5. Design and Analysis of Experiments

• 5.1. Design and analysis of experiments in context
• 5.2. Terminology
• 5.3. Usage examples
• 5.4. References and readings
• 5.5. Why learning about systems is important
  • 5.5.1. An engineering example
  • 5.5.2. Feedback control
  • 5.5.3. Another engineering example
• 5.6. Experiments with a single variable at two levels
  • 5.6.1. Recap of group-to-group differences
  • 5.6.2. How many runs at each level?
  • 5.6.3. Using linear least squares models
  • 5.6.4. The importance of randomization
• 5.7. Changing one single variable at a time (COST)
• 5.8. Full factorial designs
  • 5.8.1. Using two levels for two or more factors
  • 5.8.2. Analysis of a factorial design: main effects
  • 5.8.3. Analysis of a factorial design: interaction effects
  • 5.8.4. Analysis by least squares modelling
  • 5.8.5. Example: design and analysis of a three-factor experiment
  • 5.8.6. Assessing significance of main effects and interactions
  • 5.8.7. Summary so far
  • 5.8.8. Example: analysis of systems with 4 factors
• 5.9. Fractional factorial designs
  • 5.9.1. Half fractions
  • 5.9.2. Generators and defining relationships
  • 5.9.3. Generating the complementary half-fraction
  • 5.9.4. Generators: to determine confounding due to blocking
  • 5.9.5. Blocking into more than two groups
  • 5.9.6. Highly fractionated designs: beyond half-fractions
  • 5.9.7. Design resolution
  • 5.9.8. Saturated designs for screening
  • 5.9.9. Design foldover
  • 5.9.10. Projectivity
• 5.10. Blocking and confounding for disturbances
  • 5.10.1. Characterization of disturbances
  • 5.10.2. Blocking and confounding
• 5.11. Response surface methods
  • 5.11.1. Response surface optimization via a 2-variable system example
  • 5.11.2. Checking the fit: pure error and the lack-of-fit test
  • 5.11.3. Box-Behnken designs
  • 5.11.4. The general approach for response surface modelling
• 5.12. Evolutionary operation
• 5.13. Multi-response optimization: the sweet spot and desirability
  • 5.13.1. Continuing the bioreactor example
  • 5.13.2. The sweet spot
  • 5.13.3. Desirability
  • 5.13.4. How well is the optimum known?
  • 5.13.5. Comparing the three approaches
• 5.14. Optimal designs of experiments: D-, A-, and G-optimality and the information matrix
  • 5.14.1. When the classical designs do not fit
  • 5.14.2. The idea of an optimal design
  • 5.14.3. The information matrix and the optimality criteria
  • 5.14.4. How the algorithms search: exchange algorithms
  • 5.14.5. A worked example: a design the catalogue cannot give you
  • 5.14.6. Augmenting an existing design
  • 5.14.7. Categorical factors with several levels
• 5.15. Definitive screening designs (DSD): screen factors and detect curvature in one experiment
  • 5.15.1. The foldover construction and its consequences
  • 5.15.2. A worked DSD: generating and reading the design
• 5.16. OMARS designs: orthogonal minimally aliased response surface designs
  • 5.16.1. A spectrum from screening to response surface
  • 5.16.2. Analysing data from these designs
• 5.17. Judging and comparing experimental designs
  • 5.17.1. Prediction variance
  • 5.17.2. A worked example: augmenting a small design
  • 5.17.3. A running comparison: a DSD and an OMARS design
  • 5.17.4. The fraction-of-design-space (FDS) plot
  • 5.17.5. Separability is not the same as precision
  • 5.17.6. Variance inflation factors
  • 5.17.7. Bias from the terms left out: the alias matrix
  • 5.17.8. Statistical power
  • 5.17.9. Putting the metrics side by side
• 5.18. An omnibus comparison across design families
  • 5.18.1. Can the design fit the model?
  • 5.18.2. Power to detect an effect
  • 5.18.3. Quality metrics for the four designs
  • 5.18.4. Aliasing from the omitted interactions
  • 5.18.5. What the table compares
  • 5.18.6. Two views of prediction variance
  • 5.18.7. A checklist for choosing among designs
• 5.19. Mixture experiments
  • 5.19.1. The mixture constraint
  • 5.19.2. How the constraint changes the model
  • 5.19.3. Scheffe models
  • 5.19.4. Lower bounds and pseudocomponents
  • 5.19.5. Mixture experiments with process variables
  • 5.19.6. Constructing the design on the simplex
  • 5.19.7. References
• 5.20. General approach for experimentation
• 5.21. Extended topics related to designed experiments
  • 5.21.1. Experiments with mistakes, missing values, or belatedly discovered constraints
  • 5.21.2. Handling of constraints
  • 5.21.3. Mixture designs
• 5.22. Exercises