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Design and Analysis of ExperimentsDouglas C. Montgomery

Preface
1 Introduction to Designed Experiments
1.1 Strategy of Experimentation  
1.2 Some Typical Applications of Experimental Design
1.3 Basic Principles
1.4 Guidelines for Designing Experiments
1.5 A Brief History of Statistical Design  
1.6 Summary: Using Statistical Techniques in Experimentation  
1.7 Problems

2 Basic Statistical Methods
  2.1 Introduction  
2.2 Basic Statistical Concepts
2.3 Sampling and Sampling Distributions  
2.4 Inferences About the Differences in Means, Randomized Designs  
2.5 Inferences About the Differences in Means, Paired Comparison Designs  
2.6 Inferences About the Variances of Normal Distributions  
2.7 Problems  

3 Analysis of Variance  
3.1 An Example
3.2 The Analysis of Variance
3.3 Analysis of the Fixed Effects Model  
3.4 Model Adequacy Checking
3.5 Practical Interpretation of Results
3.6 Sample Computer Output  
3.7 Determining Sample Size  
3.8 Other Examples of Single-Factor Experiments  
3.9 The Random Effects Model
3.10 The Regression Approach to the Analysis of Variance
3.11 Nonparametric Methods in the Analysis of Variance
3.12 Problems

4 Experiments with Blocking Factors   
4.1 The Randomized Complete Block Design
4.2 The Latin Square Design  
4.3 The Graeco-Latin Square Design  
4.4 Balanced Incomplete Block Designs  
4.5 Problems  

5 Factorial Experiments
5.1 Basic Definitions and Principles  
5.2 The Advantage of Factorials
5.3 The Two-Factor Factorial Design  
5.4 The General Factorial Design  
5.5 Fitting Response Curves and Surfaces  
5.6 Blocking in a Factorial Design  
5.7 Problems  

6 Two-Level Factorial Designs
6.1 Introduction  
6.2 The 22 Design  
6.3 The 23 Design  
6.4 The General 2k Design
6.5 A Single Replicate of the 2k Design
6.6 Additional Examples of Unreplicated 2k Design
6.7 2k Designs are Optimal Designs  
6.8 The Addition of Center Points to the 2k Design  
6.9 Why We Work with Coded Design Variables  
6.10 Problems  

7 Blocking and Confounding Systems for Two-Level Factorials  
7.1 Introduction
7.2 Blocking a Replicated 2k Factorial Design  
7.3 Confounding in the 2k Factorial Design  
7.4 Confounding the 2k Factorial Design in Two Blocks  
7.5 Another Illustration of Why Blocking Is Important  
7.6 Confounding the 2k Factorial Design in Four Blocks
7.7 Confounding the 2k Factorial Design in 2p Blocks  
7.8 Partial Confounding
7.9 Problems

8 Two-Level Fractional Factorial Designs
  8.1 Introduction  
8.2 The One-Half Fraction of the 2k Design
8.3 The One-Quarter Fraction of the 2k Design  
8.4 The General 2k-p Fractional Factorial Design  
8.5 Alias Structures in Fractional Factorials and other Designs  
8.6 Resolution III Designs  
8.7 Resolution IV and V Designs  
8.8 Supersaturated Designs
8.9 Summary  
8.10 Problems

9 Other Topics on Factorial and Fractional Factorial Designs  
9.1 The 3k Factorial Design  
9.2 Confounding in the 3k Factorial Design  
9.3 Fractional Replication of the 3k Factorial Design  
9.4 Factorials with Mixed Levels  
9.5 Nonregular Fractional Factorial Designs  
9.6 Constructing Factorial and Fractional Factorial Designs Using an Optimal Design Tool
9.7 Problems  

10 Regression Modeling
10.1 Introduction  
10.2 Linear Regression Models  
10.3 Estimation of the Parameters in Linear Regression Models  
10.4 Hypothesis Testing in Multiple Regression  
10.5 Confidence Intervals in Multiple Regression  
10.6 Prediction of New Response Observations  
10.7 Regression Model Diagnostics  
10.8 Testing for Lack of Fit  
10.9 Problems  

11 Response Surface Methodology  
11.1 Introduction to Response Surface Methodology  
11.2 The Method of Steepest Ascent
11.3 Analysis of a Second-Order Response Surface  
11.4 Experimental Designs for Fitting Response Surfaces
11.5 Experiments with Computer Models  
11.6 Mixture Experiments  
11.7 Evolutionary Operation
11.8 Problems

12 Robust Design
12.1 Introduction  
12.2 Crossed Array Designs
12.3 Analysis of the Crossed Array Design
12.4 Combined Array Designs and the Response Model Approach
12.5 Choice of Designs  
12.6 Problems  

13 Random Effects Models  
13.1 Random Effects Models  
13.2 The Two-Factor Factorial with Random Factors  
13.3 The Two-Factor Mixed Model  
13.4 Sample Size Determination with Random Effects  
13.5 Rules for Expected Mean Squares
13.6 Approximate F Tests  
13.7 Some Additional Topics on Estimation of Variance Components
13.8 Problems  

14 Experiments with Nested Factors and Hard-to-Change Factors  
14.1 The Two-Stage Nested Design  
14.2 The General m-Stage Nested Design  
14.3 Designs with Both Nested and Factorial Factors
14.4 The Split-Plot Design
14.5 Other Variations of the Split-Plot Design
14.6 Problems  

15 Other Topics  
15.1 Nonnormal Responses and Transformations
15.2 Unbalanced Data in a Factorial Design
15.3 The Analysis of Covariance  
15.4 Repeated Measures  
15.5 Problems  Appendix  

Table I. Cumulative Standard Normal Distribution  
Table II. Percentage Points of the t Distribution  
Table III. Percentage Points of the X2 Distribution  
Table IV. Percentage Points of the F Distribution  
Table V. Operating Characteristic Curves for the Fixed Effects Model Analysis of Variance  
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 k <= 15 and n <=64

Bibliography  
Index