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    高師機構典藏 NKNUIR > 理學院 > 數學系 > 博碩士論文 >  Item 987654321/16748
    Please use this identifier to cite or link to this item: http://ir.nknu.edu.tw/ir/handle/987654321/16748

    題名: 2k-p設計的一些特殊性質
    Some special properties of the 2k-p designs
    Authors: 黃棨堯
    Chi-Yao Huang
    貢獻者: 黃必祥
    Pi-Hsiang Huang
    Keywords: 摺疊設計
    Date: 2002-07-31
    Issue Date: 2011-10-20 09:33:20 (UTC+8)
    Abstract:   這篇論文包含了兩部分。在第一部分,對於後續設計,一個普遍使用的方法是採用摺疊設計。對於16和32個觀察值的 設計,Li 和 Lin(2003)構造了其最佳摺疊設計。一個 2^{k-p} 設計被稱為”組合後最佳設計”是為在原先的設計與其最佳摺疊設計經過組合後,會產生一個 2^{k-p+1} 設計且其字串長度組型要最小。一個 2^{k-p} 設計被稱為”強組合後最佳設計”是為在原先的設計與其最佳摺疊設計經過組合後,會產生一個 2^{k-p+1} MA 設計。大部分的”組合後最佳設計”都是”強組合後最佳設計”,在Li 和 Lin 的論文中,唯一一個”組合後最佳設計”不是”強組合後最佳設計”是 2^{10-6} 設計。我們將研究這個課題並且探討在什麼情況之下”強組合後最佳設計”會存在。
      在第二部分,直交表常常在實驗設計被使用。我們將解釋其直交多項式的對比係數的由來,並且比較proposed method ( Hsieh and Liou (2001) )和傳統的方法在資料分析上的差異。最後,我們將把 L_27(3^13) 轉換成 3^k*2^{1+m} 設計,這會使的我們在直交表的運用上有更大的彈性。
      This article is divided into two parts. In the first part, a coimnbniy used follow-up strategy is to apply a foldover plan. The optilrial foldover designs of 16 and 32 runs were constructed by Li and Lin (2003) for practical use (under the minimal aberration criterion). A 2<sup>k-p</sup> design is called a combined-optimal design if the resulting optimal ctombined design has the mi-ninniTin aberration among all combined optimal designs. And a 2<sup>k-p</sup> strong conibined-optiinal design is the one such that the combined 2<sup>k-p+1</sup> design consisting of the original design and its optilfaal foldover is the minimum aberration (MA) design (by Li and Lin (2003)). Most combined-optimal 2<sup>k-p</sup> designs are strong combined-optimal designs. The only combined-optimal design that is not a strong combined-optimal design is 2<sup>10-6</sup> design in the paper of Li and Lin (2003). We research this topic and tell the reapers under what coflditions strong combined-optimal designs exist.
      In the second part, orthogonal arrays are often used in design of experiments. We explain how the contrast coefficients of the orthogonal polynomial come from, and compare the proposed method ( Hsieh and Liou (2001) ) with the traditional method in data analysis. Finally, we use the condition of proportional frequencies to transform a L<sub>27</sub>(3<sup>13</sup>) to a 3<sup>k</sup>x2<sub>1+m</sub>(k+m=12) orthogonal main-effect plans.
    Appears in Collections:[數學系] 博碩士論文
    [數學系] 黃必祥

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