本研究是探討有重工情況的隨機網路系統之“系統可靠度", 其中隨機網路系統是由許多隨機產能的工作站串聯而成, 系統可靠度定義為系統最後產出的總數量大於開始指定需求量的機率。最近的文獻Song (2017) 指出先前已發表的23 篇系統可靠度期刊論文中解析解的共同錯誤, 並提出正確的解析解。這些共同錯誤的原因是每工作站的產出良品數應該以隨機變數來描述, 不該以常數來描述。因為這些論文是研究離散個體的製程(如晶圓片), 卻以連續型流體(如水與電) 去分析。
Song (2017) 所提出的解析法計算速度很慢, 所以該解析法不能當成計算一般性系統可靠度的方法, 只建議當成驗證使用。Song and Lin [21] 的研究為用改良版的Song rule 縮短解析解計算時間, 研究後發現許多例子可降低約94% 的時間。本論文以系統模擬法估計出上述已發表的23 篇論文中22 個例子之系統可靠度, 並指出所提出的估計解與錯誤的解析解至少有22% 的差別。Lin [25] 也提出上述22 個例子部分的估計解, 但不完整。雖然模擬法提供的是估計解, 對於企業" 時間就是金錢"的競爭環境, 據我們所知, 系統模擬法是目前估計隨機網路系統之系統可靠度最有效的方法。

The goal of this study is to obtain the "system reliability" of stochastic network systems with reworks, defined as the probability that the produced item (output) meets the pre-determined demand for a stochastic system with many workstations. According to the latest literature Song (2017), names Song rule, points out the common errors in the analytical results of the 18 previously published documents and provided correct analytical results. These common errors are due to the number of good items produced in per workstations should be random variables, not constants, wherein entities are discrete (such as wafers), while the analysis is a continuous flow, much like a fluid and electricity, through the network. However, Song rule (2017) is computationally inefficient and is recommended to be used for verification. Lin [24] proposed a more computationally efficient method. Specifically, the proposed extended Song rule accomplishes a computation-time-reduction of about 94% for networks with more than 2 workstations.

In this thesis used the systemic simulation estimates system reliability that Song (2017) established eighteen archival publications, containing twenty-two examples and the proposed estimated results are at least 22% different from the incorrect analytical result. Although simulation provides an estimated result, for the competitive environment, "time is money", as far as we know, the system simulation is the most effective approach for estimating the system reliability of the random network system.

第1 章緒論1
1.1 名詞與符號定義. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 簡稱. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 符號. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 問題定義. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 單一常規路徑與單一重工, SNLR(1,1) . . . . . . . . . . . . . . 5
1.2.2 多條路徑以及多個重工, SNLR(h,w) . . . . . . . . . . . . . . 6
第2 章文獻回顧與闡述8
2.1 文獻一: 18 篇已發表論文. . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.1 在先前已發表論文之六種系統類型. . . . . . . . . . . . . . . . 8
2.1.2 在18 篇已發表論文中採用之方法論. . . . . . . . . . . . . . . 10
2.1.3 文獻中的共同錯誤. . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 文獻二: Song Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 參考文獻三: 林[25] 的研究. . . . . . . . . . . . . . . . . . . . . . . 14
第3 章蒙地卡羅模擬法(Monte Carlo Simulation) 於SNLR(h,w) 15
3.1 蒙地卡羅模擬法簡介. . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 蒙地卡羅模擬法SNLR(h,w) . . . . . . . . . . . . . . . . . . . . . . 16
第4 章範例18
4.1 金屬沖壓件生產製程. . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.2 22 個例子. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.3 林[25] 的研究. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
第5 章結論21
參考文獻22

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