10.1 Introduction to Design of Experiments (DOE)

Design of Experiments (DOE) is a powerful tool for optimizing processes and products. It systematically investigates how input variables affect outputs, enabling efficient optimization and quality improvement. DOE helps reduce variability and enhance understanding of complex systems.

Key components of DOE include factors, levels, responses, and interactions. Principles like randomization, replication, and blocking ensure valid results. Various design types, from full factorial to response surface, offer flexibility for different experimental needs and resource constraints.

Fundamentals of Design of Experiments (DOE)

Purpose of Design of Experiments

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• Systematically investigates effects of input variables on output variables enables efficient process optimization
• Optimizes processes and products through structured experimentation and analysis
• Reduces variability and improves quality by identifying critical factors and their optimal settings
• Enhances understanding of complex systems and their interactions (manufacturing processes, chemical reactions)

Components of DOE planning

• Factors: Input variables controlled or manipulated during experiment (temperature, pressure)
• Levels: Different values or settings of factors tested (low, medium, high)
• Responses: Output variables or results measured in experiment (yield, strength)
• Interactions: Combined effects of two or more factors on response (temperature and pressure interaction)
• Main effects: Individual effects of factors on responses isolated from other variables
• Experimental units: Subjects or items experiment conducted on (products, batches)
• Treatments: Combinations of factor levels applied to experimental units
• Control group: Baseline for comparison provides reference point for treatment effects
• Experimental error: Variability not accounted for by treatments reduces precision

Principles of experimental design

• Randomization
  • Reduces bias and ensures validity of statistical analysis
  • Randomly assigns treatments to experimental units
  • Controls for unknown or unmeasured variables (environmental factors)
• Replication
  • Estimates experimental error and increases precision of results
  • Repeats treatments on multiple experimental units
  • Improves reliability and generalizability of results across different conditions
• Blocking
  • Controls for known sources of variability improves experiment precision
  • Groups similar experimental units into blocks (time periods, batches)
  • Reduces confounding effects and isolates treatment effects

Types of experimental designs

• Full factorial designs
  • Tests all possible combinations of factor levels
  • Provides comprehensive analysis of main effects and interactions
  • Resource-intensive for many factors or levels
  • $2^k$ factorial design for k factors with two levels each (23 design for 3 factors)
• Fractional factorial designs
  • Uses subset of full factorial design reduces resource requirements
  • Efficient for screening many factors in early stages
  • Some higher-order interactions may be confounded
  • Half-fraction, quarter-fraction designs balance information and efficiency
• Response surface designs
  • Models and optimizes continuous response variables
  • Identifies optimal factor settings and explores nonlinear relationships
  • Requires more complex analysis but provides detailed response surface
  • Central composite design, Box-Behnken design for different experimental regions
• Other design types
  • Plackett-Burman designs: Screening experiments with many factors (12-run design)
  • Taguchi designs: Focuses on robustness and quality improvement (orthogonal arrays)
  • Split-plot designs: Accounts for hard-to-change factors in industrial settings