Improved Split-Plot and Multistratum Designs
Improved Split-Plot and Multistratum Designs
复制标题
改进的裂区和多层设计
作者：
L. Trinca;S. Gilmour
许多工业实验涉及一些因素，其水平比其他因素更难确定。处理这些问题的最佳方法是仔细规划实验，将其作为一个分裂图，或者更一般地说是一个多层设计。自2001年以来，文献中提出了几种不同的方法来构建分裂图型响应面设计，这使得实验者可以通过使用比经典平衡设计更有效的设计来更好地利用他们的资源。其中一种方法，逐层策略已被证明产生的设计效率低于局部d最优设计。本文给出了一种改进的逐层算法，虽然该算法的计算量比旧算法大，但它更好地利用了该方法的优点，即它可以用于任何结构，并且不依赖于方差分量的先验估计。结果表明，这几乎与局部最优设计在其自身标准方面一样好，并且在一系列标准中更加稳健。本文的补充材料可在网上获得。
Many industrial experiments involve some factors whose levels are harder to set than others. The best way to deal with these is to plan the experiment carefully as a split-plot, or more generally a multistratum, design. Several different approaches for constructing split-plot type response surface designs have been proposed in the literature since 2001, which has allowed experimenters to make better use of their resources by using more efficient designs than the classical balanced ones. One of these approaches, the stratum-by-stratum strategy has been shown to produce designs that are less efficient than locally D-optimal designs. An improved stratum-by-stratum algorithm is given, which, though more computationally intensive than the old one, makes better use of the advantages of this approach, that is, it can be used for any structure and does not depend on prior estimates of the variance components. This is shown to be almost as good as the locally optimal designs in terms of their own criteria and more robust across a range of criteria. Supplementary materials for this article are available online.