臺灣博碩士論文加值系統

系統模擬已廣泛運用於今日社會中，舉凡是各種人類活動皆可應用於模擬領域中。其中，排序與選擇程序之目的是從多個系統中，在信心水準下推薦具有競爭力之系統，提供使用者決策參考；然而，系統本身之輸出值變異數較大，將會導致效率較差，造成時間與成本之浪費。因此，藉由變異減免技術的發展，在統計的理論基礎下，建立新的估計量取代原本之樣本平均數，使變異數下降，提升各程序之效率。控制變量係以線性迴歸的手法，解釋輸出值之誤差，建立控制估計量取代原本的樣本變異數，且控制變量運用於排序與選擇程序已相當成熟。而相關性導入技術係利用在產生隨機變數時，藉由控制隨機亂數，使同一系統中之輸出值彼此具有負相關性，以達到減少變異數之目的。

本研究建立四種結合控制變量與相關性導入之模型，並運用其估計量於篩選程序、兩階段選擇程序、多階段選擇程序與完全連續選擇程序，且證明或推論程序符合信心水準，並分析何種情況下合併程序優於獨立程序。透過實驗，本研究各程序皆可滿足信心水準，且當面對的問題越困難時，帶來之好處也越大，所需樣本較低。並從實驗數據中發現兩階段選擇程序最容易藉由導入負相關，使效率下降，但該程序所需樣本卻最多；多階段選擇程序效率最佳，然而卻最不易得到負相關所帶來之好處；完全連續選擇程序則介於兩者之間。本研究建議各程序在解決不同問題時使用不同之模型。對於篩選程序，建議使用
Model 3 於樣本數與控制值個數較接近問題；Model 4用於解決複雜問題並設定較大初始樣本配合執行之；其餘情況使用 Model 1。而多階段選擇程序與完全連續選擇程序，在較困難問題中，建議使用Model 1之方法並配合對偶變量；較容易之問題則使用獨立控制變量程序。而若使用兩階段選擇程序則不論問題難度皆建議使用本研究提出之Model 1 方法。

The propose of using Ranking and Selection Procedures is to find
superior systems form all of candidate systems. However, if the
variance of system output is large, we need to sampling more sample
to find best system to guarantee confidence level. Therefore, we
apply Variance Reduction Technique to procedures, replacing the
origin estimator, sample mean, to accomplish the propose of reducing
variance; and further, decrease the number of samples we need.

In our research, we establish four model of combining Correlation
Induction and Control Variates in Screening Procedure, Multistage
Selection Procedure, Two-stage Selection Procedure, and Fully
Sequential Selection Procedure, and by inference or proving that
each procedure will guarantee confidence level, and we also analyze
in what condition our combine procedure will be better than CV
procedure. Through empirical results and a realistic illustration,
we find that the probability of correct selection of all procedures
will conform to confidence level guarantee, and when the problem is
more complicated, then we can get more benefit form our combine
procedures. In the end of our research we conclude that, for
Screening Procedure, we recommend using Model 3 when the number of
samples and the number of controls is close; using Model 4 when the
problem is complex with setting large samples to do; in the other
condition we suggest using Model 1. For Multistage Selection
Procedure and Fully Sequential Selection Procedure, we recommend
using Model 1 when facing a complicated problem, but otherwise using
the CV procedure. Finally, for Two-stage Procedure we recommend
using Model 1 in all situations.

目錄

中 文 摘 要 i
英 文 摘 要 ii
誌 謝 iii
目 錄 iv
圖 目 錄 vii
表 目 錄 viii
第一章 緒論 1
1.1 研究背景與動機 2
1.2 研究目的 4
1.3 研究流程 5
第二章 文獻回顧與基本模型介紹 6
2.1 變異減免技術 6
2.1.1 控制變量 7
2.1.2 相關性導入技術 10
2.2 合併變異減免技術 15
2.3 運用控制變量之排序與選擇程序 16
2.4 小結 18
第三章 研究方法 19
3.1合併變異減免技術之模型建立 19
3.2篩選程序 28
3.2.1 程序步驟 28
3.2.2 驗證可行性 28
3.2.3 效率分析 30
3.2.4 多階段篩選程序 32
3.3 兩階段選擇程序 36
3.3.1 程序步驟 36
3.3.2 驗證可行性 36
3.3.3 效率分析 37
3.4 完全連續選擇程序 38
3.4.1 程序步驟 39
3.4.2 驗證可行性 40
3.4.3 效率分析 40
第四章 實驗設計與分析 42
4.1 實驗評估 42
4.1.1 篩選程序 44
4.1.2 多階段選擇程序 47
4.1.3 兩階段選擇程序 52
4.1.4 完全連續選擇程序 53
4.1.5 小結 54
4.2 實例驗證 56
第五章 結論與未來研究方向 60
5.1 研究總結與建議 60
5.1.1 篩選程序 60
5.1.2 多階段選擇程序 61
5.1.3 兩階段選擇程序 61
5.1.4 完全連續選擇程序 61
5.2 未來研究方向 62
參考文獻 63




圖目錄
圖2.1 LHS 範例圖 13





表目錄
表4.1 SP-1之殘差項負相關係數門檻值與下界值之比例關係 45
表4.2 比較SP-CV 與SP-3 之殘餘系統數 45
表4.3 比較SP-CV 與 SP-1至SP-4於SC情況之殘餘系統數 46
表4.4 比較MSP-CV、MSP-1至MSP-4於SC情況之ANS 49
表4.5 比較MSP-CV、MSP-1、MSP-3與MSP-4於MDM情況之ANS 50
表4.6 比較MSP-CV、MSP-4於SC情況之ANS 51
表4.7 TSP-1之殘差項相關係數門檻值 52
表4.8 比較TSP-CV、TSP-1、TSP-2於SC情況之ANS 53
表4.9 FSP-1之殘差項相關係數門檻值 54
表4.10 比較FSP-CV、FSP-1、FSP-2於SC情況之ANS 54
表4.11 各系統之等候問題參數設定，以及穩態下之期望等候時間 56
表4.12 各程序於等候問題之結果比較 58
表4.13多階段選擇程序於表4.12所花費之時間 59
表4.14 各多階段選擇程序於大樣本情況下等候問題之結果比較 59

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