A New Design Criterion for Robust Parameter Experiments
A New Design Criterion for Robust Parameter Experiments
复制标题
鲁棒参数实验的新设计准则
DOI：
10.1080/00224065.2007.11917693
复制
发表时间：
2007
影响因子：
2.5
通讯作者：
E. Viles
中科院分区：
文献类型：
--
作者：
Enrique del Castillo;M. J. Álvarez;Laura Ilzarbe;E. Viles
实验中不同的噪声因素使我们能够找到针对这种变化的稳健条件。需要仔细选择噪声因子的水平。太宽的水平可能不可行或成本太高，如果太窄，则可能无法为预测和控制目的提供良好的模型。我们为鲁棒参数设计中使用的设计提出了一种噪声因子分离（NFS）标准，其中如果一种设计为拟合模型的噪声部分提供相同的预期均方误差，但对于未编码单元中较小范围的噪声因子，则该设计优于另一种设计。我们评估了几种实验设计，这些设计可用于拟合可控因素的二次响应模型，并且还包含噪声主效应和噪声×控制相互作用。它显示了新标准如何与斜率的方差离散图相关，并且可以与这些图结合使用来评估给定的实验设计。新标准被纳入用于寻找新的三级设计的优化公式中，该公式还包括传统的设计标准，例如 D 效率。开发了遗传算法来解决此类问题。它显示了新设计在设计尺寸、噪声因子分离以及均值和斜率的方差分散方面与复合混合分辨率设计相比如何具有竞争力。
Varying noise factors in an experiment allows us to find robust conditions against such variation. The levels of the noise factors need to be selected carefully. Levels that are too wide may be infeasible or too costly, and if too narrow they may not provide a good model for prediction and control purposes. We propose a noise-factor separation (NFS) criterion for designs used in robust parameter design, in which a design is preferred to another if it provides the same expected mean square error for the noise part of the fitted model but for a smaller range of the noise factors in uncoded units. We evaluate several experimental designs that can be used to fit a response model that is quadratic in the controllable factors and also contains noise main effects and noise × control interactions. It is shown how the new criterion is related to variance dispersion graphs for the slope and may be used in conjunction with these graphs to assess a given experimental design. The new criterion is incorporated into an optimization formulation used to find new three-level designs that also includes traditional design criteria, such a D-efficiency. A Genetic algorithm was developed to solve such formulation. It is shown how the new designs are competitive in terms of design size, noise-factor separation, and variance dispersion for the mean and slope with respect to composite mixed resolution designs.