Confounding of location and dispersion effects in unreplicated fractional factorials

Richard N. McGrath, Dennis K.J. Lin

Research output: Contribution to journalArticle

31 Scopus citations

Abstract

When studying both location and dispersion effects in unreplicated fractional factorial designs, a "standard" procedure is to identify location effects using ordinary least squares analysis, fit a model, and then identify dispersion effects by analyzing the residuals. In this paper, we show that if the model in the above procedure does not include all active location effects, then null dispersion effects may be mistakenly identified as active. We derive an exact relationship between location and dispersion effects, and we show that without information in addition to the unreplicated fractional factorial (such as replication) we can not determine whether a dispersion effect or two location effects are active.

Original languageEnglish (US)
Pages (from-to)129-139
Number of pages11
JournalJournal of Quality Technology
Volume33
Issue number2
StatePublished - Dec 1 2001

All Science Journal Classification (ASJC) codes

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

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