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研究生:侯永盛
論文名稱:計算機實驗設計--旋轉因子設計
論文名稱(外文):Designing Computer Experiments:Rotated Factorial Designs
指導教授:鄭宇庭鄭宇庭引用關係
學位類別:碩士
校院名稱:國立政治大學
系所名稱:統計學系
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:33
中文關鍵詞:有效相關拉丁超方陣最大化最小距離最大化最小內點距離
外文關鍵詞:Effect CorrelationLatin HypercubeMaximin DistanceMinimum Interpoint Distance
相關次數:
  • 被引用被引用:0
  • 點閱點閱:170
  • 評分評分:
  • 下載下載:34
  • 收藏至我的研究室書目清單書目收藏:0
計算機模型可以描述複雜的物理現象,然而這些模型應用在科學研究時其運算需要很長的時間,而且要有特定的實驗設計才能了解現象的本質。在有缺少一個或數個主效應的情形下,因子設計是不適合的,因為在缺少主效應下時其重複實驗不但不能估計誤差,只是產生重複實驗。雖然已經有學者提出許多可替代的設計,但是大部份設計的計算還是很累贅。本篇論文所提出的一些設計是從旋轉平面的二維因子設計發展而來,這些旋轉因子的設計很容易建構而且保有許多標準因子設計中吸引人的性質:(1)在每個維度的投影是均等空間投影;(2)在迴歸模型中,估計效應是不相關的(即正交的)。這些設計被稱為最大化最小拉丁超方陣,其設計與近期學者建構的最小化內點間距離的準則是同等的。

Computer models can describe complicated physical phenomena. To use these models for scientific investigation, however, their generally long running times and mostly deterministic nature require a special designed experiment. Standard factorial designs are inadequate; in the absence of one or more main effects, their replication cannot be used to estimate error but instead produces redundancy. A number of alternative designs have been proposed, but many can be burdensome computationally. This paper presents a class of designs developed from the rotation of a two-dimensional factorial design in the plane. These rotated factorial designs are very easy to construct and preserve many of the attractive properties of standard factorial designs: they have equally-spaced projections to univariate dimensions and uncorrelated regression effect estimates(orthogonality). They also rate comparably to maximin Latin hypercube designs by the minimum interpoint distance criterion used in the latter’s construction.

目 錄
摘要 1
第一章 緒論 2
第一節 研究背景 2
第二節 研究目的 4
第二章 設計準則與文獻回顧 6
第一節 設計準則 6
第二節 文獻回顧 7
第三章 旋轉因子設計 11
第一節 二維度旋轉因子設計 11
第二節 高維度旋轉因子設計 15
第三節 二維度子集合設計 18
第四章 設計方法比較 20
第一節 與最大化最小內點距離的拉丁超方陣比較 21
第二節 與最大化最小拉丁超方陣設計比較 22
第五章 結論 24
參考文獻 25
附錄 27
附表 29
附圖 30

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