Computer-Generated Minimal ( and Larger ) Response-Surface Designs : ( I ) The Sphere
Computer-Generated Minimal ( and Larger ) Response-Surface Designs : ( I ) The Sphere
复制标题
计算机生成的最小（和更大）响应面设计：(I) 球体
DOI：
--
复制
发表时间：
1991
期刊：
影响因子：
--
通讯作者：
N. Sloane
中科院分区：
文献类型：
--
作者：
R. H. Hardin;N. Sloane
描述了球体中计算机生成的设计，其对于完整的二次响应曲面设计具有最小（或更多）的运行次数。在 3 个因子的情况下，设计有 10 到 33 次试验；对于 4 个因子，运行 15 到 28 次；对于 5 个因子，运行 21 到 33 次；此处完整列出了其中一些设计；其他的可以从作者那里获得。通过最小化平均预测方差来构建设计。点的位置没有受到任何先验约束（例如中心复合结构）。程序本身决定了在中心进行的最佳运行次数。发现的最佳设计在中心重复运行，而其余的运行则在球体表面上分布良好的点处。平均预测方差有一个简单的下界；许多设计都达到了这个界限。
Computer-generated designs in the sphere are described which have the minimal (or larger) number of runs for a full quadratic response-surface design. In the case of 3 factors, the designs have 10 through 33 runs; for 4 factors, 15 through 28 runs; for 5 factors, 21 through 33 runs; etc. Some of these designs are listed here in full; the others can be obtained from the authors. The designs were constructed by minimizing the average prediction variance. No prior constraints — such as a central composite structure – are imposed on the locations of the points. The program itself determines the optimal number of runs to make at the center. The best designs found have repeated runs at the center and the remaining runs at points well spread out over the surface of the sphere. There is a simple lower bound on the average prediction variance; this bound is attained by many of the designs.