Abstract The central composite designs (CCDs [1]) and small composite designs (SCDs [2,3]) are designs for sequential experimentation for response surface optimization. The CCDs for fitting the second-order response surface require a 2-level factorial or a resolution V fraction at the first stage (screening stage). The SCDs developed for fitting the same model require many fewer runs at the first stage as they only require a resolution III* fraction. This paper introduces an algorithm which can augment a 2-level first-order design with additional 3-level runs to form a second-order design. This algorithm does not require the 2-level first-order design in stage I to be a resolution V or resolution III* fraction. These augmented runs are made up of circulant matrices. Since CCDs and SCDs are special cases of the designs constructed this way, we call the new designs generalized composite designs or GCDs. Like CCDs and SCDs, GCDs have orthogonal quadratic effects. GCDs can often be found with numbers of runs between those of SCDs and CCDs. This is useful because SCDs often have poorly estimated parameters and CCDs often require substantially more runs than required to fit a full quadratic model.

中文翻译：

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使用循环发生器构建具有正交二次效应的响应面设计

摘要 中心复合设计 (CCDs [1]) 和小型复合设计 (SCDs [2,3]) 是用于响应面优化的连续实验设计。用于拟合二阶响应面的 CCD 在第一阶段（筛选阶段）需要 2 级阶乘或分辨率 V 分数。为拟合相同模型而开发的 SCD 在第一阶段所需的运行次数要少得多，因为它们只需要分辨率 III* 级分。本文介绍了一种算法，该算法可以通过额外的 3 级运行来增强 2 级一阶设计以形成二阶设计。该算法不要求阶段 I 中的 2 级一阶设计是分辨率 V 或分辨率 III* 分数。这些增强运行由循环矩阵组成。由于 CCD 和 SCD 是以这种方式构建的设计的特例，我们将新设计称为广义复合设计或 GCD。与 CCD 和 SCD 一样，GCD 具有正交二次效应。GCD 的运行次数通常介于 SCD 和 CCD 之间。这很有用，因为 SCD 的参数估计值通常很差，而 CCD 通常需要比拟合完整二次模型所需的运行次数多得多。