本文的目的是以解析解計算所謂的 「系統可靠度」,定義為某隨機系統最後的產出值會大於或等於一個預訂需求量的機率。本文研究的隨機系統是指由許多工作站連結而成的網路,其中每個工作站都有個別的隨機產能限制,且每個進入工作站的待加工品有特定的比率成為良品或不良品。上述定義的「系統可靠度」是隨機系統的一個重要績效指標。 製造系統、網際網路系統、物流系統都是上述隨機系統的應用。本文回顧並指出已發表的錯誤。錯誤有兩類:第一類錯誤是18篇文獻假設工作網路中所產出離散且不可分割的物件是實數,正確應假設產出物件為服從二項機率分配的隨機變數。第二類錯誤是Song Rule的分析方法假設所有事件應獨立計算,對於非重工情況是有效的;但當重工和非重工路徑共享相同容量時,對於一般系統可靠度而言是事件獨立計算是不正確的,正確應為事件彼此不獨立來做計算,此為本文更正原 Song Rule的缺失之處。本文提出之“修正後的Song Rule”因計算過程耗時,僅建議作為驗證時使用,而不是問題求解最佳利。對於大規模網絡的系統可靠度,建議以模擬方法進行問題解決方案。

An important performance measure for stochastic manufacturing networks is the system reliability, defined as the probability that the production output meets or exceeds a specified demand.This paper reviews and highlights the drawbacks of the previous works, including twenty one archival publications and the most recent published analytical Song rule. The major error in the twenty one archival publications error assumes that entities in the network are discrete and indivisible, while the analysis is based upon continuous flow through the network. That is, they assume that the number of defective items is a real number, instead of a random variable following a binomial distribution. We claim that the analytical approach in Song rule is valid for non-rework case but is incorrect for general system reliability with reworking when the rework and non-rework path share the same capacity. This note corrects the mistakes in Song rule with rework when the rework and non-rework path share the same capacity. The Song rule and the proposed corrected version of Song rule in this note are computationally inefficient and are only recommended as a validator instead of a problem solver. For big-scale system reliability, simulation approach are recommended as the problem solver.

第 1 章 緒論................................................1
1.1 目的...................................................1
1.2 動機...................................................1
1.3 符號定義................................................1
1.4 以符號描述問題 ..........................................4
第 2 章 文獻回顧及延伸 .......................................7
2.1 回顧及延伸探討18篇文獻...................................7
2.1.1 18篇文獻所包括的隨機系統整理...........................7
2.1.2 18篇文獻的邏輯(錯誤的邏輯)............................10
2.2 文獻[19] Song Rule.....................................14
2.3 系統可靠度之模擬法邏輯...................................17
第 3 章 修正 Song rule 單一生產線下有單一重工製程的系統可靠度...19
第 4 章 實例............................................... 21
第 5 章 結論與未來研究 ......................................23
參考文獻................................................... 24
附錄1.......................................................26
附錄2.......................................................31

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