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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
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