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.

1. Fiondella, L., Lin, Y.-K. and Chang, P.-C. (2015). System performance and reliability modeling of a stochastic-flow production network: a confidence-based approach. IEEE Transactions on Systems, Man, and Cybernetics:Systems, 45, 11 , 1437-1447.
2. Gu, C., He, Y., Wei, Y. and Ming, X. (2015). Reliability modeling of manufacturing systems based on the task network evolved by key quality characteristics. The First International Conference on Reliability Systems Engineering (2015 ICRSE).
3. Lin, Y.-K. and Chang, P.-C. (2011). Reliability evaluation of a manufacturing network with reworking action. International Journal of Reliability,Quality and Safety Engineering, 18, 5, 445-461.
4. Lin, Y.-K., Chang, P.-C. and Chen, J. C. (2012). Reliability evaluation for a waste-reduction parallel-line manufacturing system. Journal of Cleaner Production, 35, 93-101.
5. Lin, Y.-K. and Chang, P.-C. (2012a). System reliability of a manufacturing network with reworking action and different failure rates. International Journal of Production Research, 50, 23, 6930-6944.
6. Lin, Y.-K. and Chang, P.-C. (2012b). Evaluate the system reliability for a manufacturing network with reworking actions. Reliability Engineering and System Safety, 106, 127-137.
7. Lin, Y.-K. and Chang, P.-C. (2012c). Reliability evaluation for a manufacturing network with multiple production lines. Computers & Industrial Engineering, 63, 1209-1219.
8. Lin, Y.-K. and Chang, P.-C. (2013a). Reliability assessment for a stochastic manufacturing system with reworking actions. Journal of the Chinese Institute of Engineers, 36, 3, 382-390.
9. Lin, Y.-K. and Chang, P.-C. (2013b). A novel reliability evaluation technique for stochastic-flow manufacturing networks with multiple production 22 lines. IEEE Transactions on Reliability, 62, 1, 92-104.
10. Lin, Y.-K. and Chang, P.-C. (2013c). Reliability of a production system with intersectional lines. Journal of Engineering Manufacture, 1-11. 11. Lin, Y.-K. and Chang, P.-C. (2013d). Reliability-based performance indicator for a manufacturing network with multiple production lines in parallel. Journal of Manufacturing Systems, 32, 147-153.
12. Lin, Y.-K., Huang S.-F. and Chang, P.-C. (2013). System reliability evaluation of a touch panel manufacturing system with defect rate and reworking. Reliability Engineering and System Safety, 118, 51-60.
13. Lin, Y.-K., Chang, P.-C. and Chen, J.C. (2013). Performance evaluation for a footwear manufacturing system with multiple production lines and different station failure rates. International Journal of Production Research, 51, 5, 1603-1617.
14. Lin, Y.-K. and Chang, P.-C. (2014). Decision making procedure of demand satisfaction and production policy for capacitated production systems. Expert Systems with Applications, 41, 723-734.
15. Lin, Y.-K. and Chang, P.-C. (2015). Demand satisfaction and decisionmaking for a PCB manufacturing system with production lines in parallel. International Journal of Production Research, 53, 11 , 3193-3206.
16. Lin, Y.-K., Chang, P.-C., and Huang, C.H. (2016). System reliability evaluation of a multistate manufacturory in book Quality and Reliability Management and its Applications. Springer-Verlag, London. 117-143.
17. Song, W.T. and B.W. Schmeiser. (1994), Reporting the precision of simulation experiments. In New Directions in Simulation for Manufacturing and Communications, ed. S. Morito, H. Sakasegawa, K. Yoneda, M. Fushimi, and K. Nakano, 402-407. Tokyo: Operations Research Society of Japan.
18. Song, W.-M. T. and Schmeiser, B. (2009). Omitting Meaningless Digits in Point Estimates: the Probability Guarantee of Leading-Digit Rules, Operations Research. 57, 109-117.23
19. Song, W.-M. T., and Schmeiser B. (2011). Displaying statistical point estimates using the leading-digit rule. IIE Transaction. 43, 851-862.
20. Song, W.-M. T. (2017). The Song Rule as a validator of Analytical Results —A Note Correcting “System Reliability Results" in a Review of the Literature. IEEE Transactions on Reliability, Vol 66, No 4, pp. 1012-1024.
21. Song, W-M. T. and Lin, P. (2018). System Reliability of Stochastic Networks with Multiple Reworks Reliability Engineering and System Safety, 169, pp.158-168.
22. Yang, T. and Yang, Y. (2013). Reliability evaluation of collaborative product design process considering redesigning activities. Information Technology Journal, 12, 21, 6325-6329.
23. Yang, T., Yang, Y. and Xue, C.M. (2014). Conflict analysis between task iteration and design capabilities in collaborative product development. International Journal of Security and Its Applications, 8, 2, 375-386.
24. Yeh, C. F. (2017). Study on the Improvement of Solar Cell Efficiency and Cost Reduction- Double Printing of Finger Fine-Lines. Master Thesis, Department of Industrial Enginering and Engineering Management, National Tsing Hua University, Taiwan, R.O.C.
25. 林姵萱(2016)。考慮多個重工隨機系統之系統可靠度(未出版之碩士論文)。國立清華大學工業工程與工程管理學系, 新竹市。