最小像差的一般理论及其应用
A general theory of minimum aberration and its applications
摘要：
最小像差是比较和评价部分析因设计的一个越来越流行的标准，现在很少有人会质疑它的重要性和实用性。在过去的十几年里，人们对最小像差及其各种扩展做了大量的工作。本文根据可靠的统计原理，提出了最小像差的一般理论。我们的理论提供了一个统一的框架，最小像差，并进一步扩展了现有的工作在该领域。更重要的是，该理论提供了一种系统的方法，使实验者能够推导出自己的像差标准。我们的一般理论也汇集了两个看似独立的研究领域：一个是最小像差设计，另一个是要求集的设计。为了便于设计施工，我们开发了一个互补的设计理论相当一般的一类像差准则。作为一个直接的应用程序，我们提出了一些建设的结果，这类标准的弱版本。
英文摘要：
Minimum aberration is an increasingly popular criterion for comparing and assessing fractional factorial designs, and few would question its importance and usefulness nowadays. In the past decade or so, a great deal of work has been done on minimum aberration and its various extensions. This paper develops a general theory of minimum aberration based on a sound statistical principle. Our theory provides a unified framework for minimum aberration and further extends the existing work in the area. More importantly, the theory offers a systematic method that enables experimenters to derive their own aberration criteria. Our general theory also brings together two seemingly separate research areas: one on minimum aberration designs and the other on designs with requirement sets. To facilitate the design construction, we develop a complementary design theory for quite a general class of aberration criteria. As an immediate application, we present some construction results on a weak version of this class of criteria.
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