# 臺灣博碩士論文加值系統

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 投票系統為一個進行投票行為的系統，其系統中包含了n 個單位。此篇論文中，將投票系統分為兩類，第一類為權重式投票系統，另一類為非權重式投票系統。投票系統中的每個單位在經過投票行為後都有一個二元(0或1)或棄權的決策產出。若權重式投票系統中決策為1的單位其所屬的權重加總後至少大於系統門檻值 乘上決策非棄權的單位所屬的權重加總值，則該投票系統的決策為1，相反的，其投票系統決策為0；而非權重式投票系統中，系統的每一個單位權重皆相等，因此，此投票系統將根據系統的單位數量做決策。當決策為1的單位數量至少大於系統門檻值乘上決策為非棄權的單位總數，則該非權重式投票系統決策為1，相反則為0。在規劃、設計、控制系統的研究方面，關於計算、估計投票系統的可靠度是一項重要的議題。此篇論文中，蒙地卡羅模擬法是最先發展出用來計算非權重式投票系統可靠度，並且應用反應曲面法中Box-Behnken 設計法及類神經網路演算法用以求得其系統可靠度函數。在論文範例中得知，當使用類神經網路演算法求得其可靠度函數的效果優於使用反應曲面法中的設計法BBD。並且在章節的案例中應用其模擬法計算出台灣的總統大選選舉投票系統可靠度。
 The voting system which has been studied normally consists of n units. It is divided into two types in this thesis. One is the weighted voting system, and the other is the un-weighted voting system. Each of these provides a binary decision (0 or 1), or a decision of abstaining from voting. The weighted voting system output is 1 if the cumulative weight of all 1-opting units is at least a pre-specified fraction of the cumulative weight of all non-abstaining units. Otherwise, the system output is 0. The un-weighted voting system output is 1 if the number of unit of all 1-opting decisions is at least a pre-specified fraction of the cumulative units of all non-abstaining ones.Evaluating the reliability of the voting system is an important topic in the field of planning, designing and control. Compared with other studies in the field, in the present thesis, an intuitive Monte Carlo simulation (MCS) was first developed to find the estimated reliability of un-weighted voting system. Then, the response surface methodology (RSM) with the Box-Behnken design (BBD) and the algorithm of Neural Network are used to obtain the reliability function. In the case of the present study, using the Neural Network is more effective than using the BBD. In the last section, the reliability of a real case presidential election is evaluated.
 Table of Contents中文摘要 iAbstract iiTable of Contents iiiList of Figures vList of Tables viChapter 1 Introduction 11.1 Background 11.2 Significance and Motivation 21.3 Research Aims and Research Scope 21.4 Organization of Thesis 3Chapter 2 Literature Review 52.1 Concept of general decision making system 52.2 K-out-of-N System 62.3 Voting System Reliability Evaluation 72.3.1 Problem Description 72.3.2 Methods of Evaluating Voting System Reliability 82.4 Voting System Reliability Model Application 11Chapter 3 Reliability of Voting System Evaluating Model 133.1 voting system 133.1.1 Notations 133.1.2 Voting System introduce 143.1.3 Un-weighted Voting System reliability 153.1.4 Weighted Voting System reliability 173.2 Monte Carlo Simulation 193.2.1 Monte Carlo Simulation to Un-weighted Voting System 193.3 Response Surface Methodology 213.3.1 Response Surface Methodology to Un-weighted Voting System 21Chapter 4 Empirical Study 244.1 Problem Definition 244.2 MCS-RSM of first model design 254.3 MCS-RSM of second model design 274.4 Monte Carlo Simulation to the presidential election in Taiwan 28Chapter 5 Conclusion 31References 32
 ReferencesG. Levitin , A.Lisnianski “Reliability optimization for weighted voting system”. Reliab Engng Syst Safety, vol71, 2001, 131-138.Lars Nordmann , Hoang Pham “Weighted Voting Systems”. IEEE Trans. Reliability, Vol48 , NO. 1,1999 MARCHWei-Chang Yeh “A MCS-RSM approach for network reliability to minimize the total cost”. Int J Adv Manuf Technol, vol 22, 2003, 681-688.G. Levitin ,”Optimal unit grouping in weighted voting systems”. Reliab Engng Syst Safety, vol 72 ,2001, 179-191.B. Parhami “Threshold voting is fundamentally simpler than plurality voting”. Int’l J. Reliability, Quality and Safety Eng’g, vol 1, num 1, 1994, 95-102.Y. Ben-Dov “Optimal reliability design of k-out-of-n systems subject to two kinds of failure”. J. Operations Research Soc, vol 31, 1980, 743-748J. Wu, R. Chen “Efficient algorithms for k-out-of-n & consecutive-weighted- k-out-of-n system”. IEEE Trans. Reliability, vol 43, 1994 Dec, 650-655.H. Pham, M Pham ”Optimal design of {k,n-k+1} systems subject to two modes”, IEEE Trans. Reliability, vol 40, 1991 Dec, 559-562.J. Wu, R. Chen “An algorithm for computing the reliability of a weighted k-out-of-n system”. IEEE Trans. Reliability, vol 43, 1994 Jun, 327-328.H. Pham, D.M. Malon “Optimal design of systems with competing failure modes”, IEEE Trans. Reliability, vol 43, 1994 Jun, 251-254.B. Parhami “Voting algorithms”. IEEE Trans. Reliability, vol 43, 1994 Dec, 617-629.H. Pham “Optimal system size for k-out-of-n systems with competing failure modes”. Mathematical and Computer Modeling, vol 15, 1991, 77-82.J. Biernat “The effect of compensating fault models on n-tuple modular redundant (NMR) system reliability”. IEEE Trans. Reliability, vol 43, 1994 Jun, 294-300.H. Pham “Reliability analysis for dynamic configurations of systems with three failure modes”. Reliability Eng’g and System Safety, vol 63, 1999, 13-23.B. Parhami “The parallel complexity and weighted voting”. Proc. Int’l Symp. Parallel and Distributed Computing and Systerms, 1991, 382-385.D.M. Blough, G.F. Sullivan “Voting using predispositions”. IEEE Trans. Reliability, vol 43, 1994 Dec, 604-616.F.P. Mathur, P.T. de Sousa “Reliability models of NMR systems”. IEEE Trans. Reliability, vol R-24, 1975 Jun, 108-113.Gregory Levitin “Maximizing survivability of vulnerable weighted voting system”. Reliab Engng Syst Safety, vol 83, 2004, 17-26.Harri Niska, Teri Hiltunen, Ari Karppinen, Juhani Ruuskanen, Mikko Kolehmainen “Evolving the neural network model for forecasting air pollution time series”. Engineering Applications of Artificial Intelligence , vol 17 ,2004, 159-167.Douglas C. Montgomery(2005) Design And Analysis of Experiments ,Wiley New York.Myers RH, Montgomery DC(1995) Response Surface Methodology-process and product optimization using designed. Wiley New York.
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 1 以類神經網路為基礎之品質設計系統之研究 2 類神經網路最佳學習參數值找尋之研究:以空調溫濕度異常診斷與處理為例 3 光耦合器產品品質之發展 4 以類神經網路求解負載溫度敏感度並應用於系統可靠度分析 5 以類神經網路結合遺傳演算法探討複置系統可用度之最適配當 6 積層陶瓷電容印刷製程機器參數最佳化之研究 7 溢洪道容量之可靠度分析 8 應力調整策略對系統保養行為之探討 9 利用迴歸方法分析相同尺寸晶片堆疊式封裝之最佳化 10 滑動葉片旋轉式壓縮機之葉片研究 11 裝配公差最佳化組合之研究 12 在步進應力衰減資料下發展類神經網路模式預測發光二極體可靠度 13 步進試驗衰退性資料之壽命預估 14 高可靠度產品壽命預估-以發光二極體為例 15 運用類神經網路於彈性裝配系統之動態可靠度之探討

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