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Choosing a design

In the field of Design of Experiments (DOE), the choice of experimental design is crucial for effectively testing hypotheses and optimizing processes. This guide will break down various experimental designs based on their classification as Screening Designs, Optimization Designs, and Mixture Designs, along with their specific applications and rationales.

1. Screening Designs​

Screening designs are used primarily to identify the most important factors among many, helping researchers focus their efforts on significant variables.

a. Full-Factorial Design​

  • Description: In a full-factorial design, all possible combinations of factors and levels are tested.
  • When to Use:
    • When you have a manageable number of factors (typically up to five) and levels.
    • When interactions between factors are of interest.
  • Why: Provides comprehensive information about the effects and interactions of factors, allowing for robust conclusions.

b. Fractional-Factorial Design​

  • Description: A fractional-factorial design examines only a subset of the possible combinations of factors, reducing the total number of experiments.
  • When to Use:
    • When you have many factors (typically more than five) and need to screen for the most significant ones.
    • When time and resources are limited.
  • Why: This design allows for efficient testing while still providing insights into main effects and some interactions.

c. Plackett-Burman Design​

  • Description: A Plackett-Burman design is a type of fractional factorial design that is particularly efficient for screening large numbers of factors (usually up to 11).
  • When to Use:
    • When you want to screen many factors quickly and do not need to estimate interactions.
  • Why: It enables the identification of significant factors with a minimal number of experimental runs, focusing solely on main effects.

2. Optimization Designs​

Optimization designs focus on finding the optimal levels of factors that result in the best response. These designs often involve exploring responses in more detail after screening.

a. Box-Behnken Design​

  • Description: A Box-Behnken design is a type of response surface design that does not include the extremes of each factor's levels, allowing for a more efficient exploration of the response surface.
  • When to Use:
    • When you want to optimize a response with three or more factors.
    • When you have limited resources for experimentation.
  • Why: This design minimizes the number of runs needed while still providing enough information to model the response surface.

b. Central Composite Design (CCD)​

  • Description: Central Composite Designs are used to build a second-order (quadratic) model for the response variable without needing a full three-level factorial experiment.
  • When to Use:
    • When you want to estimate a quadratic model and explore curvature in response.
    • When you have multiple factors and want to optimize a response.
  • Why: CCD efficiently captures curvature in the response surface while requiring fewer runs than a full factorial design.

3. Mixture Designs​

Mixture designs are specifically used when the factors are proportions of components that sum to a constant, commonly found in formulation problems (e.g., chemical mixtures, food formulations).

a. Simplex Lattice Design​

  • Description: Simplex lattice designs sample from the vertices and edges of the mixture space, creating a balanced representation of component proportions.
  • When to Use:
    • When you have three or more components in a mixture.
    • When you want to explore interactions among the components.
  • Why: This design allows for the exploration of the mixture's effect on the response without needing excessive runs.

b. Simplex Centroid Design​

  • Description: This design includes runs at the vertices of the mixture space and the centroid of the mixture.
  • When to Use:
    • When you want to examine the effects of multiple components on a response, particularly focusing on the average behavior.
  • Why: The centroid run provides additional information about the overall mixture behavior.

4. Optimal Designs​

Optimal designs are tailored to specific objectives and can vary based on the goals of the experiment.

a. D-Optimal Design​

  • Description: A D-optimal design selects a subset of experimental runs to maximize the determinant of the information matrix, providing the most precise estimates of model parameters.
  • When to Use:
    • When you need to maximize the information gained from a limited number of runs.
    • When the experimental space is complex or high-dimensional.
  • Why: D-optimal designs are particularly useful for estimating parameters with minimal variance.

5. Bayesian Optimization​

Bayesian optimization is a strategy that applies Bayesian inference to optimize black-box functions.

a. Random Strategy​

  • Description: A random strategy involves randomly sampling the input space to find optimal solutions.
  • When to Use:
    • When the function being optimized is noisy or expensive to evaluate.
    • When initial information about the system is limited.
  • Why: This strategy can help in exploring the input space and is a good starting point for more sophisticated optimization techniques.

Conclusion​

Choosing the appropriate design in the Design of Experiments is critical for achieving valid results and obtaining valuable insights. By understanding the characteristics and appropriate applications of various experimental designs, researchers can effectively optimize processes and make informed decisions. Whether you are screening factors, optimizing responses, or dealing with mixture problems, selecting the right design will lead to more meaningful and reliable results.