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| 研究生： |
張富凱 Chang, Fu-Kai |
|---|---|
| 論文名稱： |
分散效應存在下位置主效應之最適部份因子設計 Optimal Two-Level Fractional Factorial Designs for Location Main Effects with Dispersion Effects |
| 指導教授： |
丁兆平
Ting, Chao-Ping |
| 學位類別： |
碩士
Master |
| 系所名稱： |
商學院 - 統計學系 Department of Statistics |
| 論文出版年： | 2006 |
| 畢業學年度： | 94 |
| 語文別： | 英文 |
| 論文頁數： | 43 |
| 中文關鍵詞： | 同名關係 、分散效應 、位置效應 |
| 外文關鍵詞： | defining relation, dispersion effect, location effect, defining contrast |
| 相關次數： | 點閱：191 下載：46 |
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In two-level fractional factorial designs, homogeneous variance is a commonly made assumption in analysis of variance. When the variance of the response variable changes when a factor changes from one level to another, we called the factor dispersion factor. Formerly, many researches have discussed about how to define the dispersion effects, but the problem of finding optimal designs when dispersion effects present is relatively unexplored. However, a good design not only save the experiment cost but also let the estimation more efficiency.
In this research, we focus on finding optimal designs for the estimation of location main effects when there are one or two dispersion factors, in the class of regular unreplicated two-level fractional factorial designs of resolution Ⅲ and higher. We show that by an appropriate choice of the defining contrasts, A-optimal and D-optimal designs can be identified. Efficiencies of an arbitrary design are also investigated.
1. Introduction 1
2. Preliminaries 4
3. Regular Two-Level Fractional Factorial Design with One Dispersion Factor 8
3.1.Optimal Two-Level fractional factorial design with one dispersion factor 9
4. Regular Two-Level Fractional Factorial Design with Two Dispersion Factors 14
4.1. Optimal Two-Level fractional factorial designs with two dispersion factors 17
4.2. Efficient Resolution Ⅳ Designs 18
4.3. Efficient Resolution Ⅲ Designs 20
5. Conclusion and Future Research 33
5.1. Conclusion 33
5.2. Future research 34
References 36
Appendix
Derivation of information matrix with one dispersion effect 38
Derivation of information matrix with two dispersion effect 39
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