{"product_id":"design-of-experiments","title":"Design of Experiments","description":"\u003cp\u003eStudent Solution Available in Interactive e-Text\u003c\/p\u003e \u003cp\u003ePreface iii\u003c\/p\u003e \u003cp\u003eAbout the Authors v\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 \u003c\/b\u003e\u003cb\u003eExperimental Design: Principles and Practices and Statistics Review 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 The Strategy of Experimentation 1\u003c\/p\u003e \u003cp\u003e1.2 Basic Principles 8\u003c\/p\u003e \u003cp\u003e1.3 Practical Guidelines for Designing an Experiment 10\u003c\/p\u003e \u003cp\u003e1.3.1 Recognition of and Statement of the Problem 10\u003c\/p\u003e \u003cp\u003e1.3.2 Selection of the Response Variable 11\u003c\/p\u003e \u003cp\u003e1.3.3 Choice of Factors, Levels, and Ranges 11\u003c\/p\u003e \u003cp\u003e1.3.4 Experimental Design Generation 13\u003c\/p\u003e \u003cp\u003e1.3.5 Performing the Experiment 14\u003c\/p\u003e \u003cp\u003e1.3.6 Statistical Analysis of the Data 14\u003c\/p\u003e \u003cp\u003e1.3.7 Conclusions and Recommendations 15\u003c\/p\u003e \u003cp\u003e1.4 A Brief History of Designed Experiments 15\u003c\/p\u003e \u003cp\u003e1.5 A Review: Using Statistical Techniques in Experimentation 17\u003c\/p\u003e \u003cp\u003e1.6 Review of Some Basic Statistical Concepts and Methods 18\u003c\/p\u003e \u003cp\u003e1.6.1 Data Description 18\u003c\/p\u003e \u003cp\u003e1.6.2 Random Samples, Statistics and Sampling Distributions 23\u003c\/p\u003e \u003cp\u003e1.6.3 Statistical Intervals and Tests of Hypotheses 28\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 \u003c\/b\u003e\u003cb\u003eSimple Comparative Experiments 42\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 42\u003c\/p\u003e \u003cp\u003e2.2 Statistical Methods for Comparing Two Population Means 42\u003c\/p\u003e \u003cp\u003e2.2.1 Parameter Estimation and Confidence Intervals 42\u003c\/p\u003e \u003cp\u003e2.2.2 Statistical Hypothesis Testing on the Difference in Means 47\u003c\/p\u003e \u003cp\u003e2.3 Comparison of Two Means, Variances Unknown 51\u003c\/p\u003e \u003cp\u003e2.3.1 Confidence Intervals on the Difference in Means of Two Normal Distributions, Variances Unknown 52\u003c\/p\u003e \u003cp\u003e2.3.2 Hypothesis Testing on the Difference in Means of Two Normal Distributions with Unknown Variances 54\u003c\/p\u003e \u003cp\u003e2.3.3 Comparison of Means of Two Normal Distributions with Variances Unknown but Assumed Equal 56\u003c\/p\u003e \u003cp\u003e2.3.4 Power and Sample Size Calculations 57\u003c\/p\u003e \u003cp\u003e2.3.5 The Normality Assumption 57\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 \u003c\/b\u003e\u003cb\u003eExperiments With a Single Categorical Factor: Design Issues and the Analysis of Variance 59\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Motivating Example 59\u003c\/p\u003e \u003cp\u003e3.2 Statistical Model for the Data 61\u003c\/p\u003e \u003cp\u003e3.3 Design Considerations 62\u003c\/p\u003e \u003cp\u003e3.4 Statistical Analysis of the Data 62\u003c\/p\u003e \u003cp\u003e3.4.1 Partitioning the Variance of the Response 63\u003c\/p\u003e \u003cp\u003e3.4.2 The ANOVA 64\u003c\/p\u003e \u003cp\u003e3.4.3 Post-ANOVA Comparison of Treatment Means 65\u003c\/p\u003e \u003cp\u003e3.4.4 Comparing Treatment Means with a Control 68\u003c\/p\u003e \u003cp\u003e3.4.5 The Effects Model 70\u003c\/p\u003e \u003cp\u003e3.5 Model Adequacy Checking 71\u003c\/p\u003e \u003cp\u003e3.5.1 Checking the Normality Assumption 71\u003c\/p\u003e \u003cp\u003e3.5.2 Checking for Nonconstant Variance 73\u003c\/p\u003e \u003cp\u003e3.6 Power and Sample Size 75\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 \u003c\/b\u003e\u003cb\u003eExperiments With a Single Continuous Factor: Design Issues and the Regression Analysis 77\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Motivating Example 77\u003c\/p\u003e \u003cp\u003e4.2 Statistical Models for the Data 77\u003c\/p\u003e \u003cp\u003e4.3 Fitting a Statistical Model Using the Data 79\u003c\/p\u003e \u003cp\u003e4.4 Design Considerations 82\u003c\/p\u003e \u003cp\u003e4.5 Design Comparison 83\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 \u003c\/b\u003e\u003cb\u003eTwo-Factor Factorial Experiments 87\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Basic Concepts 87\u003c\/p\u003e \u003cp\u003e5.2 Two Categorical Factors 89\u003c\/p\u003e \u003cp\u003e5.3 The Analysis of Variance for a Two-factor Factorial 92\u003c\/p\u003e \u003cp\u003e5.4 One Categorical Factor and One Continuous Factor 98\u003c\/p\u003e \u003cp\u003e5.5 Two Continuous Factors 100\u003c\/p\u003e \u003cp\u003e5.6 Design and Analysis When Some Factor Level Combinations Are Infeasible 105\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 \u003c\/b\u003e\u003cb\u003eBlocking 109\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 The Randomized Complete Block Design 109\u003c\/p\u003e \u003cp\u003e6.2 Statistical Analysis of the RCBD 110\u003c\/p\u003e \u003cp\u003e6.3 Blocking and Optimal Designs 113\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 \u003c\/b\u003e\u003cb\u003eThe 2\u003ci\u003e\u003csup\u003ek\u003c\/sup\u003e \u003c\/i\u003eFactorial Design 118\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 118\u003c\/p\u003e \u003cp\u003e7.2 The 2\u003csup\u003e2\u003c\/sup\u003e Factorial Design 118\u003c\/p\u003e \u003cp\u003e7.2.1 How Much Replication is Necessary? 119\u003c\/p\u003e \u003cp\u003e7.3 The 2\u003csup\u003e3\u003c\/sup\u003e Factorial Design 123\u003c\/p\u003e \u003cp\u003e7.3.1 Replication of the 2\u003csup\u003e3\u003c\/sup\u003e Design 128\u003c\/p\u003e \u003cp\u003e7.4 A Single Replicate of the 2\u003ci\u003e\u003csup\u003ek\u003c\/sup\u003e \u003c\/i\u003eDesign 129\u003c\/p\u003e \u003cp\u003e7.5 2\u003ci\u003e\u003csup\u003ek\u003c\/sup\u003e \u003c\/i\u003eDesigns are Optimal Designs 133\u003c\/p\u003e \u003cp\u003e7.6 More About Replication of 2\u003ci\u003e\u003csup\u003ek\u003c\/sup\u003e \u003c\/i\u003eDesigns 135\u003c\/p\u003e \u003cp\u003e7.6.1 Adding Center Runs to a 2\u003ci\u003e\u003csup\u003ek\u003c\/sup\u003e \u003c\/i\u003eDesign 137\u003c\/p\u003e \u003cp\u003e7.7 Blocking in 2\u003csup\u003ek\u003c\/sup\u003e Designs 138\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 \u003c\/b\u003e\u003cb\u003eScreening Experiments 140\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 140\u003c\/p\u003e \u003cp\u003e8.2 Regular Fractional Factorial Designs for Factor Screening 141\u003c\/p\u003e \u003cp\u003e8.2.1 A General Method for Finding the Alias Relationships in Fractional Factorial Designs 144\u003c\/p\u003e \u003cp\u003e8.2.2 Dealiasing Effects 148\u003c\/p\u003e \u003cp\u003e8.3 Nonregular Orthogonal Designs 150\u003c\/p\u003e \u003cp\u003e8.4 Nonorthogonal Screening Designs 153\u003c\/p\u003e \u003cp\u003e8.5 Definitive Screening Designs 156\u003c\/p\u003e \u003cp\u003e8.5.1 Statistical Properties of a DSD 158\u003c\/p\u003e \u003cp\u003e8.5.2 Constructing DSDs Using Conference Matrices 158\u003c\/p\u003e \u003cp\u003e8.5.3 Constructing DSDs with Additional Two-level Categorical Factors 159\u003c\/p\u003e \u003cp\u003e8.5.4 Constructing Orthogonally Blocked DSDs 159\u003c\/p\u003e \u003cp\u003e8.5.5 Situations When You Should Use a Screening Design Other Than a DSD 159\u003c\/p\u003e \u003cp\u003e8.5.6 Recommendations 160\u003c\/p\u003e \u003cp\u003e8.6 Screening Summary 160\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 \u003c\/b\u003e\u003cb\u003eExperiments With Random Blocks 163\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 163\u003c\/p\u003e \u003cp\u003e9.2 Motivating Example: Design and Analysis 164\u003c\/p\u003e \u003cp\u003e9.3 Matrix Formulation of the Model for an Experiment with Random Blocks 165\u003c\/p\u003e \u003cp\u003e9.4 Design Considerations 166\u003c\/p\u003e \u003cp\u003e9.5 A Screening Design with a Random Blocking Factor 166\u003c\/p\u003e \u003cp\u003e9.6 Recommendations for Use of Designs with Random Blocks 170\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 \u003c\/b\u003e\u003cb\u003eSplit-Plot Experiments 172\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 172\u003c\/p\u003e \u003cp\u003e10.2 Motivating Example: Design and Analysis 173\u003c\/p\u003e \u003cp\u003e10.3 Matrix Formulation of the Model for a Split-plot Experiment 174\u003c\/p\u003e \u003cp\u003e10.4 Design Considerations 176\u003c\/p\u003e \u003cp\u003e10.5 Split-plot Screening Design 176\u003c\/p\u003e \u003cp\u003e10.6 Recommendations for Use of Split-plot Designs 177\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 \u003c\/b\u003e\u003cb\u003eResponse Surface Methods 180\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 180\u003c\/p\u003e \u003cp\u003e11.2 Optimization Techniques in RSM 182\u003c\/p\u003e \u003cp\u003e11.3 Response Surface Designs 196\u003c\/p\u003e \u003cp\u003e11.3.1 Classical Response Surface Designs 196\u003c\/p\u003e \u003cp\u003e11.3.2 Definitive Screening Designs 197\u003c\/p\u003e \u003cp\u003e11.3.3 Optimal Designs in RSM 201\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 \u003c\/b\u003e\u003cb\u003eDesign For Models That are Nonlinear in the Parameters 203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 203\u003c\/p\u003e \u003cp\u003e12.2 Design and Analysis of Exponential Decay 204\u003c\/p\u003e \u003cp\u003e12.3 Analysis and Locally Optimal Design of the Michaelis–Menten Model 206\u003c\/p\u003e \u003cp\u003e12.4 Yield Optimization as a Function of Reaction Temperature and Time 207\u003c\/p\u003e \u003cp\u003e12.5 Mathematical Details for Constructing Optimal Designs for Nonlinear Models 208\u003c\/p\u003e \u003cp\u003e12.6 Optimal Design for Situations Where the Response is Binary 210\u003c\/p\u003e \u003cp\u003e12.7 Multifactor Binomial Model Experiments 212\u003c\/p\u003e \u003cp\u003e12.8 Mathematical Details for Constructing Optimal Designs for Generalized Linear Models 213\u003c\/p\u003e \u003cp\u003eProblems P-1\u003c\/p\u003e \u003cp\u003eA JMP Scripting Commands For Computing Distribution Probabilities and Quantiles A-1\u003c\/p\u003e \u003cp\u003eReferences R-1\u003c\/p\u003e \u003cp\u003eIndex I-1\u003c\/p\u003e","brand":"Douglas C. 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