(3.235.25.169) 您好!臺灣時間:2021/04/18 04:21
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果

詳目顯示:::

我願授權國圖
: 
twitterline
研究生:楊尚佳
研究生(外文):Shang-Chia Yang
論文名稱:在2^(k-p)分裂實驗中做半摺疊設計
論文名稱(外文):Semifolding 2^(k-p) Design in the Split-Plot Experiments
指導教授:黃必祥黃必祥引用關係
指導教授(外文):Pi-Hsiang Huang
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:2012
畢業學年度:100
語文別:英文
論文頁數:52
中文關鍵詞:半摺疊分裂設計
外文關鍵詞:SemifoldingSplit-Plot
相關次數:
  • 被引用被引用:0
  • 點閱點閱:123
  • 評分評分:系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔
  • 下載下載:6
  • 收藏至我的研究室書目清單書目收藏:0
一般常見的實驗設計中,我們廣泛的使用部分因子分裂設計(fractional factorial split-plot designs, FFSP designs)。我們期望透過增加一部分的實驗值去估計更多我們感興趣的主效應及二因子交互作用。其中有一種方法摺疊技巧(the technique of fold-over)是在原本的設計上再加入與原實驗值一樣多新的實驗值讓我們可以估計更多我們感興趣的主效應及二因子交互作用,但是時間及成本
將會增加太多,我們希望有更節省成本的方法。John (2000)介紹了半摺疊技巧(the technique of semifolding),只要增加原實驗值的一半數量的新實驗值就可以達到與使用摺疊技巧後一樣的效果。Kowalski(2002)曾提出一些24個實驗值 分裂設計利用在每一個whole-plot下各增加兩個新的subplot處理組合,但是他舉的例子只有限制在whole-plot與subplot的因子只有2,3 and 4個的狀況下。在這篇論文中我們將所有16個實驗值分裂設計利用半摺疊技巧構造成24個實驗值分裂設計,我們將找出可以估計最多主效應
及二因子交互作用的24個實驗值設計。
在本文中的第一節,我們介紹如何使用半摺疊技巧(the technique of semifolding)。在第二節中,我們將所有16個實驗值設計利用半摺疊技巧構造成可以估計最多主效應及二因子交互作用的分裂設計。在第三節中,我們
提供了一些相關的例子。在附錄裡,我們製作表格提供較佳的24個實驗值分裂設計,以最估計最多主效應及二因子交互作用為標準。
There are many situations which need performing of split-plot designs. Recently the fractional factorial split-plot designs are studied by many researchers such as Box and Jones (1992), Haung, Chen, and Voelkel (1998), Bingham and Sitter (1999), Bisgaard (2000), Yang, Li, Liu, and Zhang (2006), and Jones (2009). Adding another fraction to an initial factorial design may be necessary in order to break the aliasing in the initial experiment and to increase the precision of factorial effects estimates. Repeating an experiment of the same size can be costly and time consuming. John (2000) proposes the technique of semifolding which we make only half of the runs required for a complete fold over to break alias chains that estimate more main effects and two-factor interactions. Kowalski(2002) introduces 24-run designs using confounding to obtain two extra subplot treatments for each whole-plot treatment. But he considers three cases that use combinations of two, three and four whole-plot and sub-plot factors. We extend the semi-folding technique to break the alias chains of split-plot experiments in all 16-run designs. In the fractional factorial split-plot designs, the two-factor interactions between whole-plot and sub-plot factors are as important as the whole-plot main effects and sub-plot main effects. In this article, we discuss the 2^{6-2}, 2^{7-3}, 2^{8-4}, 2^{9-5} and 2^{10-6} designs which could estimate the most main effects and two-factor interactions between whole-plot and sub-plot factors in Section 2; some examples of 2^{6-2} designs and their combined designs are shown in Section 3; conclusion is given in Section 4 .
1. Introduction............................1
2. The semi-folding technique............. 9
2.1 2^(6-2)...............................12
2.2 2^(7−3)...............................23
2.3 2^(8−4)...............................27
2.4 2^(9−5)...............................30
2.5 2^(10−6)..............................34
3. Examples...............................37
4. Conclusion.............................43
Appendix..................................44
References................................47
Almimi, Kulahci, Montgomery. (2008). “Follow-Up Designs to Resolve Confounding in Split-Plot Experiment,”Journal of Quality Technique, 40,2, 154-166.
Bingham, D. and Sitter, R.R. (1999). “Minimum-Aberration Two-level Fractional Factorial Split-Plot Designs,” Technometrics, 41,1, 62-70.
Bingham, D. and Sitter, R.R. (2001). “Design Issues In Fractional Factorial Split-Plot Experiments,” Journal of Quality Technology, 33,1, 2-15.
Bingham, D.R., Schoen, E.D., and Sitter, R.R. (2004). “Designing fractional factorial split-plot experiments with few whole-plot factors,” Royal Statistical Society, 53, 2, 325-339.
Bisgaard, S. (2000). “The Design and Analysis of 2k−p× 2q−rSplit Plot Experiments,” Journal of Quality Technology, 32, 1, 39-56.
Box, G.E.P. and Jones, S. (1992). “Split-Plot Designs for Robust Product Experimentation,” Journal of Applied Statistics, 19, 1, 3-26.
Chen, J., Sun, D.X., and Wu,C.F.J. (1993). “A Catalogue of Two-level and Three-level Fractional Factorial Designs with Small Runs,” International Statistical Review, 61, 1. 131-145.
Huang, P., Chen, D., and Voelkel, J.O. (1998). “Minimum-Aberration Two-Level Split-Plot Designs,” Technometrics, 40, 4, 314-326.
John, P. W. M. (1962).“Three quarter replicates of 2ndesigns,”Biomeirics, 18, 172-184.
John, P. W. M. (2000).“Breaking alias chains in fractional factorials,” Communications in Statistics-Theory and Methods 29, pp.2143-2155.
Jones, B. (2009). “Split-Plot Designs: What, Why, and How,” Journal of Quality Technology, 41, 4, 340-361.
Kowalskl, S. M. (2002).“24 Run Split-Plot Experiments for Robust Parameter Design,”Journal of Quality Technology , 34, pp.399-410
Montgomery, D. C. (2009). Design and Analysis of Experiments,7thed., John Wiley &; Sons, New York, NY.
Wang, P. C., Carl Lee (2005).“Strategies for semifolding Fractional Designs,”Quality and Reliability Engineering International 2006, 22. 265-273.
Wu, C.F.J. and Hamada, M. (2000). Experiments— Planning,Analysis, and Parameter Design Optimization, JohnWiley &; Sons, New York, NY.
Yang, J.F., Li, P.F., Liu, M.Q., and Zhang, R.C. (2006).“2^(n1+n2)−(k1+k2)Fractional Factorial Split-Plot DesignsContaining Clear Effects,” Journal of Statistical Planning andInference, 136, 4450-4458

連結至畢業學校之論文網頁點我開啟連結
註: 此連結為研究生畢業學校所提供,不一定有電子全文可供下載,若連結有誤,請點選上方之〝勘誤回報〞功能,我們會盡快修正,謝謝!
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top
無相關論文
 
系統版面圖檔 系統版面圖檔