在日常生活中有許多系統都是網路架構的應用，像是基地台配置，電力傳輸系統等等。系統能否運作順暢，網路可靠度的評估是一個非常重要的衡量指標，所以估算網路可靠度成為了一個非常重要的問題。而最小路徑集合是估算網路可靠度基本的工具之一，由於網路可靠度的評估是一個NP-hard問題，在先前的研究中，我們已經可以運用通用生成函數找出網路圖形中所有最小路徑，但當在原始的網路圖形中新增或減少一條邊的時候，必須再重頭執行一次演算法的所有流程。因為在現實世界裡的網路圖型幾乎都是非常複雜的，所以每次運算都會花很長的時間。
本研究提供一種特定的通用生成函數，由於特定通用生成函數旨在應用來找尋出增加或減少路徑後所獲得或失去的最小路徑，所以能夠藉由將沒有影響的因子盡可能在特定通用生成函數的 中移除，以簡化 的計算，使運算的複雜度大幅降低，減少運算所需時間。最後將用一個例子去說明增加或減少一條邊後網路圖型將會獲得或損失哪些最小路徑，再以此計算增加或減少路徑後網路可靠度的變化。

Chapter 1 Introduction
1.1 Background and Motivation
1.2 Objectives
1.3 Organization of This Article
Chapter 2 Literature Review
2.1 Network Reliability
2.2 Minimal Path
2.3 The Universal Generating Function Technique
Chapter 3 Acronyms, Nomenclature, Notation and Assumptions
3.1 Acronyms
3.2 Nomenclature
3.3 Notation
3.4 Assumptions
Chapter 4 SUGFM Formulation and Preliminaries
4.1 Basic Element, Concept and Useful Rules of SUGFM.
4.2 Algorithm
Chapter 5 An Illustrative Example
5.1 Example
5.2 Reliability
Chapter 6 Conclusion and Future Research
6.1 Conclusion
6.2 Future Research
REFERENCE

1.Ahuja, S.P. Performance based reliability optimization for computer networks. in Southeastcon '97. Engineering new New Century., Proceedings. IEEE. 1997.
2.Aven, T., Availability evaluation of oil/gas production and transportation systems. Reliability Engineering, 1987. 18(1): p. 35-44.
3.Hongshan, Z., Z. Chao, and H. Ren. Power transmission network vulnerable region identifying based on complex network theory. in Electric Utility Deregulation and Restructuring and Power Technologies, 2008. DRPT 2008. Third International Conference on. 2008.
4.Nam, P., B.M. Wilamowski, and A. Malimowski. Computer networks as human system interface. in Human System Interactions (HSI), 2010 3rd Conference on. 2010.
5.Wei-Chang, Y., A Simple Heuristic Algorithm for Generating All Minimal Paths. Reliability, IEEE Transactions on, 2007. 56(3): p. 488-494.
6.Wei-Chang, Y., The Extension of Universal Generating Function Method to Search for all one-to-many d-Minimal Paths of Acyclic Multi-State-Arc Flow-Conservation Networks. Reliability, IEEE Transactions on, 2008. 57(1): p. 94-102.
7.Wei-Chang, Y., A Simple Universal Generating Function Method to Search for All Minimal Paths in Networks. Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on, 2009. 39(6): p. 1247-1254.
8.Yeh, W.-C., A simple algorithm to search for all d-MPs with unreliable nodes. Reliability Engineering & System Safety, 2001. 73(1): p. 49-54.
9.Yeh, W.-C., Search for minimal paths in modified networks. Reliability Engineering & System Safety, 2002. 75(3): p. 389-395.
10.Yeh, W.C., A Simple Method to Verify All d-Minimal Path Candidates of a Limited-Flow Network and its Reliability. The International Journal of Advanced Manufacturing Technology, 2002. 20(1): p. 77-81.
11.Aven, T., Reliability Evaluation of Multistate Systems with Multistate Components. Reliability, IEEE Transactions on, 1985. R-34(5): p. 473-479.
12.Aven, T., Some considerations on reliability theory and its applications. Reliability Engineering & System Safety, 1988. 21(3): p. 215-223.
13.Colbourn, C.J., The Combinatorics of Network Reliability. 1987: Oxford University Press, Inc. 176.
14.Fei, H., et al. Reliability Evaluation of Wireless Sensor Networks Using Logistic Regression. in Communications and Mobile Computing (CMC), 2010 International Conference on. 2010.
15.Greenberg, A.G., B.D. Lubachevsky, and I. Mitrani. Unboundedly parallel simulations via recurrence relations for network and reliability problems. in Simulation Conference, 1990. Proceedings., Winter. 1990.
16.Lee, S.H., Reliability Evaluation of a Flow Network. Reliability, IEEE Transactions on, 1980. R-29(1): p. 24-26.
17.Levitin, G., Reliability evaluation for acyclic transmission networks of multi-state elements with delays. Reliability, IEEE Transactions on, 2003. 52(2): p. 231-237.
18.Lin, Y.-K. and C.-T. Yeh, Computer network reliability optimization under double-resource assignments subject to a transmission budget. Information Sciences, 2011. 181(3): p. 582-599.
19.Shier, D.R., Network reliability and algebraic structures. 1991: Clarendon Press. 144.
20.Wei-Chang, Y. and Y. Yuan-Ming, A Novel Label Universal Generating Function Method for Evaluating the One-to-all-Subsets General Multistate Information Network Reliability. Reliability, IEEE Transactions on, 2011. 60(2): p. 470-478.
21.YuKai, L., et al. Reliability Computation for Multipath Transmission in Wireless Sensor Networks. in Computational Sciences and Optimization, 2009. CSO 2009. International Joint Conference on. 2009.
22.I., U., Universal generating function. Computer and System Sciences, 1986: p. 118-129.
23.G., L., Universal generating function in reliability analysis and optimization. 2005: Springer-Verlag.
24.Wei-Chang, Y., A Convolution Universal Generating Function Method for Evaluating the Symbolic One-to-All-Target-Subset Reliability Function of Acyclic Multi-State Information Networks. Reliability, IEEE Transactions on, 2009. 58(3): p. 476-484.
25.Wei-Chang, Y., A Modified Universal Generating Function Algorithm for the Acyclic Binary-State Network Reliability. Reliability, IEEE Transactions on, 2012. 61(3): p. 702-709.
26.Wei-Chang, Y. and M. El Khadiri, A New Universal Generating Function Method for Solving the Single (d, )-Quick path Problem in Multi-state Flow Networks. Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on, 2012. 42(6): p. 1476-1484.
27.Wei-Chang, Y. and H. Xiangjian, A New Universal Generating Function Method for Estimating the Novel Multiresource Multistate Information Network Reliability. Reliability, IEEE Transactions on, 2010. 59(3): p. 528-538.
28.Forghani-elahabad, M. and N. Mahdavi-Amiri, A New Efficient Approach to Search for All Multi-State Minimal Cuts. Reliability, IEEE Transactions on, 2014. 63(1): p. 154-166.
29.Yeh, W.-C., A simple approach to search for all d-MCs of a limited-flow network. Reliability Engineering & System Safety, 2001. 71(1): p. 15-19.
30.Yeh, W.-C., Search for MC in modified networks. Computers & Operations Research, 2001. 28(2): p. 177-184.
31.Yeh, W.-C., Search for all MCs in networks with unreliable nodes and arcs. Reliability Engineering & System Safety, 2003. 79(1): p. 95-101.
32.Yeh, W.-C., Multistate-node acyclic networks reliability evaluation based on MC. Reliability Engineering & System Safety, 2003. 81(2): p. 225-231.
33.Yeh, W.-C., A simple MC-based algorithm for evaluating reliability of stochastic-flow network with unreliable nodes. Reliability Engineering & System Safety, 2004. 83(1): p. 47-55.