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Design Of Experiment: A Modern Approach

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Design Of Experiment: A Modern Approach

Douglas C. Montgomery

ISBN: 978-1-119-61119-6 November 2019

TABLE OF CONTENTS

1. Introduction to Experimental Design 1.1 The Strategy of Experimentation
1.2 Basic Principles
1.3 Practical Guidelines for Designing an Experiment
1.4 A brief History of Designed Experiments
1.5 A Review: Using Statistical Techniques in Experimentation
1.6 Review of Some Basic Statistical Concepts and Methods
1.6.1 Data Description
1.6.2 Random Samples, Statistics and Sampling Distributions
1.6.3 Statistical Intervals and Tests of Hypotheses
Problems

2. Simple Comparative Experiments
2.1 Introduction
2.2 Statistical Methods for Comparing Two Population Means
2.2.1 Parameter Estimation and Confidence Intervals
2.2.2 Statistical Hypothesis Testing on the Difference in Means
2.3 Comparison of Two Means, Variances Unknown
2.3.1 Confidence Intervals on the Difference in Means of Two Normal Distributions, Variances Unknown
2.3.2 Hypothesis Testing on the Difference in Means of Two Normal Distributions, Variances Unknown
2.3.3 Comparison of Means of Two Normal Distributions with Variances Unknown but Assumed Equal
2.3.4 Power and Sample Size Calculations
2.3.5 The Normality Assumption
Problems

3. Experiments with a Single Categorical Factor: Design Issues and the Analysis of Variance
3.1 Motivating Example
3.2 Statistical Model for the Data
3.3 Design Considerations
3.4 Statistical Analysis of the Data
3.4.1 Partitioning the Variance of the Response
3.4.2 The ANOVA
3.4.3 Post-ANOVA Comparison of Treatment Means
3.4.4 Comparing Treatment Means with a Control
3.4.5 The Effects Model
3.5 Model Adequacy Checking
3.5.1 Checking the Normality Assumption
3.5.2 Checking for Non constant Variance
3.6. Power and Sample Size
Problems

4. Experiments with a Single Continuous Factor: Design Issues and the Regression Analysis
4.1 Motivating Example
4.2 Statistical Models for the data
4.3 Fitting a Statistical Model Using the Data
4.4 Design Considerations
4.5 Design Comparison
Problems

5. Two-Factor Factorial Experiments
5.1 Basic Concepts
5.2 Two Categorical Factors
5.3 The Analysis of Variance for a Two-Factor Factorial
5.4 One Categorical Factor and One Continuous Factor
5.5 Two Continuous factors
Problems

6. Blocking
6.1 The Randomized Complete Block Design
6.2 Statistical Analysis of the Randomized Complete Block Design
6.3 Blocking and Optimal Designs
Problems

7. The 2k Factorial Design
7.1 Introduction
7.2 The 22 Factorial Design
7.3 The 23 Factorial Design
7.4 A Single Replicate of the 2k Design
7.5 2k Designs are Optimal Designs
7.6 More about Replication of 2k Designs
7.7 Blocking in 2k Designs
Problems

8. Screening Experiments
8.1 Introduction
8.2 Regular Fractional Factorial Designs for Factor Screening
8.3 Nonregular Orthogonal Designs
8.4 Nonorthogonal Screening Designs
8.5 Definitive Screening Designs
8.6 Screening Summary
Problems

9. Experiments with Random Blocks
9.1 Introduction
9.2 Motivating Example: Design and Analysis
9.3 Matrix Formulation of the Model for an Experiment with Random Blocks
9.4 Design Considerations
9.5 A Screening Design with a Random Blocking Factor
9.6 Recommendations for use of Designs with Random Blocks
Problems

10. Split-plot Experiments
10.1 Introduction
10.2 Motivating Example: Design and Analysis
10.3 Matrix Formulation of the Model for a Split-Plot Experiment
10.4 Design Considerations
10.5 Split-plot Screening Design
10.6 Recommendations for use of Split-plot Designs
Problems

11. Response Surface Methods
11.1 Introduction
11.2 Optimization Techniques in Response Surface Methodology
11.3 Response Surface Designs
11.3.1 Classical Response Surface Designs
11.3.2 Definitive Screening Designs
11.3.3 Optimal Designs in RSM
Problems

12. Design for Models that are Nonlinear in the Parameters
12.1 Introduction
12.2 Design and Analysis of Exponential Decay
12.3 Analysis and Locally Optimal Design of the Michaelis-Menten Model
12.4 Yield Optimization as a Function of Reaction Temperature and Time
12.5 Mathematical Details for Constructing Optimal Designs for Nonlinear Models
12.6 Optimal Design for Situations where the Response is Binary
12.7 Multifactor Binomial Model Experiments
12.8 Mathematical Details for Constructing Optimal Designs for Generalized Linear Models
Problems