Abstract Row–column designs involve two crossed blocking factors. We propose three combinatorial criteria and a criterion based on D-efficiency to identify optimal row–column arrangements of fractional factorial two-level designs. We search for such arrangements in complete catalogs of 16-run and 24-run orthogonal arrays of strength 2 with two-level treatment factors and two multi-level blocking factors. One of the combinatorial criteria is a good surrogate for the efficiency-based criterion. For searching similar catalogs of strength-3 orthogonal arrays, we adapt the criteria and conduct a complete search for optimal row–column arrangements in catalogs with 64 and 72 runs.

中文翻译：

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规则和非规则部分因子两水平设计的行列排列

摘要 行列设计涉及两个交叉的分块因子。我们提出了三个组合标准和一个基于 D 效率的标准，以确定部分因子两水平设计的最佳行列排列。我们在强度为 2 的 16 次和 24 次正交阵列的完整目录中搜索此类安排，其中包含两级处理因子和两个多级阻塞因子。组合标准之一是基于效率的标准的良好替代品。为了搜索强度 3 正交阵列的类似目录，我们调整了标准，并在 64 和 72 次运行的目录中进行了最佳行列排列的完整搜索。