Improving the probability of correct selection in two - stage ranking and selection method

• Main Authors: Jia-Lun Lee, 李嘉倫
• Other Authors: Ying-chieh Yeh
• Format: Others
• Language: zh-TW
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/dtyww7

碩士 === 國立中央大學 === 工業管理研究所 === 105 === 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.