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| 研究生： |
朱正中 Chu, Cheng-Chung |
|---|---|
| 論文名稱： |
Construction of Minimal Partially Replicated Orthogonal Main-Effect Plans with 3 Factors |
| 指導教授： |
郎冰瑩
Lin, Bin-Ying |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2000 |
| 畢業學年度： | 88 |
| 語文別： | 英文 |
| 論文頁數： | 36 |
| 中文關鍵詞： | 正交主效應計畫 |
| 外文關鍵詞： | Orthogonal main-effect plans, Replicated runs, Factorial plans, Latin square, Mutually orthogonal Latin squares |
| 相關次數： | 點閱：83 下載：47 |
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正交主效應計畫(Orthogonal main-effect plans)因可無相關地估計主效應，故常被應用於一般工業上作為篩選因子之用。然而，實驗通常費時耗財。因此，如何設計一個較經濟且有效的計劃是很重要的。回顧過去相關的研究，Jacroux (1992)提供了最小正交主效應計劃的充份條件及正交主效應計畫之最少實驗次數表(Jacroux 1992)，張純明(1998)針對此表提出修正與補充。在此，我們再次的補足此表。
正交主效應計畫中，如有重複實驗點，則純誤差可被估計，且據此檢定模型之適合度。Jacroux (1993)及張純明(1998)皆曾提出具最多部份重複之正交主效應計畫(Partially replicated orthogonal main-effect plans)。在此，我們討論所有三因子部份重複正交主效應計畫中，可能重複之最大次數，且具體提出建構此最大部份重複之最小正交主效應計畫之方法。
Orthogonal main-effect plans (OMEP's), being able to estimate the main effects without correlation, are often employed in industrial situations for screening purpose. But experiments are expensive and time consuming. When an economical and efficient design is desired, a minimal orthogonal main-effect plans is a good choice. Jacroux (1992) derived a sufficient condition for OEMP's to have minimal number of runs and provided a table of minimal OMEP run numbers. Chang (1998) corrected and supplemented the table. In this paper, we try to improve the table to its perfection.
A minimal OMEP with replicated runs is appreciated even more since then the pure error can be estimated and the goodness-of-fit of the model can be tested. Jacroux (1993) and Chang (1998) gave some partially replicated orthogonal main-effect plans (PROMEP's) with maximal number of replicated points. Here, we discuss minimal PROMEP's with 3 factors in detail. Methods of constructing minimal PROMEP's with replicated runs are provided, and the number of replicated runs are maximal for most cases.
封面頁
證明書
論文摘要
目錄
表目錄
Chapter 1 Introduction
Chapter 2 Minimal Orthogonal Main-Effect Plans
Chapter 3 Partially Replicated OMEP's with 3 Factors
3.1 The Case s1=ms2
3.1.1 s1=s1 and s2=s2
3.1.2 s1=s1 and s2＞s2
3.1.3 s1＞s1 and s2=s2
3.1.4 s1＞s1 and s2＞s2
3.2 The Case s1≠=ms2
3.2.1 s1=s1 and s2＞s2
3.2.2 s1＞s1 and s2＝s2
3.2.3 s1＞s1 and s2＞s2
Concluding Remarks
Reference
英文文獻
Addelman, S. (1962). Orthogonal main-effect plans for asymmetrical factorial experiments. Technometrics 4, 21-46.
Chang, C.M. (1998). Minimal orthogonal main-effect plans and partial repli-cation. Journal of statistical planning and inference 70, 167-179.
Jacroux, M. (1992). A note on the determination and construction of minimal orthogonal main-effect plans. Technometrics 34, 92-96.
Jacroux, M (1993). On the construction of minimal partially replicated ortho-gonal main-effect plans. Technometrics 35, 32-36.
Pigeon, J., McAllister, P.R. (1989). A note on partially replicated orthogonal main-effect plans. Technometrics 31, 249-251.
Plackett, R.L. (1946). Some generalization in the multifactorial design. Biometrika 33, 328-332.