在各個領域中存在許多具有隨機性或是難以透過數學模式分析之複雜問題，此時決策者可以利用電腦模擬生成樣本觀察值來協助分析。然而各領域中除一般事件外，許多重要問題屬罕見事件，在模擬罕見事件時，由於事件發生機率過低，導致可取得之有效估計點過少，因此要得到一有效樣本需耗費大量抽樣成本，不但花費長時間抽樣，其取得的樣本變異數大、準確度低，不符效益，為此在模擬領域中發展一套方法 — 變異縮減技術，其利用統計上之估計方法取代一般的樣本平均估計量 ，在新估計量維持不偏的情況下，使其樣本變異數下降且低於原始變異數的技術，藉此獲得更精準之結果並有效提升使用者決策之準確度。
本研究所提出之模型結合了控制變量與重要性取樣法，在一般情況下，變異縮減技術中縮減效果較好之方法為控制變量，亦是研究中較常被用來與其他變異縮減技術合併探討；而在罕見事件中，重要取樣法是各方法中最適合用來解決樣本抽取的問題，但相對的此方法在使用上較為困難。因此本研究提出將控制變量與重要性取樣法兩種同為輸出型之變異縮減技術依不同形式結合，期望兩變異縮減技術之合併能優於單獨使用變異縮減技術之效益，並使合併後之變異縮減技術所能使用之範圍較單一使用變異縮減技術時廣泛。
透過數值實驗發現本研究所提出之模型 Model 1 僅於特定事件上能有效優於單一使用 VRT，而其中 CV+ISreg 較於 CV+ISint 穩定，其表現均不劣於單一使用 VRT；提出之模型 Model 2 表現範圍較廣，在使用 IS 方法之變數與輸出值兩者相關性高的前提下，其均適用此方法予以估計，有效達到變異縮減的效果並且優於單一使用 VRT。

Simulation can help us to identify the best systems and make the best decisions. In this paper, we propose two estimators that combine two different Variance Reduction Techniques (VRT), respectively Control Variates (CV) and Importance Sampling (IS). Here we use two types of IS, integration IS (ISint) and regression IS (ISreg). To choose the optimal change of measure in the context of importance sampling, we use a stochastic optimization approach -- Sample Average Approximation (SAA). The idea is to use IS to adjust the original output, then use CV to reduce the variance of the control variable. We applied the proposed methods to two cases : Normal and Stochastic Activity Networks (SAN). Numerical experiments show that Model 2 has better performance in terms of variance reduction which is related to the correlation between output, control variable, and the importance sampling variable. However, the performance of Model 1 is not as expected; it only works in special case. But the performance of CV+ISreg estimator is better than CV+ISint estimator. CV+ISint estimator may be worse than single method, but CV+ISreg estimator will not. Combining these two VRTs can achieve 95% confidence level of variance reduction benefit from a single method.

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