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MANE 6313

Week 7, Module H

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

Explain extensions of two-level factorial designs

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.

Extensions of Two-level Factorial Designs

  • Two-level factorial designs are used extensively in practice
  • Will form basis for much of the remainder of the course
  • Screening Designs
  • Central Composite Designs

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

  • Goal is to determine if variable should be in model rather than building highly-accurate models

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

  • A single replicate of two-level factorial design is an example of a screening experiment

  • Fractional factorial experiments involve using a portion of a two-level factorial design

Central Composite Design

  • Central composite designs are an important model used in response surface methodology

  • Central composite designs yield highly accurate prediction models

  • 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.

Examples of Central Composite Designs

Figure 11.20 from textbook

CCD

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