Abstract We introduce a modification to the coordinate-exchange algorithm for generating optimal experimental designs that incorporates off-face axial value runs similar to a central composite design (CCD). This improvement addresses a weakness of current optimal designs relative to classical designs: the superior properties of CCDs with off-face axial values relative to equal-sized optimal designs that are constrained to the cuboidal experimental design region. CCDs tend to have significantly less collinearity among quadratic effects, which results in higher power for quadratic terms, better D-efficiency, and lower average prediction variance (i.e., I-optimality). Optimal designs offer greater flexibility in design size, model specification, and the ability to incorporate categorical factors. By incorporating axial values into an optimal design algorithm, the strengths of both approaches can be combined in a single design that generally outperforms both CCDs and current optimal designs.

中文翻译：

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具有轴向值的优化设计

摘要 我们对坐标交换算法进行了修改，以生成最佳实验设计，该算法结合了类似于中心复合设计 (CCD) 的面外轴向值运行。这种改进解决了当前优化设计相对于经典设计的弱点：相对于受限于立方体实验设计区域的等尺寸优化设计，具有离面轴向值的 CCD 具有优越的特性。CCD 的二次效应之间的共线性往往显着降低，这导致二次项的功率更高、D 效率更高、平均预测方差更低（即 I 最优性）。优化设计在设计尺寸、模型规格和合并分类因素的能力方面提供了更大的灵活性。