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研究生:魏嶸
研究生(外文):JungWei
論文名稱:以固定樣本方法解決多項式選擇之與標準系統比較問題
論文名稱(外文):Using Fixed-Sample Procedure to Solve Multinomial Selection for Comparisons with a Standard Problem
指導教授:蔡青志
指導教授(外文):Shing-Chih Tsai
學位類別:碩士
校院名稱:國立成功大學
系所名稱:工業與資訊管理學系碩博士班
學門:商業及管理學門
學類:其他商業及管理學類
論文種類:學術論文
論文出版年:2010
畢業學年度:98
語文別:中文
論文頁數:66
中文關鍵詞:多項式選擇問題與標準比較問題子集合選擇程序固定樣本程序
外文關鍵詞:Multinomial Selection ProblemComparisons with a StandardSubset Selection ProcedureFixed-Sample Procedure
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在與標準比較(comparisons with a standard)的問題中,此標準可視為一現存的系統(system)或是政策(policy)。由於在現實環境之中,更換掉原有的標準,可能需要耗費極多的成本(人力、時間)。因此若沒有其它的系統顯著地勝過它時,我們會保留原有的標準;反之如果有其它的系統表現遠勝過此標準,則進行汰換的活動。

系統模擬的系統選擇程序(ranking and selection)中大部分的比較和選擇的方法(comparison and selection methods)都希望選出擁有最大或最小期望值的系統,然而在某些情況下,其它衡量的基準會較期望值來的合適,此時就看我們如何定義最佳的系統。

而在本研究中,希望選出的是在單次試驗(single trial)中產生最大值機率最高的系統,也就是所謂的多項式選擇(multinomial selection)問題。我們發展二種固定樣本(fixed sample)的選擇程序,分別是大樣本及小樣本選擇程序。實驗的結果顯示出此二種程序皆能達成預先設定的信心水準,因此不論是在大樣本或小樣本的情況下,都能找到合適的樣本數N,解決多項式選擇之與標準系統比較問題。

In comparisons with a standard problem, the standard could be considered as an existing system or policy. Due to time and costs associated with replacement, we try to protect the standard as long as no alternative system is substantially better than the standard. However, if an alternative system shows a significant improvement, then we want to select it correctly.

The comparison and selection methods in simulation almost tries to find the system with largest or smallest expected value. However, in some situations other criteria may be more appropriate. It depends on how we define "best".


In this paper we want to select the system with highest probability to generate the largest observation in a single trial, which referred as multinomial selection problem. Two fixed-sample procedures are provided to deal with different situations, and both achieve the desired nominal level experimetally. Thus, appropriate samples N could be determined under different situations by adopting the proposed procedures to solve multinomial selection for
comparison with a standard problem.
中文摘要. i
英文摘要. ii
誌謝 iii
目錄 iv
表目錄 vi
第一章 緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 研究背景 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究目的與動機_ . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . 4
第二章 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .7
2.1 多項式選擇問題 . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . 7
2.1.1 無差異區間程序 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.2 子集合選擇程序 . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 14
2.2 與標準比較問題 . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . 18
2.2.1 二階段程序 . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . 18
2.2.2 完全連續程序 . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . 19
2.2.3 完全成對比較程序 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
第三章 研究方法. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .21
3.1 研究目標與假設.' . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 21
3.2 小樣本選擇程序 . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 23
3.3 大樣本選擇程序. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . 25
3.3.1大樣本選擇程序PCS之證明. . . . . . .. . . . . . . . . . . . . . . . 27
第四章 實驗設計與數據分析. . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1 實驗設計 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.1 小樣本選擇程序之實驗設計. . . . . . . . . . . . . . . . . . . . . 37
4.1.2 大樣本選擇程序之實驗設計. . . . . . . . . . . . . . . . . . . . . 38
4.2實驗數據與分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2.1 小樣本選擇程序之實驗數據與分析. . . . . . . . . .. . . . . 40
4.2.2 大樣本選擇程序之實驗數據與分析. . . . . . . . . . . . . 43
4.2.3 樣本數之敏感度分析 . . . . . . . . . . . . . . . . . . . . . .. . . . . 47
第五章 結論與未來研究方向. . . . . . . . . . . . . . . . .. . . . . . . . .50
5.1 論文總結. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.2 未來研究方向之建議 . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
附錄 52
參考文獻 64

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