
Introduction 1
Strategy of Experimentation
Some Typical Applications of Experimental Design
Basic Principles
Guidelines for Designing Experiments
A Brief History of Statistical Design
Summary: Using Statistical Techniques in Experimentation
Chapter 1.
Simple Comparative Experiments 21
Basic Statistical Concepts
Sampling and Sampling Distributions
Inferences About the Differences in Means, Randomized Designs
2-4.1 Hypothesis Testing
2-4.2 Choice of Sample Size
2-4.3 Confidence Intervals
2-4.6 Comparing a Single Mean to a Specified Value
2-4.7 Summary
Inferences About the Differences in Means, Paired Comparison
2-5.1 The Paired Comparison Problem
2-5.2 Advantages of the Paired Comparison Design
Inferences About the Variances of Normal Distributions
Chapter 2.
Experiments with a Single Factor: The Analysis of Variance 60
An Example
The Analysis of Variance
Analysis of the Fixed Effects Model
3-3.1 Decomposition of the Total Sum of Squares
3-3.2 Statistical Analysis
3-3.3 Estimation of the Model Parameters
3-3.4 Unbalanced Data
Chapter 3.
3-4 Model Adequacy Checking
3-4.1 The Normality Assumption
3-4.2 Plot of Residuals in Time Sequence
3-4.3 Plot of Residuals Versus Fitted Values
3-4.4 Plots of Residuals Versus Other Variables
Practical Interpretation of Results
3-5.1 A Regression Model
3-5.2 Comparisons Among Treatment Means
3-5.3 Graphical Comparisons of Means
3-5.4 Contrasts
3-5.5 Orthogonal Contrasts
3-5.6 Scheffe’s Method for Comparing All Contrasts
3-5.7 Comparing Pairs of Treatment Means
3-5.8 Comparing Treatment Means with a Control
Sample Computer Output
Determining Sample Size
3-7.1 Operating Characteristic Curves
3-7.2 Specifying a Standard Deviation Increase
3-7.3 Confidence Interval Estimation Method
Discovering Dispersion Effects
The Regression Approach to the Analysis of Variance
3-9.1 Least Squares Estimation of the Model Parameters
3-9.2 The General Regression Significance Test
Nonparametric Methods in the Analysis of Variance
3-10.1 The Kruskal-Wallis Test
3-10.2 General Comments on the Rank Transformation
Chapter 4. Randomized Blocks, Latin Squares, and Related Designs
The Randomized Complete Block Design
4-1.1 Statistical Analysis of the RCBD
4-1.2 Model Adequacy Checking
4-1.3 Some Other Aspects of the Randomized Complete Block
4-1.4 Estimating Model Parameters and the General Regression
Significance Test
The Latin Square Design
The Graeco-Latin Square Design
Balanced Incomplete Block Designs
4-4.1 Statistical Analysis of the BIBD
4-4.2 Least Squares Estimation of the Parameters
4-4.3 Recovery of Interblock Information in the BIBD
4-5 164CONTENTS ix
Introduction to Factorial Designs 170
Basic Definitions and Principles
The Advantage of Factorials
The Two-Factor Factorial Design
5-3.1 An Example
5-3.2 Statistical Analysis of the Fixed Effects Model
5-3.3 Model Adequacy Checking
5-3.4 Estimating the Model Parameters
5-3.7 One Observation per Cell
The General Factorial Design
Fitting Response Curves and Surfaces
Blocking in a Factorial Design
Chapter 5.
Choice of Sample Size 189
The Assumption of No Interaction in a Two-Factor Model
The 2k Factorial Design
The 22 Design
The 23 Design
The General 2k Design
A Single Replicate of the 2k Design
The Addition of Center Points to the 2k Design
Blocking and Confounding in the 2* Factorial Design
Blocking a Replicated 2k Factorial Design
Confounding in the 2k Factorial Design
Confounding the 2k Factorial Design in Two Blocks
Confounding the 2k Factorial Design in Four Blocks
Confounding the 2k Factorial Design in 2P Blocks
Partial Confounding
Chapter 6.
Chapter 7.
Two-Level Fractional Factorial Designs 303
The One-Half Fraction of the 2k design
The One-Quarter Fraction of the 2k Design
The General 2k ~ p Fractional Factorial Design
Resolution III Designs
Resolution IV and V Designs
Chapter 8. CONTENTS
Three-Level and Mixed-Level Factorial and Fractional
Factorial Designs
Chapter 9.
The 3k Factorial Design
9-1.1 Notation and Motivation for the 3* Design
9-1.2 The 32 Design
9-1.3 The 33 Design
9-1.4 The General 3k design
Confounding in the 3k Factorial Design
The 3* Factorial Design in Three Blocks
The 3* Factorial Design in Nine Blocks
The 3k Factorial Design in 3P Blocks
Fractional Replication of the 3k Factorial Design
9-3.1 The One-Third Fraction of the 3k Factorial Design
9-3.2 Other 3k ~ p Fractional Factorial Designs
Factorials with Mixed Levels
9-4.1 Factors at Two and Three Levels 384
9-4.2 Factors at Two and Four Levels
Fitting Regression Models 392
Linear Regression Models
Estimation of the Parameters in Linear Regression Models
Hypothesis Testing in Multiple Regression
10-4.1 Test for Significance of Regression
10-4.2 Tests on Individual Regression Coefficients and Groups
of Coefficients
Confidence Intervals in Multiple Regression
10-5.1 Confidence Intervals on the Individual Regression
10-5.2 Confidence Interval on the Mean Response
Prediction of New Response Observations
Regression Model Diagnostics
10-7.1 Scaled Residuals and PRESS
10-7.2 Influence Diagnostics
Testing for Lack of Fit
Chapter 10
Response Surface Methods and Other Approaches
to Process Optimization
Introduction to Response Surface Methodology
The Method of Steepest Ascent
Analysis of a Second-Order Response Surface
11-3.1 Location of the Stationary Point
Chapter 11.
11-3.2 Characterizing the Response Surface 440
11-3.3 Ridge Systems
11-3.4 Multiple Responses
Experimental Designs for Fitting Response Surfaces
11-4.1 Designs for Fitting the First-Order Model
11-4.2 Designs for Fitting the Second-Order Model
11-4.3 Blocking in Response Surface Designs
11-4.4 Computer-Generated (Optimal) Designs
Mixture Experiments
Evolutionary Operation
Robust Design
11-7.1 Background
11-7.2 The Response Surface Approach to Robust Design
Chapter 12. Experiments with Random Factors 511
The Random Effects Model 511
The Two-Factor Factorial with Random Factors
The Two-Factor Mixed Model
Sample Size Determination with Random Effects
Rules for Expected Mean Squares
Approximate F Tests
Some Additional Topics on Estimation of Variance Components
12-7.1 Approximate Confidence Intervals on Variance
12-7.2 The Modified Large-Sample Method
12-7.3 Maximum Likelihood Estimation of Variance
12-8 Problems 552
Nested and Split-Plot Designs 557
The Two-Stage Nested Design
1.1 Statistical Analysis
13-1.2 Diagnostic Checking
13-1.3 Variance Components
13-1.4 Staggered Nested Designs
The General m-Stage Nested Design
Designs with Both Nested and Factorial Factors
The Split-Plot Design
Other Variations of the Split-Plot Design
13-5.1 Split-Plot Designs with More Than Two Factors
13-5.2 The Split-Split-Plot Design
13-5.3 The Strip-Split-Plot Design
Chapter 13.
Chapter 14. Other Design and Analysis Topics
14-1 Nonnormal Responses and Transformations
14-1.1 Selecting a Transformation: The Box-Cox Method
14-1.2 The Generalized Linear Model
14-2 Unbalanced Data in a Factorial Design
14-2.1 Proportional Data: An Easy Case
14-2.2 Approximate Methods
14-2.3 The Exact Method
14-3 The Analysis of Covariance
14-3.1 Description of the Procedure
14-3.2 Computer Solution
14-3.3 Development by the General Regression Significance
14-3.4 Factorial Experiments with Covariates
14-4 Repeated Measures
14-5 Problems
Cumulative Standard Normal Distribution
Percentage Points of the t Distribution
Percentage Points of the x2, Distribution
Percentage Points of the F Distribution
Operating Characteristic Curves for the Fixed Effects Model
Analysis of Variance
Operating Characteristic Curves for the Random Effects Model
Analysis of Variance
Significant Ranges for Duncan’s Multiple Range Test
Percentage Points of the Studentized Range Statistic
Critical Values for Dunnett’s Test for Comparing Treatments
with a Control
Coefficients of Orthogonal Polynomials
Random Numbers
Alias Relationships for 2k~ p Fractional Factorial Designs
with k 15 and n 64
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