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MANE 6313

Week 11, 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 Plackett-Burman Designs.

Saturated Designs

  • Saturated design is a resolution III design for investigating up to \(k=N-1\) factors in only \(N\) runs, where \(N\) is a multiple of 4
  • Examples of saturated include designs for 4 runs for up to 3 factors, 8 runs for up to 7 factors, 16 runs for up to 15 factors, etc.

Supersatured Designs

  • Supersatured designs are designs in which the number of variables \(k>N-1\) is greater than the number of runs minus 1
  • Concept was introduced by Satterthwaite in 1959
  • More details are found in section 8.8

Regular vs. Nonregular Designs

  • A regular design is one which all of the effects can be estimated independently of the other effects, and in the case of a fractional factorial, the effects that cannot be estimated are completely aliased with other effects
  • Nonregular designs are designs in which effect estimates are partially aliased with other effects
  • Nonregular designs are much more difficult to analyze

Geometric vs. Nongeometric Designs

  • Geometric designs are designs that can be represented as cubes
  • Nongeometric designs are designs that cannot be represented as cubes

Plackett-Burman Designs

  • Two-level fractional factorial design for studying up to \(k=N-1\) variables in \(N\) runs were \(N\) is a multiple of 4
  • If \(N\) is a power of 2, these designs are identical to resolution III fractional factorial designs
  • For \(N=12,20,24,28,36\), these designs are often of interest
  • Plackett-Burman designs may be nonregular and nongeometric
  • Nonregular and nongeometric designs have very complicated aliasing schemens and may not project well (cannot fold-over)

Plackett-Burman Designs in R

  • Gromping provides the following table of Plackett-Burman designs

Plackett-Burman Designs in R

Problem 8.38 (Textbook 9th edition)

  • Problem 8.38 utilize a Plackett-Burman design for 19 factors requiring 20 runs
  • Your instructor could not get the pb function within FrF2 to produce any Plackett-Burman designs greater than 16 runs
  • Therefore, this problem cannot be analyzed