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MANE 6313

Week 13, 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

Employ rsm() to design and analyze RSM models.

RSM Design in Package rsm()

  • rsm() supports two designs:
  • Box-Behnken design with 2 to 7 factors
  • Center Composite Design (ccd)
  • Details and examples of using both designs will be provided in separate modules

Model Types

  • The model formula for designs in rsm() is different
  • FO() specifies first-order model
  • TWI() is used to generate two-way interations
  • PQ() is used to add pure quadratic terms to model
  • SO() creates all terms (FO(),TWI(),PQ()) in a model

Coded Variables

  • When analyzing RSM models, variables should be coded
  • The R chunk for creating coded variables in a model is shown below
library(rsm)
bb3.design <- bbd(3,n0=2,coding=list(x1~(Force-20)/3,x2~(Rate-50)/10,x3~Polish-4))
print(bb3.design)

Coded Variables Output

bbd() Output

Adding a Response Variable

y <- rnorm(14)
bb3.design$y <- y
print(bb3.design)

Adding a Response Variable Output

Adding Response Variable

Model Fitting

bb3.fitted <- rsm(y~SO(x1,x2,x3),data=bb3.design)
summary(bb3.fitted)

Model Fitting Output

rsm() Output