Generating and assessing exact G-optimal designs

Myrta Rodríguez, Bradley Jones, Connie M. Borror, Douglas Montgomery

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


We introduce a new algorithm for generating near G-optimal designs for second-order models over cuboidal regions. The algorithm involves the use of Brent's minimization algorithm with coordinate exchange to create designs for 2 to 5 factors. Designs created using this new method either match or exceed the G-efficiency of previously reported designs. We also introduce a new graphical tool, the variance ratio fraction of design space (VRFDS) plot, which is useful for easy comparison of the prediction variance for competing designs over a given region of interest. Using the VRFDS plot to compare G-optimal designs to I-optimal designs shows that the G-optimal designs have higher prediction variance over the vast majority of the design region. This suggests that, for many response surface studies, G-optimal designs may not be the best choice.

Original languageEnglish (US)
Pages (from-to)3-20
Number of pages18
JournalJournal of Quality Technology
Issue number1
StatePublished - Jan 2010


  • Computer-generated designs
  • D-efficiency
  • Fraction of design space plots
  • G-efficiency
  • I-efficiency
  • Optimality criteria
  • Prediction variance

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Strategy and Management
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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