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MANE 6313

Week 14, 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

Apply Sequential Analysis for CCD

Sequential Analysis in rsm()

  • Package rsm() provides capabilities of adding center points and/or star points to factorial analysis
  • Consider example for Dean, Voss and Draguljic1

Initial Design

  • The initial design is a single replicate of a \(2^4\) factorial with no center points

Initial Design with Response

First Model

  • Only coefficient information is shown
  • Model can not be further refined

Star Points

  • One centerpoint and the axial points are added
  • Since \(\alpha=\sqrt(2)\), the value must inputted manually

Augmented Design with Response

Model 2

Model 3

  • \(\alpha=0.05\) used to determine if a terms should be kept in the model

Partial F-test

Model 3 Discussion

  • Partial F-test indicates all terms removed for model 2 when model 3 was created all are statistically not significant
  • Bad design because lack of fit test is not available (see below)
  • Adding two or more centerpoints would allow Lack of Fit test to be performed (at least 2 replicated values required)

  • Remaining analysis should be performed:

    • Residual analysis
    • Graphical analysis
    • Stationary point analysis

  1. Dean, Voss and Draguljic (2017). Design and Analysis of Experiments, 2nd Edition. Springer Press. ↩