排序與選取（Ranking and Selection）為蒙地卡羅法之範疇，探討多個獨立候選系統或選項中選取最佳情形，在統計上運用重複抽樣減少抽樣誤差，排序與選取法則應用較少抽樣達到相同或者更高之選取機率。此法大致可分為單一階段選取法（Single-stage selection procedure）及兩階段選取法（Two-stage selection procedure），由於單一階段法無法保證正確選取所求解，而後發展出兩階段選取法。此篇論文根據Rinott（1978）中兩階段選取法改善，為探討是否能夠在多個候選系統中正確選取最佳情形，並稱此機率為正確選取機率（Probability of Correct Selection, P(CS)）。兩階段選取法為單一階段選取法之延伸，是於第一階段抽取完觀測值，依據條件再抽取一次，此法在執行上能夠以較少的抽樣數達到正確選取機率。 學者Rinott利用Slepian不等式計算出P(CS) 的下界值，以確保產生的機率將大於信心水準，另學者Wilcox（1984）應用學者Rinott所提出計算P(CS)的方式推算出h常數，並建立常數h表格。有鑑於此，本研究主要目標為提升正確選取機率，應用多元常態分配累積機率函數計算選取機率。依照選取情形不同，透過程式演算發現正確選取機率在學者Rinott的h值下，應用多元常態累積機率計算出的選取機率略大於以往的選取機率，並發現在相同機率下所得新的h值較過往的小，並依此選取機率推得新的h常數，建立新的h表格，以提供讀者往後作R&S領域選取時作為參考。 ;Ranking and selection is a part of Monte Carlo method selecting the best one among the systems. We apply duplicate sampling to reduce the sampling error in statistic, but ranking and selection have same or less observations to achieve the same or higher probability. This method can be divided into two parts, one is the single-stage selection procedure and the other is the two-stage selection procedure. The single-stage method can’t guarantee the correct selection, so that the two-stage selection method is developed. This thesis, based on the two-stage selection proposed by Rinott (1978), is to find out whether the best case can be selected correctly in multiple systems, and this probability is called probability of correct selection. The two-stage selection method is an extension of the single-stage method, as it samples the observations in the first stage, then sample the observations again according to the condition. In practice, the two-stage selection method can achieve probability of correct selection with less observations. Rinott implemented the Slepian inequality to calculate the probability of correct selection lower bound ensuring the probability of correct selection is higher than the confidence level accessing the mode Rinott proposed, Wilcox also provided the constant h, and the table of constant h. In view of these, this thesis is to enhance the probability of correct selection through the two-stage selection method by using the way of multivariate normal cumulative distribution. Under different circumstances, using this approach allows us to get the higher probability than Rinott’s procedure. We also get the higher correct probability with lower constants h. The new table of constant h will be provided to readers as the references, and using some examples to discuss whether the probability of correct selection is improved.
