生活中的問題隨著科技發展越來越複雜，當問題難以使用數學模式分析時，利用系統模擬的技術，能夠放寬許多不合理假設以建立模型幫助決策。模擬領域發展排序與選擇程序，在問題的候選解不多時，幫助決策者選擇最佳系統。而排序與選擇程序在估計變異較大的系統績效表現值時，容易面臨抽樣過多及運算時間長等問題；模擬領域中發展之變異減免技術則可改善此問題，以變異數較小的估計量取代原本的平均數估計量，降低平均抽樣數，增加完全連續選擇程序之效率。在過去文獻中已有許多研究結合控制變量於完全連續選擇程序中，但皆需要假設導入控制變量的估計量符合線性模型假設。本研究欲放寬在完全連續選擇程
序中的線性假設，使程序的應用範圍能擴大至非線性的領域，得以處理更複雜的問題。因此結合非線性控制變量於完全連續選擇程序中，討論導入非線性模型的影響，也證明新程序之統計保證性。
在本研究中使用兩個隨機最佳化的方法幫助估計沒有封閉形式之非線性參數 。其一為樣本平均近似法，利用一組樣本定義變異數估計量，將其表示為非線性參數的函數，並求解出使變異數估計量最小化的非線性參數估計量 ；第二個方法為隨機近似法，在多階段的程序中，每個階段利用已設定好的步長函數，及用樣本估計而得的變異數之梯度來調整非線性參數 ，最後得到對於 非線性參數最佳解的估計。
經由實驗發現本研究提出之FSP-SAA 及FSP-SA 除了能夠處理非線性的控制變量外，其平均抽樣數比過往文獻更少，並同時能符合信心水準。最後以選擇最高可靠度系統的問題為實例驗證，除了再次證實本研究之程序較過往文獻佳，也討論了使用線性及非線性控制變量的應用。

In past studies, the Fully Sequential Selection Procedure (FSP) algorithm combined with Control Variate (CV) can only be applied under linear CV model. We propose two FSP algorithms with CV that allow the use of nonlinear CV estimation. In contrast to the linear CV model, we cannot expect to find a closed form expression for the parameter in nonlinear CV model. Therefore, we solve this problem by using two stochastic optimization approaches, which are Sample Average Approximation (SAA) and Stochastic Approximation (SA) respectively. The numerical experiments indicate that the probability of correct selection (PCS) can meet the desired confidence
level, in addition, the effectiveness of variance reduction is more significant in our procedures.

宋奇檠. (2016). 合併變異數縮減技術於完全連續選擇程序. 成功大學工業與資訊管
理學系學位論文.
蔡承濂. (2017). 以更有效率之方式結合控制變量於完全連續選擇程序. 成功大學工
業與資訊管理學系學位論文.
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