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MANE 6313

Week 11, 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 sequential analysis and full fold-over design.

Sequential Experimentation

  • This is particularly applicable for resolution III experiments
  • Conduct another fraction based upon information gained in the initial model
  • A fold-over design can be either a full fold-over or fold-over on an effect

Example Problem

  • Taken from Devore, Change and Sutherland
  • \(2^{7-4}\) resolution III design
  • Generators are 4=12, 5=13, 6=23 and 7=123 (DCS uses numbers instead of letters)

Example Problem DCS

Example Problem - Design Matrix

Design Matrix for Example Problem

Design using R

Base Design in R

R Design Details

Design Details in R

FrF2 Catalog Information

  • Design is 7-4.1

  • Design.info is shown below

FrF2 Catalog Information

R: Response Variable

Response Variable for Example Problem

Half-normal Plot

Half Normal Plot

Interpreting Half-Normal Plot Results

  • Factors A, B, and F alone are responsible for large effect estimates
  • From aliasing scheme of A, BD and/or CE and/or FG could be responsible for large effect estimate for A (with or without A being large),
  • From aliasing scheme of B, AD and/or DF and/or EG could be responsible for large effect estimate for B (with or without B being large),
  • From aliasing scheme of F, AG and/or BC and/or DE could be respnosible for large effect estimate for F (with or without F being large)
  • No clear pattern

Full Fold-over

  • Full fold-over occurs when you change all the signs in the design matrix; run another fraction
  • A full fold-over will break the alias links between the main effects and two-factor interactions
  • Two-factor interactions may (still) be aliased with each other

DCS Full Fold-Over

Full Fold-Over in R

Full Fold-over in R

Full Fold-over Design

Full fold-Over in R

Full Fold-over Design, part 2

Full Fold-Over Design, Part 2

Fold-over Design with Response

Response Variable for Fuill Fold-over

Half-Normal Plot for Fold-over

Half Normal Plot for Full fold-over Design

Interpretation of Half Normal Plot

  • All main effects are not aliased with other main effects or two factor interactions (A, B, F, D, G)
  • From aliasing scheme for AB, CH and/or -DE and/or FG (with or without AB being large)
  • From aliasing scheme for AD, -BE and/or -DF and/or -Gh (with or withont AD being large)
  • From aliasing scheme for AE, -DB and/or CG and/or FH (with or without AE being large)

Initial Model

Aliasing in Initial Model