A Modified Universal Generating Function Algorithm for the Acyclic Binary-State Network Reliability

Network reliability is an important part of planning, designing, and controlling networks. Now, the most general binary-state network (BSN) reliability evaluation methods are based on Minimal Paths (MPs), or Minimal Cuts (MCs). The universal generating function method (UGFM) is a novel, efficient scheme for determining network reliability. Because the current best-known UGFM can only search for all MPs, it needs to be coupled with another routine such as Sum-of-Disjoint-Product method to calculate the final flow network reliability in terms of obtained MPs. In this study, a straightforward, novel UGFM is presented for calculating the acyclic BSN (ABSN) reliability between the source node and the sink node (i.e. one-to-one reliability). The proposed method is the first UGFM for the ABSN reliability problem without searching for all MPs in advance, which can reduce computational complexity. The computational complexity of the proposed algorithm is analysed, and its efficiency is well illustrated by a numerical example.

[1]  Xiangjian He,et al.  A New Universal Generating Function Method for Estimating the Novel Multiresource Multistate Information Network Reliability , 2010, IEEE Transactions on Reliability.

[2]  Wei-Chang Yeh.  A simple algorithm to search for all d-MPs with unreliable nodes , 2001, Reliab. Eng. Syst. Saf..

[3]  Wei-Chang Yeh.  Multistate-node acyclic network reliability evaluation , 2002, Reliab. Eng. Syst. Saf..

[4]  Way Kuo,et al.  Recent Advances in Optimal Reliability Allocation , 2007, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[5]  Jacek Malinowski.  Non-binary decomposition trees - a method of reliability computation for systems with known minimal paths/cuts , 2004, Reliab. Eng. Syst. Saf..

[6]  Wei-Chang Yeh.  The k-out-of-n acyclic multistate-node networks reliability evaluation using the universal generating function method , 2006, Reliab. Eng. Syst. Saf..

[7]  Terje Aven,et al.  Availability evaluation of oil/gas production and transportation systems , 1987 .

[8]  Wei-Chang Yeh,et al.  A Greedy Branch-and-Bound Inclusion-Exclusion Algorithm for Calculating the Exact Multi-State Network Reliability , 2008, IEEE Transactions on Reliability.

[9]  Wei-Chang Yeh.  Search for all d-Mincuts of a limited-flow network , 2002, Comput. Oper. Res..

[10]  Wei-Chang Yeh.  An improved sum-of-disjoint-products technique for the symbolic network reliability analysis with known minimal paths , 2007, Reliab. Eng. Syst. Saf..

[11]  Gregory Levitin,et al.  The Universal Generating Function in Reliability Analysis and Optimization , 2005 .

[12]  Gregory Levitin,et al.  Reliability evaluation for acyclic consecutively connected networks with multistate elements , 2001, Reliab. Eng. Syst. Saf..

[13]  Alistair G. Sutcliffe,et al.  Automating Scenario Analysis of Human and System Reliability , 2007, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[14]  Yuanlong Shen,et al.  A new simple algorithm for enumerating all minimal paths and cuts of a graph , 1995 .

[15]  Liudong Xing.  An Efficient Binary-Decision-Diagram-Based Approach for Network Reliability and Sensitivity Analysis , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[16]  Hoang Pham.  Guest Editorial Special Issue on Critical Reliability Challenges and Practices , 2007 .

[17]  S. Kuo,et al.  Determining terminal-pair reliability based on edge expansion diagrams using OBDD , 1999 .

[18]  Gregory Levitin,et al.  Multi-State System Reliability - Assessment, Optimization and Applications , 2003, Series on Quality, Reliability and Engineering Statistics.

[19]  N. A. Mokhles,et al.  A new technique in a cutset evaluation , 1993 .

[20]  Sayeed Ahmad.  Simple enumeration of minimal cutsets of acyclic directed graph , 1988 .

[21]  J. M. Nahman.  Minimal paths and cuts of networks exposed to common-cause failures , 1992 .

[22]  Yi-Kuei Lin,et al.  Extend the quickest path problem to the system reliability evaluation for a stochastic-flow network , 2003, Comput. Oper. Res..

[23]  D. Shier.  Network Reliability and Algebraic Structures , 1991 .

[24]  Xiaolong Wang,et al.  A Heuristic Algorithm for Reliability Modeling and Analysis of Grid Systems , 2007, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[25]  D. R. Shier,et al.  Algorithms for Generating Minimal Cutsets by Inversion , 1985, IEEE Transactions on Reliability.

[26]  Hoang Pham.  Special Issue on Critical Reliability Challenges and Practices [Guest Editorial] , 2007, IEEE Trans. Syst. Man Cybern. Part A.

[27]  Wei-Chang Yeh.  Search for minimal paths in modified networks , 2002, Reliab. Eng. Syst. Saf..

[28]  Kishor S. Trivedi,et al.  A BDD-Based Algorithm for Analysis of Multistate Systems with Multistate Components , 2003, IEEE Trans. Computers.

[29]  Sofia Cassel,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 2012 .

[30]  Wei-Chang Yeh.  Multistate network reliability evaluation under the maintenance cost constraint , 2004 .

[31]  Wei-Chang Yeh,et al.  A Simple Universal Generating Function Method to Search for All Minimal Paths in Networks , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[32]  Wei-Chang Yeh.  Search for MC in modified networks , 2001, Comput. Oper. Res..

[33]  Yung-Ruei Chang,et al.  A cut-based algorithm for reliability analysis of terminal-pair network using OBDD , 2003, Proceedings 27th Annual International Computer Software and Applications Conference. COMPAC 2003.

[34]  Charles J. Colbourn,et al.  The Combinatorics of Network Reliability , 1987 .

[35]  Yi-Kuei Lin,et al.  Performance evaluation for the logistics system in case that capacity weight varies from arcs and types of commodity , 2007 .

[36]  Yi-Kuei Lin,et al.  Reliability Evaluation for an Information Network With Node Failure Under Cost Constraint , 2007, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.