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研究生:郭怡君
論文名稱:SomeConcernedComponentsofTwo-FactorInteractionsinthe3^{n}Designs
論文名稱(外文):Some Concerned Components of Two-Factor Interactions in the 3^{n} Designs
指導教授:黃必祥黃必祥引用關係
學位類別:碩士
校院名稱:國立高雄師範大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:54
中文關鍵詞:部分因子設計複製點混合因子實驗D判別準則Ds判別準則
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假如實驗者可以合理地假設某些三因子或三個以上因子的交互作用可忽略不計,則主效應和二因子交互作用的資訊可能由全因子設計的部份中獲得.我們可能去結合兩個(或兩個以上)部分因子設計去組成一個較大的設計來估計我們所感興趣的主效應和二因子交互作用.
本篇論文中,我們討論一些3^n設計的建造方法,而這種設計是可以用來估計主效應和二因子交互作用中一些所關心的部分.

If the experimenter can reasonably assume that certain three-factor and higher interaction are negligible, then information on the main effects and two-factor interactions may be obtained by running only a fraction of the complete factorial experiment. It is possible to combine the runs of two ( or more ) fractional factorials to assemble sequentially a larger design to estimate the main effects and the two-factor interactions of interest.
In this article, we discuss some construction methods of
3^{n} designs which can estimate the main effects and some concerned components of two-factor interactions.

1. Introduction 1
2. The 3^{4} design with 18 runs 11
3. The 3^{3}*2 mixed design with 18 runs 26
4. The 3^{4} design with 16 runs 35
5. Examples 40
6. Summary 53
Reference 54

[1] Addelman, S. and Kempthorne, O. (1961)
{Some main-effect plans and orthogonal arrays of strength
two}
Annals of Mathematical Statistics 32, 1167-1176.
[2] Bose, R. C. and Bush, K. A. (1952)
{Orthogonal arrays of strength two and three}
Annals of Mathematical Statistics 23, 508-524.
[3] Dey, Aloke (1985 )
{Orthogonal Fractional Factorial Designs}
Wiley Eastern Limited, New Delhi, India.
[4] Franklin, M. F. (1985)
{Selecting contrasts and confounded effects in factorial
experiments}
Technometrics 27, 165-172.
[5] Liau, P. H.(1998)
{Combining 3^{3} and 3^{4} Fractional Factorial Designs}.
JCSA Vol.36, No.4, 377-398.
[6] Margolin, B. H. (1969)
{Orthogonal main-effect plans permitting estimation of all
two-factor interactions for the factorial series of
designs}.
Technometrics 11, 747-762.
[7] Montgomery, D. C. (1999)
{Design and analysis of experiments}.
5th edition. Wiley, New York.
[8] Wang, J. C. and Wu, C. F. J. (1995 )
{A Hidden Projection Property of Plackett-Burman and
Related Designs}.
Statistica Sinica 5, 235-250.

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