Replication of Axial Points in Two-Factor Doehlert and Central Composite Designs with a Single Centre Point
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Abstract
This study investigated the effect of replicating axial points in two-factor second-order experimental designs with a single centre point. The designs considered include the Doehlert design (DD), Inscribed Central Composite Design (ICCD), and Face-Centred Central Composite Design (FCCCD), all configured with a common radial distance of 1.0. Among these, the DD and ICCD exhibit spherical geometry, while the FCCCD does not. The objective was to evaluate how replication of axial points influences the statistical properties of these designs compared to their un-replicated counterparts. To assess the impact, various design evaluation metrics were employed, including D-optimality, T-optimality, prediction variance, and G-efficiency. The results showed that the un-replicated FCCCD exhibited both D- and T-optimality. The un-replicated Doehlert and ICCD designs were only D-optimal, whereas their replicated versions were T-optimal. This indicates a consistent shift from D-optimality to T-optimality upon replication of the axial points across all designs. Additionally, the findings suggested that the Doehlert design shares more structural and statistical similarities with the ICCD than with the FCCCD. Based on these results, the study recommended replicating axial distance of Doehlert and Central Composite designs in order to obtain T-optimal designs.
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References
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