Design and Analysis of Experiments (Montgomery)

Table of Contents

Preface.

1. Introduction.

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. Simple Comparative Experiments.

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. Experiments with a Single Factor: The 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 A Real Economy Application of a Designed Experiment.

3.9 Discovering Dispersion Effects.

3.10 The Regression Approach to the Analysis of Variance.

3.11 Nonparametric Methods in the Analysis of Variance.

3.12 Problems.

4. Randomized Blocks, Latin Squares, and Related Designs.

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. Introduction to Factorial Designs.

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. The 2^k Factorial Design.

6.1 Introduction.

6.2 The 2² Design.

6.3 The 2³ Design.

6.4 The General 2^k Design.

6.5 A Single Replicate of the 2^k Design.

6.6 Additional Examples of Unreplicated 2^k Design.

6.7 2^k Designs are Optimal Designs.

6.8 The Addition of Center Points to the 2^k Design.

6.9 Why We Work with Coded Design Variables.

6.10 Problems.

7. Blocking and Confounding in the 2^k Factorial Design.

7.1 Introduction.

7.2 Blocking a Replicated 2^k Factorial Design.

7.3 Confounding in the 2^k Factorial Design.

7.4 Confounding the 2^k Factorial Design in Two Blocks.

7.5 Another Illustration of Why Blocking Is Important.

7.6 Confounding the 2^k Factorial Design in Four Blocks.

7.7 Confounding the 2^k Factorial Design in 2^p 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 2^k Design.

8.3 The One-Quarter Fraction of the 2^k Design.

8.4 The General 2^k–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. Three-Level and Mixed-Level Factorial and Fractional Factorial Designs.

9.1 The 3^k Factorial Design.

9.2 Confounding in the 3^k Factorial Design.

9.3 Fractional Replication of the 3^k Factorial Design.

9.4 Factorials with Mixed Levels.

10. Fitting Regression Models.

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 Methods and Designs.

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 Parameter Design and Process Robustness Studies.

12.1 Introduction.

12.2 Crossed Array Designs.

12.3 Analysis of the Crossed Array Design.

12.4 Combined Array Design and the Response Model Approach.

12.5 Choice of Designs.

12.6 Problems.

13. Experiments with Random Factors.

13.1 The Random Effects Model.

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. Nested and Split-Plot Designs.

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 Design and Analysis Topics.

15.1 Non-normal 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 2^k–p Fractional Factorial Designs with k <</u>15 and n <</u> 64.

Bibliography

Index