Space-Filling Designs for Robustness Experiments

To identify the robust settings of the control factors, it is very important to understand how they interact with the noise factors. In this article, we propose space-filling designs for computer experiments that are more capable of accurately estimating the control-by-noise interactions. Moreover, the existing space-filling designs focus on uniformly distributing the points in the design space, which are not suitable for noise factors because they usually follow nonuniform distributions such as normal distribution. This would suggest placing more points in the regions with high probability mass. However, noise factors also tend to have a smooth relationship with the response and therefore, placing more points toward the tails of the distribution is also useful for accurately estimating the relationship. These two opposing effects make the experimental design methodology a challenging problem. We propose optimal and computationally efficient solutions to this problem and demonstrate their advantages using simulated examples and a real industry example involving a manufacturing packing line. Supplementary materials for the article are available online.

为确定控制因子的稳健设置，明晰其与噪声因子的交互作用至关重要。本文针对计算机实验提出空间填充设计（space-filling designs），该类设计可更精准地估计控制因子-噪声因子交互作用（control-by-noise interactions）。现有空间填充设计多致力于在设计空间内实现实验点的均匀分布，但此类设计并不适用于噪声因子——后者通常服从正态分布（normal distribution）等非均匀分布（nonuniform distributions），这意味着需在概率质量较高的区域布设更多实验点。然而，噪声因子与响应变量间往往存在平滑关联，因此在分布尾部区域布设更多实验点，也有助于精准估计二者的关联关系。这两种相反的效应使得实验设计方法成为一项极具挑战性的课题。针对该问题，本文提出了最优且计算高效的解决方案，并通过仿真示例与一则涉及制造业包装生产线的真实工业案例验证了所提方法的优势。本文补充材料可在线获取。