三水平设计β-字长型性质的进一步分析-further analysis of β - word length property of three-level design.docxVIP

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三水平设计β-字长型性质的进一步分析-further analysis of β - word length property of three-level design.docx

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三水平设计β-字长型性质的进一步分析-further analysis of β - word length property of three-level design

Further study on properties of β-wordlength pattern for three-level designsAbstractMinimum aberration criterion is an important concept in Experimental Design and is often adopted to compare di?erent fractional factorial designs with qualitative factors. However, when a design contains quantitative factors, a polynomial model is often established to conduct statistical inference. Two designs that are combina- torially equivalent to each other may have di?erent statistical inference ability under the polynomial model. However, these two designs cannot be distinguished by mini- mum aberration criterion. Under this consideration, Cheng and Ye (2004) proposed the concept of β-wordlength pattern, which can be regarded as a generalized version of the minimum aberration criterion. They pointed out that a good design should sequentially minimize its β1, β2,...,βK .The β-wordlength pattern is de?ned using characteristic polynomial, which makes its calculation much more complicated. Tang and Xu (2014) provided some interesting properties of the β-wordlength pattern for three-level regular designs, but their method and result cannot be directly applied for non-regular designs. In this article, we will introduce a parameter m, and provide a simple condition, which can be used to determine whether the β3 of the design is 0. So, we can compare all permuted designs having β3 = 0, and ?nally select the best one. Keywords: Orthogonal array; β-wordlength pattern; linearly permutationWritten by Feiyi Xu Supervised by Prof. Yu Tang目录第一章绪论 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1§1.1课题研究的背景和发展概况 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1§1.2基本概念和常用符号 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3第二章预备性条件 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .