标题： 强大的折叠设计 显示英文标题

标题： Powerful Foldover Designs

摘要： 折叠技术用于筛选设计，众所周知可以保证主要效应估计量与两因子交互作用和二次效应之间没有混淆。它是许多流行的响应面设计的关键特性，包括中心复合设计、确定性筛选设计以及大多数正交、最小混淆的响应面设计。在本文中，我们表明折叠技术更为强大，因为它产生的方差估计量的自由度独立于模型选择。这些自由度被描述为纯误差或假因子自由度。提出了一种快速的设计构造算法，以最小化期望置信区间准则，从而最大化筛选主要效应的功效。还提出了一种增强的设计和分析方法，以避免估计方差时有太多自由度，并提高二阶模型的模型选择性能。模拟研究显示，当效应稀疏性和层次性成立时，我们的新设计至少和传统设计一样好，但当这些效应原则不成立时，表现要好得多。给出一个20次运行实验的真实数据例子，其中通过操纵八个工艺参数来优化乙烯浓度。 显示英文摘要

摘要： The foldover technique for screening designs is well known to guarantee zero aliasing of the main effect estimators with respect to two factor interactions and quadratic effects. It is a key feature of many popular response surface designs, including central composite designs, definitive screening designs, and most orthogonal, minimally-aliased response surface designs. In this paper, we show the foldover technique is even more powerful, because it produces degrees of freedom for a variance estimator that is independent of model selection. These degrees of freedom are characterized as either pure error or fake factor degrees of freedom. A fast design construction algorithm is presented that minimizes the expected confidence interval criterion to maximize the power of screening main effects. An augmented design and analysis method is also presented to avoid having too many degrees of freedom for estimating variance and to improve model selection performance for second order models. Simulation studies show our new designs are at least as good as traditional designs when effect sparsity and hierarchy hold, but do significantly better when these effect principles do not hold. A real data example is given for a 20-run experiment where optimization of ethylene concentration is performed by manipulating eight process parameters.