半導體產業日益進步，探針卡在半導體測試中成為不可或缺的工具，必須不斷適應新挑戰，以確保可靠的測試和診斷。其電路通電正確運作才能達到正常測試的效果。因此探針卡電路在通電後，每一根探針均能正常通電測試就顯得格外重要，本研究透過網路可靠度特性，將探針卡電路圖轉換為通用網路後，對圖形進行求解以得到探針卡每根探針均能正常通電運作的可靠度值，方便掌握探針卡正常運作的可靠度。
隨著網路圖規模的增大，對於圖形求解的困難度也隨之增加，使用傳統的數學求解方法求出精確可靠度值是一個NP-hard問題，因此本研究提出了最優計算量分配與蒙地卡羅之二元累加窮舉演算法(Optimal Computing Budget Allocation and Monte Carlo Simulation based on Binary-Addition-Tree algorithm, BAT-MCS-OCBA)以更快的獲得可靠度近似值，BAT-MCS-OCBA結合了二元累加窮舉演算法 (Binary-Addition-Tree algorithm, BAT)的精確性，應用超級向量概念簡化了BAT在列舉變數組合時耗費大量時間的問題與使用蒙地卡羅模擬(Monte Carlo Simulation, MCS)對超級向量未考慮之後續情形進行模擬增加準確率，最後應用最優計算量分配(Optimal Computing Budget Allocation, OCBA)對模擬進行了適當的資源分配，讓演算法更快速且精準的求得可靠度值，在研究的最後，BAT-MCS-OCBA也與BAT、MCS、BAT-MCS(Novel self-adaptive Monte Carlo simulation based on binary-addition-tree algorithm)進行比較，並在五個不同探針網路結構、四張常見網路圖中更快的求得近似可靠度值與更好的可靠度解品質。

Probe cards have become indispensable tools in semiconductor testing, requiring continuous adaptation to new challenges to ensure reliable testing and diagnosis. The correct operation of the circuit when powered is essential for effective testing. Therefore, it is crucial that each probe on the probe card functions properly when the circuit is powered. In this study, the network reliability characteristics are utilized to convert the probe card circuit diagram into a general network. The reliability values of each probe operating correctly when powered are then obtained by solving the network graph, facilitating the assessment of the reliability of the probe card's normal operation.
As the size of the network graph increases, the difficulty of graph solving also increases. Using traditional mathematical methods to obtain precise reliability values is an NP-hard problem. Therefore, this study proposes the Optimal Computing Budget Allocation and Monte Carlo Simulation based on Binary-Addition-Tree algorithm(BAT-MCS-OCBA) to quickly obtain approximate reliability values. BAT-MCS-OCBA combines the precision of the Binary-Addition-Tree algorithm (BAT) with the application of the super vector concept to simplify the time-consuming variable combination enumeration issue in BAT. It incorporates Monte Carlo Simulation (MCS) to simulate subsequent scenarios not considered by the super vector, increasing accuracy. Additionally, Optimal Computing Budget Allocation (OCBA) is applied to appropriately allocate resources for simulation, enabling the algorithm to quickly determine reliability values. In the study's conclusion, BAT-MCS-OCBA is compared with BAT, MCS, and BAT-MCS((Novel self-adaptive Monte Carlo simulation based on binary-addition-tree algorithm). It demonstrates faster approximation of reliability values and better reliability solution quality across five different probe network structures and four common network graphs.

摘要 i
Abstract ii
目錄 iii
圖目錄 vi
表目錄 ix
第一章、 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 3
1.3 研究架構 5
第二章、 文獻探討 7
2.1 探針卡 7
2.2 網路可靠度 8
2.2.1 可靠度問題的基礎網路型態 9
2.2.2 二元狀態網路可靠度演算法 9
2.3 新型自適應蒙地卡羅之二元累加窮舉演算法 10
2.3.1 超級向量 11
2.3.2 蒙地卡羅模擬 14
2.3.3 自適應模擬次數演算法 15
2.4 最優計算量分配 17
2.5 文獻回顧小結 19
第三章、 問題模型 20
3.1 探針卡電路圖 20
3.2 探針卡電路圖轉通用網路 22
第四章、 研究方法 29
4.1 BAT-MCS-OCBA演算法符號 29
4.2 BAT演算法窮舉超級向量 30
4.3 判斷超級向量種類 31
4.4 自適應模擬次數演算法 34
4.5 MCS結合OCBA 36
第五章、 實驗結果 42
5.1 資料集說明 42
5.2 BAT-MCS-OCBA演算法參數 46
5.2.1 探針卡網路(一)參數分析結果 47
5.2.2 探針卡網路(二)參數分析結果 48
5.2.3 探針卡網路(三)參數分析結果 49
5.2.4 探針卡網路(四)參數分析結果 50
5.2.5 探針卡網路(五)參數分析結果 51
5.2.6 常見網路(一)參數分析結果 53
5.2.7 常見網路(二)參數分析結果 54
5.2.8 常見網路(三)參數分析結果 55
5.2.9 常見網路(四)參數分析結果 56
5.3 BAT-MCS-OCBA統計驗證 58
5.3.1 探針卡網路(一)統計分析結果 58
5.3.2 探針卡網路(二)統計分析結果 60
5.3.3 探針卡網路(三)統計分析結果 62
5.3.4 探針卡網路(四)統計分析結果 64
5.3.5 探針卡網路(五)統計分析結果 66
5.3.6 常見網路(一)統計分析結果 68
5.3.7 常見網路(二)統計分析結果 70
5.3.8 常見網路(三)統計分析結果 72
5.3.9 常見網路(四)統計分析結果 74
5.4 實驗結果比較分析 76
第六章、 結論與未來研究方向 82
6.1 結論 82
6.2 未來展望 83
參考文獻 84

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