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Projection properties of three‐level screening designs

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  • Mohammed A. Alomair
  • Stelios D. Georgiou
  • Manohar Aggarwal

Abstract

Screening designs are important for finding the factors that have a major effect on industrial experiments. In regard to quantitative factors, certain experimenters prefer three‐level rather than two‐level factors because having three levels can provide some assessments for capturing curvature in the response. In a recent paper, Jones and Nachtsheim, Journal of Quality Technology43, 1–15, proposed a new class of designs called definitive screening designs. Definitive screening designs have more favourable properties than classical screening designs. In this paper, we study the projection properties of three‐level screening designs. The comparison is based on several criteria such as D‐efficiency, G‐efficiency, A‐efficiency and average of variance over a range of models that include main effects, interaction and quadratic terms. New designs are generated as projections of the full designs into a smaller factor dimensional space. The best projections and their properties are presented in a tabular form.

Suggested Citation

  • Mohammed A. Alomair & Stelios D. Georgiou & Manohar Aggarwal, 2020. "Projection properties of three‐level screening designs," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(4), pages 407-425, December.
    • Handle: RePEc:bla:anzsta:v:62:y:2020:i:4:p:407-425
    DOI: 10.1111/anzs.12306
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    References listed on IDEAS

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    1. Lin, Dennis K. J. & Draper, Norman R., 1993. "Generating alias relationships for two-level Plackett and Burman designs," Computational Statistics & Data Analysis, Elsevier, vol. 15(2), pages 147-157, February.
    2. Yong-Dao Zhou & Hongquan Xu, 2017. "Composite Designs Based on Orthogonal Arrays and Definitive Screening Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1675-1683, October.
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