Abstract This paper introduces a new class of Hadamard matrix-based mixed-level foldover designs (MLFODs) and an algorithm which facilitates the construction of MLFODs. Our new MLFODs were constructed by converting some 2-level columns of a Hadamard matrix to 3-level ones. Like the 2-level foldover designs (FODs), each new MLFOD was constructed by a half fraction and its foldover. Our Hadamard-matrix based MLFODs are compared with the conference matrix-based FODs of Jones & Nachtsheim (2013) in terms of the D-efficiencies and the maximum of the absolute values of the correlation coefficients among the columns of the model matrix. Like the latter, our designs are also definitive in the sense that the estimates of all main effects are unbiased with respect to any active second order effects. In addition, they require fewer runs and can be used to study the presence of the second-order effects more efficiently. Examples illustrating the use of our new MLFODs are given.

中文翻译：

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使用 Hadamard 矩阵构建 D-Efficient 混合级折叠设计

摘要 本文介绍了一类新的基于 Hadamard 矩阵的混合级折叠设计 (MLFOD) 和一种有助于构建 MLFOD 的算法。我们的新 MLFOD 是通过将 Hadamard 矩阵的一些 2 级列转换为 3 级列来构建的。与 2 级折叠设计 (FOD) 一样，每个新的 MLFOD 都由一半部分及其折叠构成。我们的基于 Hadamard 矩阵的 MLFOD 与 Jones & Nachtsheim (2013) 的基于会议矩阵的 FOD 在 D 效率和模型矩阵列之间相关系数的绝对值的最大值方面进行了比较。与后者一样，我们的设计也是确定的，因为所有主效应的估计对于任何活跃的二阶效应都是无偏的。此外，它们需要较少的运行，可用于更有效地研究二阶效应的存在。给出了说明使用我们的新 MLFOD 的示例。