Abstract Response surface designs (RSDs) are a core component of the response surface methodology, which is widely used in the context of product and process optimization. In this contribution, we consider three-level RSDs, which can be viewed as matrices with entries equal to . Each column of an RSD corresponds to a factor and each row to an experimental test. We define a new family of orthogonal RSDs, for which there is no aliasing between the main effects and the second-order effects (two-factor interactions and quadratic effects). Using integer programming techniques, we construct a database of 55,531 such RSDs for 3–7 factors. We name these designs orthogonal minimally aliased RSDs (or OMARS designs). Each design in the catalog is extensively characterized in terms of efficiency, power, fourth-order correlations, fraction of design space plots, projection capabilities, etc. We identify interesting designs and investigate trade-offs between different quality criteria. Finally, we present a multiattribute decision algorithm to select designs from the catalog. An important result of our study is that we discovered some novel and interesting designs that challenge standard RSDs.

中文翻译：

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正交最小混叠响应面设计的枚举和多标准选择

摘要 响应面设计 (RSD) 是响应面方法的核心组成部分，广泛用于产品和过程优化的背景下。在这篇文章中，我们考虑了三级 RSD，可以将其视为条目等于 的矩阵。RSD 的每一列对应一个因子，每一行对应一个实验检验。我们定义了一个新的正交 RSD 系列，其中主效应和二阶效应（双因子相互作用和二次效应）之间没有混叠。我们使用整数规划技术构建了一个包含 55,531 个此类 RSD 的数据库，其中包含 3-7 个因子。我们将这些设计命名为正交最小混叠 RSD（或 OMARS 设计）。目录中的每个设计都在效率、功率、四阶相关性、部分设计空间图、投影能力等。我们确定有趣的设计并研究不同质量标准之间的权衡。最后，我们提出了一种多属性决策算法来从目录中选择设计。我们研究的一个重要结果是我们发现了一些挑战标准 RSD 的新颖有趣的设计。