Response surface designs within a split-plot structure

G. Geoffrey Vining, Scott M. Kowalski, Douglas Montgomery

Research output: Contribution to journalArticlepeer-review

106 Scopus citations


In many industrial experiments, time and/or cost constraints often force certain factors in a designed experiment to be much harder to change than others. An appropriate approach to such an experiment restricts the randomization, which leads to a split-plot structure. This paper first establishes how one can modify the common central-composite design to efficiently accommodate a split-plot structure. The proposed designs allow pure-error estimates of the two variance components. We next discuss the conditions on the design that make ordinary least squares and weighted least squares estimates equivalent. These conditions are easy to obtain in practice. An important consequence is that people can use standard experimental design software to analyze second-order response surfaces. We give examples of central composite and Box-Behnken designs that meet the conditions. We conclude with an example.

Original languageEnglish (US)
Pages (from-to)115-129
Number of pages15
JournalJournal of Quality Technology
Issue number2
StatePublished - Apr 2005


  • Central Composite Designs
  • Design of Experiments
  • Split-Plot Experiments

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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