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Optimal row-column designs

Author

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  • Zheng Zhou
  • Yongdao Zhou

Abstract

SummaryRow-column designs have been widely used in experiments involving double confounding. Among them, one that provides unconfounded estimation of all main effects and as many two-factor interactions as possible is preferred, and is called optimal. Most current work focuses on the construction of two-level row-column designs, while the corresponding optimality theory has been largely ignored. Moreover, most constructed designs contain at least one replicate of a full factorial design, which is not flexible as the number of factors increases. In this study, a theoretical framework is built up to evaluate the optimality of row-column designs with prime level. A method for constructing optimal row-column designs with prime level is proposed. Subsequently, optimal full factorial three-level row-column designs are constructed for any parameter combination. Optimal fractional factorial two-level and three-level row-column designs are also constructed for cost saving.

Suggested Citation

  • Zheng Zhou & Yongdao Zhou, 2023. "Optimal row-column designs," Biometrika, Biometrika Trust, vol. 110(2), pages 537-549.
    • Handle: RePEc:oup:biomet:v:110:y:2023:i:2:p:537-549.
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    File URL: http://hdl.handle.net/10.1093/biomet/asac046
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