Contents -- PART I: BACKGROUND -- 1 Introduction -- 1.1 Some Examples -- 1.2 Scope and Limitations -- 1.3 Background Reading -- 2 Some Key Ideas -- 2.1 Scaled Variables -- 2.2 Design Regions -- 2.3 Random Error -- 2.4 Unbiasedness, Validity, and Efficiency -- 3 Experimental Strategies -- 3.1 Objectives of the Experiment -- 3.2 Stages in Experimental Research -- 3.3 The Optimization of Yield -- 3.4 Further Reading -- 4 The Choice of a Model -- 4.1 Linear Models for One Factor -- 4.2 Non-linear Models -- 4.3 Interaction -- 4.4 Response Surface Models -- 5 Models and Least Squares -- 5.1 Simple Regression -- 5.2 Matrices and Experimental Design -- 5.3 Least Squares -- 5.4 Further Reading -- 6 Criteria for a Good Experiment -- 6.1 Aims of a Good Experiment -- 6.2 Confidence Regions and the Variance of Prediction -- 6.3 Contour Plots of Variances for Two-Factor Designs -- 6.4 Variance-Dispersion Graphs -- 6.5 Some Criteria for Optimum Experimental Designs -- 7 Standard Designs -- 7.1 Introduction -- 7.2 2[sup(m)] Factorial Designs -- 7.3 Blocking 2[sup(m)] Factorial Designs -- 7.4 2[sup(m-f)] Fractional Factorial Designs -- 7.5 Plackett-Burman Designs -- 7.6 Composite Designs -- 7.7 Standard Designs in SAS -- 7.8 Further Reading -- 8 The Analysis of Experiments -- 8.1 Introduction -- 8.2 Example 1.1 Revisited: The Desorption of Carbon Monoxide -- 8.3 Example 1.2 Revisited: The Viscosity of Elastomer Blends -- 8.4 Selecting Effects in Saturated Fractional Factorial Designs -- 8.5 Robust Design -- 8.6 Analysing Data with SAS -- PART II: THEORY AND APPLICATIONS -- 9 Optimum Design Theory -- 9.1 Continuous and Exact Designs -- 9.2 The General Equivalence Theorem -- 9.3 Exact Designs and the General Equivalence Theorem -- 9.4 Algorithms for Continuous Designs and the General Equivalence Theorem -- 9.5 Function Optimization and Continuous Design.

9.6 Finding Continuous Optimum Designs Using SAS/IML Software -- 10 Criteria of Optimality -- 10.1 A-, D-, and E-optimality -- 10.2 D[sub(A)]-optimality (Generalized D-optimality) -- 10.3 D[sub(S)]-optimality -- 10.4 c-optimality -- 10.5 Linear Optimality: C- and L-optimality -- 10.6 V-optimality: Average Variance -- 10.7 G-optimality -- 10.8 Compound Design Criteria -- 10.9 Compound D[sub(A)]-optimality -- 10.10 D-optimum Designs for Multivariate Responses -- 10.11 Further Reading and Other Criteria -- 11 D-optimum Designs -- 11.1 Properties of D-optimum Designs -- 11.2 The Sequential Construction of Optimum Designs -- 11.3 An Example of Design Efficiency: The Desorption of Carbon Monoxide. Example 1.1 Continued -- 11.4 Polynomial Regression in One Variable -- 11.5 Second-order Models in Several Variables -- 11.6 Further Reading -- 12 Algorithms for the Construction of Exact D-optimum Designs -- 12.1 Introduction -- 12.2 The Exact Design Problem -- 12.3 Basic Formulae for Exchange Algorithms -- 12.4 Sequential Algorithms -- 12.5 Non-sequential Algorithms -- 12.6 The KL and BLKL Exchange Algorithms -- 12.7 Example 12.2: Performance of an Internal Combustion Engine -- 12.8 Other Algorithms and Further Reading -- 13 Optimum Experimental Design with SAS -- 13.1 Introduction -- 13.2 Finding Exact Optimum Designs Using the OPTEX Procedure -- 13.3 Efficiencies and Coding in OPTEX -- 13.4 Finding Optimum Designs Over Continuous Regions Using SAS/IML Software -- 13.5 Finding Exact Optimum Designs Using the ADX Interface -- 14 Experiments with Both Qualitative and Quantitative Factors -- 14.1 Introduction -- 14.2 Continuous Designs -- 14.3 Exact Designs -- 14.4 Designs with Qualitative Factors in SAS -- 14.5 Further Reading -- 15 Blocking Response Surface Designs -- 15.1 Introduction -- 15.2 Models and Design Optimality -- 15.3 Orthogonal Blocking.

15.4 Related Problems and Literature -- 15.5 Optimum Block Designs in SAS -- 16 Mixture Experiments -- 16.1 Introduction -- 16.2 Models and Designs for Mixture Experiments -- 16.3 Constrained Mixture Experiments -- 16.4 Mixture Experiments with Other Factors -- 16.5 Blocking Mixture Experiments -- 16.6 The Amount of a Mixture -- 16.7 Optimum Mixture Designs in SAS -- 16.8 Further Reading -- 17 Non-linear Models -- 17.1 Some Examples -- 17.2 Parameter Sensitivities and D-optimum Designs -- 17.3 Strategies for Local Optimality -- 17.4 Sampling Windows -- 17.5 Locally c-optimum Designs -- 17.6 The Analysis of Non-linear Experiments -- 17.7 A Sequential Experimental Design -- 17.8 Design for Diffierential Equation Models -- 17.9 Multivariate Designs -- 17.10 Optimum Designs for Non-linear Models in SAS -- 17.11 Further Reading -- 18 Bayesian Optimum Designs -- 18.1 Introduction -- 18.2 A General Equivalence Theorem Incorporating Prior Information -- 18.3 Bayesian D-optimum Designs -- 18.4 Bayesian c-optimum Designs -- 18.5 Sampled Parameter Values -- 18.6 Discussion -- 19 Design Augmentation -- 19.1 Failure of an Experiment -- 19.2 Design Augmentation and Equivalence Theory -- 19.3 Examples of Design Augmentation -- 19.4 Exact Optimum Design Augmentation -- 19.5 Design Augmentation in SAS -- 19.6 Further Reading -- 20 Model Checking and Designs for Discriminating Between Models -- 20.1 Introduction -- 20.2 Parsimonious Model Checking -- 20.3 Examples of Designs for Model Checking -- 20.4 Example 20.3. A Non-linear Model for Crop Yield and Plant Density -- 20.5 Exact Model Checking Designs in SAS -- 20.6 Discriminating Between Two Models -- 20.7 Sequential Designs for Discriminating Between Two Models -- 20.8 Developments of T-optimality -- 20.9 Nested Linear Models and D[sub(s)]-optimum Designs -- 20.10 Exact T-optimum Designs in SAS.

20.11 The Analysis of T-optimum Designs -- 20.12 Further Reading -- 21 Compound Design Criteria -- 21.1 Introduction -- 21.2 Design Efficiencies -- 21.3 Compound Design Criteria -- 21.4 Polynomials in One Factor -- 21.5 Model Building and Parameter Estimation -- 21.6 Non-linear Models -- 21.7 Discrimination Between Models -- 21.8 DT-Optimum Designs -- 21.9 CD-Optimum Designs -- 21.10 Optimizing Compound Design Criteria in SAS -- 21.11 Further Reading -- 22 Generalized Linear Models -- 22.1 Introduction -- 22.2 Weighted Least Squares -- 22.3 Generalized Linear Models -- 22.4 Models and Designs for Binomial Data -- 22.5 Optimum Design for Gamma Models -- 22.6 Designs for Generalized Linear Models in SAS -- 22.7 Further Reading -- 23 Response Transformation and Structured Variances -- 23.1 Introduction -- 23.2 Transformation of the Response -- 23.3 Design for a Response Transformation -- 23.4 Response Transformations in Non-linear models -- 23.5 Robust and Compound Designs -- 23.6 Structured Mean-Variance Relationships -- 24 Time-dependent Models with Correlated Observations -- 24.1 Introduction -- 24.2 The Statistical Model -- 24.3 Numerical Example -- 24.4 Multiple Independent Series -- 24.5 Discussion and Further Reading -- 25 Further Topics -- 25.1 Introduction -- 25.2 Crossover Designs -- 25.3 Biased-coin Designs for Clinical Trials -- 25.4 Adaptive Designs for Clinical Trials -- 25.5 Population Designs -- 25.6 Designs Over Time -- 25.7 Neural Networks -- 25.8 In Brief -- 26 Exercises -- Bibliography -- Author Index -- A -- B -- C -- D -- E -- F -- G -- H -- J -- K -- L -- M -- N -- O -- P -- R -- S -- T -- U -- V -- W -- Y -- Z -- Subject Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- X -- Z.