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Construction of D-optimal saturated designs for main effects and F1-second-order interactions in the presence of a free factor

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  • Francois K. Domagni
  • Yujia Zhang
  • A. S. Hedayat

Abstract

The allocation of resources in a $ 2^k $ 2k-factorial experiment is crucial when the experimental resources are limited. In practice, when resources are limited, it is common for investigators to use all the information at their disposal to reduce the amount of resources needed for an experiment without trading the accuracy of the experiment. Suppose we have k + 1 factors and the investigator knows one of the factors (we call this factor an extra factor throughout the paper) does not interact with any of the remaining k factors. Furthermore, the investigator believes among the remaining k factors, one factor potentially interacts with the rest of the k−1 factors. In this paper, we show how a D-optimal saturated design can be constructed for this problem with the minimum number of runs. In the process, we show the investigator can even forgo the presence of the extra factor in certain runs without compromising the D-optimality of the saturated design.

Suggested Citation

  • Francois K. Domagni & Yujia Zhang & A. S. Hedayat, 2025. "Construction of D-optimal saturated designs for main effects and F1-second-order interactions in the presence of a free factor," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 9(3), pages 315-330, July.
    • Handle: RePEc:taf:tstfxx:v:9:y:2025:i:3:p:315-330
    DOI: 10.1080/24754269.2025.2537504
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