系統模擬包含的應用領域十分廣泛，當遇到不確定性以及擁有隨機變因的問題時，
均可以使用模擬來進行分析，而在決策者面對模擬最佳化問題時，若問題維度不大，則
可使用排序與選擇程序使得在一信心水準下，正確選擇最佳或近似最佳系統使決策者參
考； 然而排序與選擇程序只適用系統個數較小的前提下，若系統之績效值變異程度過
大，將影響程序執行速度，使得抽樣成本及運算時間提高。 因此透過統計中的變異縮減
技術，利用替代估計量取代一般的樣本平均數估計量，使其樣本變異數將較原本變異數
更低，達到變異縮減之效果。 變異縮減技術可分之為兩種：輸入型技術及輸出型技術，
前者是使用相關性的輸入變量，藉此產生具有正或負相關的輸出值；而後者是使用輔助
變數試圖修正輸出值，使得變異數下降。 而本研究將控制變量、條件期望法、事後分層
法等三種不同的變異縮減技術結合所形成的合併變異縮減技術，期望能優於單獨使用變
異縮減技術之效益，以求達到更顯著的變異縮減效果。
本研究建立控制變量結合條件期望法、控制變量結合事後分層法等兩種合併變異縮
減技術之模型，並將推算所得之估計量以及變異數估計量應用於完全連續選擇程序中，
且在滿足信心水準下，比較原始程序以及合併型程序的優劣，並將程序用於一範例加
以實驗比較。 歸納出合併之變異縮減技術之效果皆可優於單一使用，其中在控制變量
與條件期望法合併的部分，在原本的控制變量外，再選擇一個條件變量 (Conditioning
Variate)，其可同時對觀察值與控制值取條件觀察值，其合併效果最佳。 而在控制變量
結合事後分層法的部分，只要選擇與觀察值具有相關性的分層變數，而此分層變數與控
制值獨立下，能獲得最佳之合併效果。

Simulation optimization can help us to identify the best systems from all candidate
systems. In this paper, we propose two estimators that combine three different variance
reduction techniques, and use the combined estimators in Fully Sequential Selection
Procedures (FSP). First we combine Control Variates (CV) with Condition Expectation
(CE). The idea is to use a condition variable to replace the origin output or the variable
use in CV with condition expectation. So there are three schemes. And with the case
where the condition variable may not be fully used, we also show that partial condition
expectation can be used as ordinary CE . Second, we combine Control Sum (CS) with
Post-stratified Sampling (PS). The idea is like ordinary PS, but we use CS to estimate
each stratum and to combine each stratum with its weight as in ordinary PS. Then we
replace the ordinary estimator used in FSP with these combined estimators. Empirical
results show that the procedure using CE to replace both the output and control variates
has the most significant reduction effects in CV+CE, and the reduction effects are
related to the correlation between output, control variables, and the condition variable.
When the condition variable can only replace the partial estimators, it still works better
than the ordinary CV, in CS+PS, if we use a stratified variable that is independent to
control variable. Combining the two techniques can obtain a guarantee benefit from a
single method.

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