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Confounding of Location and Dispersion Effects in Unreplicated Fractional Factorials

Summary: [This abstract is based on the authors' abstract. A longer abstract is available on the journal's website]

Standard industry procedure when studying both location and dispersion effects in unreplicated fractional factorial designs is to identify location effects using ordinary least squares analysis, fit a model, and then identify dispersion effects by analyzing the residuals. The authors demonstrate that if the model does not include all active location effects, null dispersion effects may be mistakenly identified as active. An exact relationship between location and dispersion effects is derived, and it is then shown that without information in addition to the unreplicated fractional factorial, it cannot be determined whether a dispersion effect or two location effects are active.

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  • Topics: Design of Experiments
  • Keywords: Scale parameter,Fractional factorial design,Factorial experiments,Dispersion,Replication
  • Author: McGrath, Richard N.; Lin, Dennis K.J.
  • Journal: Journal of Quality Technology