Abstract

Two fractional factorial designs are called isomorphic if one can be obtained from the other by relabeling the factors, reordering the runs and switching the levels of factors. Given a set of all orthogonal designs (ODs) with n runs, q levels and s factors, it may have several non-isomorphic subclasses. Once a new OD with this design size is generated, it is interesting to know which subclass it belongs to. In this paper, we review several existing methods, which can classify newly generated ODs to the correct non-isomorphic subclass. We also propose two new non-isomorphic detection methods. They can be utilized for the design classification purpose and take some advantages over the existing methods in terms of computation efficiency and classification capability.

摘要

如果可以通过重新标记因子、重新排序运行和切换因子水平从另一个获得一个，则两个部分因子设计被称为同构。给定一组具有n次运行、q水平和s的所有正交设计 (OD)因素，它可能有几个非同构的子类。一旦生成具有此设计尺寸的新 OD，了解它属于哪个子类就很有趣了。在本文中，我们回顾了几种现有的方法，这些方法可以将新生成的 OD 分类到正确的非同构子类。我们还提出了两种新的非同构检测方法。它们可用于设计分类目的，并在计算效率和分类能力方面优于现有方法。