Nonregular fractional factorial designs can be a preferable alternative to regular Resolution IV designs, because they avoid complete confounding of two-factor interactions. Consequently, nonregular designs can estimate and identify a few active two-factor interactions. However, due to the sometimes-complex alias structure of nonregular designs, standard factor screening strategies can fail to identify all active effects. Previous research by these authors has developed an alias-informed-model-selection (AIMS) technique (Metcalfe et al. Qual Reliab Eng Int 37(7):3055–3065;2021). We have shown how the AIMS technique can be applied to six-, seven-, and eight-factor nonregular designs. We have compared AIMS to three other standard analysis methods for nonregular designs, stepwise regression, the lasso, and the Dantzig selector. AIMS consistently outperforms these methods in identifying the set of active factors. This paper provides a method for augmenting no-confounding designs based on model spaces and maximum average D-efficiency criterion. Several augmented design strategies are provided for different situations. A simulation study with the augmented designs shows significant performance improvement for augmenting the 16-run designs with 4 additional runs. We recommend this strategy if time and experimental resources permit.

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Augmentation of No-Confounding 16-Run Fractional Factorial Designs

  • Carly E. Metcalfe,
  • Douglas C. Montgomery,
  • Bradley Jones

摘要

Nonregular fractional factorial designs can be a preferable alternative to regular Resolution IV designs, because they avoid complete confounding of two-factor interactions. Consequently, nonregular designs can estimate and identify a few active two-factor interactions. However, due to the sometimes-complex alias structure of nonregular designs, standard factor screening strategies can fail to identify all active effects. Previous research by these authors has developed an alias-informed-model-selection (AIMS) technique (Metcalfe et al. Qual Reliab Eng Int 37(7):3055–3065;2021). We have shown how the AIMS technique can be applied to six-, seven-, and eight-factor nonregular designs. We have compared AIMS to three other standard analysis methods for nonregular designs, stepwise regression, the lasso, and the Dantzig selector. AIMS consistently outperforms these methods in identifying the set of active factors. This paper provides a method for augmenting no-confounding designs based on model spaces and maximum average D-efficiency criterion. Several augmented design strategies are provided for different situations. A simulation study with the augmented designs shows significant performance improvement for augmenting the 16-run designs with 4 additional runs. We recommend this strategy if time and experimental resources permit.