Design and Analysis of Experiments with R

TL;DR: In this paper, the authors present an example of a two-factor Factorial Plan in R with fixed and random factors for estimating variance components of two-Factor Factorial Plans.

Abstract: Introduction Statistics and Data Collection Beginnings of Statistically Planned Experiments Definitions and Preliminaries Purposes of Experimental Design Types of Experimental Designs Planning Experiments Performing the Experiments Use of R Software Completely Randomized Designs with One Factor Introduction Replication and Randomization A Historical Example Linear Model for Completely Randomized Design (CRD) Verifying Assumptions of the Linear Model Analysis Strategies When Assumptions Are Violated Determining the Number of Replicates Comparison of Treatments after the F-Test Factorial Designs Introduction Classical One at a Time versus Factorial Plans Interpreting Interactions Creating a Two-Factor Factorial Plan in R Analysis of a Two-Factor Factorial in R Factorial Designs with Multiple Factors-Completely Randomized Factorial Design (CRFD) Two-Level Factorials Verifying Assumptions of the Model Randomized Block Designs Introduction Creating a Randomized Complete Block (RCB) Design in R Model for RCB An Example of a RCB Determining the Number of Blocks Factorial Designs in Blocks Generalized Complete Block Design Two Block Factors Latin Square Design (LSD) Designs to Study Variances Introduction Random Sampling Experiments (RSE) One-Factor Sampling Designs Estimating Variance Components Two-Factor Sampling Designs-Factorial RSE Nested SE Staggered Nested SE Designs with Fixed and Random Factors Graphical Methods to Check Model Assumptions Fractional Factorial Designs Introduction to Completely Randomized Fractional Factorial (CRFF) Half Fractions of 2k Designs Quarter and Higher Fractions of 2k Designs Criteria for Choosing Generators for 2k-p Designs Augmenting Fractional Factorials Plackett-Burman (PB) Screening Designs Mixed-Level Fractional Factorials Orthogonal Array (OA) Definitive Screening Designs Incomplete and Confounded Block Designs Introduction Balanced Incomplete Block (BIB) Designs Analysis of Incomplete Block Designs Partially Balanced Incomplete Block (PBIB) Designs-Balanced Treatment Incomplete Block (BTIB) Row Column Designs Confounded 2k and 2k-p Designs Confounding 3 Level and p Level Factorial Designs Blocking Mixed-Level Factorials and OAs Partially CBF Split-Plot Designs Introduction Split-Plot Experiments with CRD in Whole Plots (CRSP) RCB in Whole Plots (RBSP) Analysis Unreplicated 2k Split-Plot Designs 2k-p Fractional Factorials in Split Plots (FFSP) Sample Size and Power Issues for Split-Plot Designs Crossover and Repeated Measures Designs Introduction Crossover Designs (COD) Simple AB, BA Crossover Designs for Two Treatments Crossover Designs for Multiple Treatments Repeated Measures Designs Univariate Analysis of Repeated Measures Design Response Surface Designs Introduction Fundamentals of Response Surface Methodology Standard Designs for Second-Order Models Creating Standard Response Surface Designs in R Non-Standard Response Surface Designs Fitting the Response Surface Model with R Determining Optimum Operating Conditions Blocked Response Surface (BRS) Designs Response Surface Split-Plot (RSSP) Designs Mixture Experiments Introduction Models and Designs for Mixture Experiments Creating Mixture Designs in R Analysis of Mixture Experiment Constrained Mixture Experiments Blocking Mixture Experiments Mixture Experiments with Process Variables Mixture Experiments in Split-Plot Arrangements Robust Parameter Design Experiments Introduction Noise Sources of Functional Variation Product Array Parameter Design Experiments Analysis of Product Array Experiments Single Array Parameter Design Experiments Joint Modeling of Mean and Dispersion Effects Experimental Strategies for Increasing Knowledge Introduction Sequential Experimentation One-Step Screening and Optimization An Example of Sequential Experimentation Evolutionary Operation Concluding Remarks Appendix: Brief Introduction to R Answers to Selected Exercises Bibliography Index A Review and Exercises appear at the end of each chapter.