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MANE 6313

Week 10, Module D

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 resolution of an experimental design.

Resolution of Experimental Design

  • Definition. A design is of resolution \(R\) if no \(p\)-factor effect is aliased with another effect containing less than \(R-p\) factors.

  • The three most common design resolutions are:

    • Resolution III designs. No main effect is aliased with any other main effect, but main effects are aliased with two-factor interactions and two-factor interactions may be aliased with each other.

    • Resolution IV designs. No main effect is aliased with any other main effect or with any two-factor interaction, but two interactions are aliased with other two-factor interactions

    • Resolution V designs. No main effect or two-factor interactions is aliased with any other main effect or two-factor interaction, but two-factor interactions are aliased with three-factor interactions.

  • In general, the resolution of a two-level fractional factorial design is equal to the smallest number of letters in the defining relation.

Projection of Fractions into Factorials

  • Any fractional factorial design of resolution \(R\) contains complete factorial designs (possibly replicated factorials) in any subset of \(R-1\) factors

  • Very useful result in screening experiments

  • If we can eliminate variables as being non-significant, the fractional factorial design may become a (replicated) factorial design

  • See figure 8.2 on page 278 of your textbook.

Figure 8.2

Sources of Design Resolution

  • Textbook
  • Table 8.14
  • Table VIII (appendix a-16)
  • R
  • FrF2

Textbook Table 8.14

Table 8.14

Textbook Table VIII (A-16)

Table VIII

FrF2 Design Catalog

Source: Grompig, U. (2014). R Package FrF2 for Creating and Analyzing Fractional Factorial 2-Level Designs. Journal of Statistical Software, 56(1), 1-56.

FrF2 Design Catalog

Review Problem 20.17

Review Problem 20.17

FrF2 Design Resolution

Creating Designs with known resolution