Skip to content

MANE 6313

Week 11, Module F

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 sequential analysis and addition of center points.

Center Points for Fractional Factorial

  • Same concept as introduced in Chapter 6.8 - The Addition of Center Points to the 2^k Design

  • R documentation provides the following reasons to add center points to fractional factorial designs

  • "Provide a repeated benchmark run that can alert the experiment to unplanned changes in experimental conditions,"

  • "Provide an independent estimate of experimental error," and
  • "Provide a possibility for checking whether a first order model is sufficient"

Source: https://search.r-project.org/CRAN/refmans/FrF2/html/add.center.html

Example Problem

  • Devore, Chang and Sutherland provided an example
  • One-eight fraction of a seven factor design (16 runs)
  • 7 center points are added

Base Design

Example Problem - Base Design

Combined Design

Combined Design

Design Details for Combined Design

Design Details for Combined Design

Design Info

Design Info

Half Normal Plot

Half-Normal Plot for Combined Data

Initial Model

Initial Model

Test for Pure Quadratic Curvature

  • See Week Seven - Module G

Test for Pure Quadratic Curvature

Plot of A vs. Y

Plot of Factor A vs. Y