Three‐Dimensional Quantile Plots and Dynamic Quantile Plots of the Prediction Variance for Response Surface Designs
Three‐Dimensional Quantile Plots and Dynamic Quantile Plots of the Prediction Variance for Response Surface Designs
复制标题
响应曲面设计的预测方差的三维分位数图和动态分位数图
DOI：
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发表时间：
2012
影响因子：
2.3
通讯作者：
Youngil Kim
中科院分区：
文献类型：
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作者：
Dae;C. Anderson‐Cook;Youngil Kim
历史上评估响应曲面设计的常见选择是使用字母最优性标准。 D、A、G 和 V 最优性等单数标准并不能完全反映相关设计的估计或预测方差特征。对于基于预测的评估，单数汇总的替代方案包括跨设计区域的预测方差的图形显示。建议使用方差分散图、设计空间分数图和分位数图来评估响应曲面设计的整体预测能力。分位数图使用百分位数。这些分位数图使用给定半径处的分布百分位数，而不仅仅是感兴趣区域内同心球上的平均值、最大和最小预测方差值。以前，用户必须选择多个半径值并绘制相应的分位数图来评估响应曲面设计的整体预测能力。用户指定的要检查的半径选择使得绘图有些主观。 Alternately, we propose to remove this subjectivity by using a three‐dimensional quantile plot.作为分位数图的另一个扩展，我们建议使用动态分位数图来动画分位数图，并使用它们来比较和评估响应曲面设计。版权所有 © 2011 约翰·威利父子有限公司
A historically common choice for evaluating response surface designs is to use alphabetic optimality criteria. Single‐number criteria such as D, A, G, and V optimality do not completely reflect the estimation or prediction variance characteristics of the designs in question. For prediction‐based assessment, alternatives to single‐number summaries include the graphical displays of the prediction variance across the design regions. Variance dispersion graphs, fraction of design space plots, and quantile plots have been suggested to evaluate the overall prediction capability of response surface designs. The quantile plots use the percentiles. These quantile plots use the percentiles of the distribution at a given radius instead of just the mean, maximum, and minimum prediction variance values on concentric spheres inside the region of the interest. Previously, the user had to select several values of radius and draw corresponding quantile plots to evaluate the overall prediction capability of response surface designs. The user‐specified choice of radii to examine makes the plot somewhat subjective. Alternately, we propose to remove this subjectivity by using a three‐dimensional quantile plot. As another extension of the quantile plots, we suggest dynamic quantile plots to animate the quantile plots and use them for comparing and evaluating response surface designs. Copyright © 2011 John Wiley & Sons, Ltd.