Design of Experiments

Design of Experiments (DOE) is a systematic and rigorous approach within statistics for planning, conducting, and analyzing controlled tests to understand and optimize a process or system. It involves purposefully changing one or more input variables, known as factors, to observe and identify the corresponding changes in an output variable, or response. By applying principles such as randomization, replication, and blocking, DOE allows researchers to efficiently determine cause-and-effect relationships, identify the most influential factors, and find the optimal settings for those factors, all while minimizing the effects of lurking variables and ensuring the conclusions are statistically valid.

1. Introduction to Design of Experiments
   1. Definition and Scope of DOE
   2. Core Concepts and Terminology
      1. Definition of an Experiment
      2. Experimental vs. Observational Studies
      3. Factors and Input Variables
         1. Quantitative Factors
         2. Qualitative Factors
         3. Controllable Factors
         4. Uncontrollable Factors
         5. Nuisance Factors
      4. Levels of a Factor
         1. Fixed Levels
         2. Random Levels
         3. Continuous vs. Discrete Levels
      5. Response Variables
         1. Single Response
         2. Multiple Responses
         3. Quantitative Responses
         4. Qualitative Responses
      6. Treatment Combinations
      7. Experimental Units
      8. Observational Units
      9. Effects and Interactions
         1. Main Effects
         2. Two-Factor Interactions
         3. Higher-Order Interactions
      10. Randomization Concepts
      11. Replication Concepts
      12. Blocking Concepts
      13. Confounding
      14. Aliasing
   3. Objectives of Experimentation
      1. Factor Screening
      2. Optimization
      3. Model Building
      4. Confirmation Studies
      5. Discovery Research
      6. Process Improvement
      7. Robustness Assessment
      8. Sensitivity Analysis
   4. Historical Development of DOE
      1. Early Agricultural Experiments
      2. Contributions of R.A. Fisher
      3. Industrial Applications Development
      4. Modern Statistical Methods
      5. Computer-Age Developments
   5. The Scientific Method and DOE
      1. Problem Formulation
      2. Hypothesis Development
      3. Experimental Design Selection
      4. Data Collection
      5. Statistical Analysis
      6. Interpretation and Conclusions
      7. Validation and Follow-up