Skip to content

MANE 6313

Week 7, Module G

Student Learning Outcome

  • Select an appropriate experimental design with one or more factors,
  • Select an appropriate model with one or more factors,
  • Evaluate statistical analyses of experimental designs,
  • Assess the model adequacy of any experimental design, and
  • Interpret model results.

Module Learning Outcome

Describe screening designs

Resources for the Week 7, Module G micro-lecture are:

Guidelines for use of centerpoints

  1. When a factorial experiment is on-going, consider the current operating conditions as the centerpoint in the design

  2. If the centerpoint is the usual operating condition, the observed values of the centerpoint can be compared to past information to check for anything "unusual."

  3. Consider running the replicates at the centerpoint in nonrandom order: start and end to check for drift

  4. Run some centerpoints early in an experiment to "peek" at the process.

  5. Usually used when all factors are quantitative.

Central Composite Design

  • Should the test for pure quadratic curvature prove to be significant, central composite design are an ideal choice.

  • Central composite design is composed of three parts

    • Factorial (or fractional) factorial design

    • A number of centerpoints

    • Axial or star points

  • Central composite design is easy to understand for 2 and 3 factor experiments.

Screening Experiments

  • Often used very early to determine which factors are important and which factors are not important

  • Typically only a single replicate is used to reduce the number of runs

  • The assumption that the response variable is approximately linear over the experimental space. Can be validated.

  • Fractional factorial experiments are the other very important type of screening designs.

Coded Variables

  • Variables transformed to +1, -1
\[ x_i=\frac{X_i-\frac{1}{2}\left(X_{iL}+X_{iH}\right)}{X_{iH}-X_{iL}} \]

  • Benefit 1 - Computational ease and increase accuracy in estimating model coefficients

  • Benefit 2 - Enhanced interpretability of the coefficient estimates in the model

Face-centered Central Composite Design

Source: (http://www.pccc.icrc.ac.ir/article_81574_8027f0c371795aec2305b3d9a00ed756.pdf))

face-centered central composite design, part one

face-centered central composite design, part two