An improved algorithm for solving all d-MPs in multi-state networks

Ahuja, R.K., Magnanti, T.L. & Orlin, J.B. (1993). Network Flows–Theory, Algorithms, and Applications. Englewood Cliffs, NJ: Prentice-Hall International.

Ahuja, R.K., Kodialam, M., Mishra, A.K. & Orlin, J.B. (1997). Computational investigations of maximum flow algorithms. European Journal of Operational Research, 97: 509–542.

Aggarwa, K.K., Misra, K.B. & Gupta, J.S. (1975). A simple method for reliability evaluation of a communication system. IEEE Transaction on Communications, 23: 563–565.

Alexopoulos, C. (1995). Note on state-space decomposition methods for analyzing stochastic flow networks. IEEE Transaction on Communications, 44: 354–357.

Ball, M.O. (1993). Computational complexity of network reliability analysis an overview. IEEE Transaction on Reliability, 35: 230–239.

Bai, G.H., Zuo, M.J. & Tian, Z.G. (2015). Ordering heuristics for reliability evaluation of multistate networks. IEEE Transaction on Reliability, 64: 1015–1023.

Bai, G.H., Tian, Z.G. & Zuo, M.J. (2016). An improved algorithm for finding all minimal paths in a network. Reliability Engineering and System Safety, 150: 1–10.

Bai, G.H., Zuo, M.J. & Tian, Z.G. (2015). Search for all d-MPs for all d levels in multistate two-terminal networks. Reliability Engineering & System Safety, 142: 300–309.

Colbourn, C.J. (1987). The Combinatorics of Network Reliability. New York: Oxford University Press.

Cook, J. & Ramirez-Marquez, J.E. (2007). Two-terminal reliability analyses for a mobile ad hoc wireless network. Reliability Engineering and System Safety, 92: 821–829.

Chen, S.G. (2013). Efficiency improvement in explicit enumeration for integer programming problems. IEEE International Conference on Industrial Engineering and Engineering Management, Bangkok, Thailand, 98–100.

Chen, S.G. & Lin, Y.K. (2016). Searching for d-MPs with fast enumeration. Journal of Computational Science, 17: 139–147.

Chen, S.G. & Lin, Y.K. (2012). Search for all minimal paths in a general large flow network. IEEE Transaction on Reliability, 61: 949–956.

Chen, S.G. (2011). Search for all minimal paths in a general directed flow network with unreliable nodes. International Journal of Reliability and Quality Performance, 2: 63–70.

Doulliez, P. & Jamoulle, E. (1972). Transportation networks with random arc capacities. RAIRO, 6: 45–60.

Forghani-elahabad, M. & Mahdavi-Amiri, N. (2014). A new efficient approach to search for all multi-state minimal cuts. IEEE Transaction on Reliability, 63: 154–66.

Gebre, B.A. & Ramirez-Marquez, J.E. (2007). Element substitution algorithm for general two-terminal network reliability analyses. IIE Transaction, 39: 265–275.

Hagstrom, J.N. (1984). Note on independence of arcs in antiparallel for network flow problems. Networks, 14: 567–570.

Jane, C.C., Lin, J.S. & Yuan, J. (1993). On reliability evaluation of a limited-flow network in terms of minimal cutsets. IEEE Transaction on Reliability, 42: 354–361.

Jane, C.C & Laih, Y.W. (2008). A practical algorithm for computing multi-state two-terminal reliability. IEEE Transaction on Reliability, 57: 295–302.

Jane, C.C & Laih, Y.W. (2010). Computing multi-state two-terminal reliability through critical arc states that interrupt demand. IEEE Transaction on Reliability, 59: 338–344.

Jiang, T. & Liu, Y. (2017). Parameter inference for non-repairable multi-state system reliability models by multi-level observation sequences. Reliability Engineering and System Safety. DOI: 10.1016/J.ress.2016.11.019.

Levitin, G. (2003). The Universal Generating Function in Reliability Analysis and Optimization. London: Springer-Verlag.

Levitin, G. (2004). A universal generating function approach for the analysis of multi-state systems with dependent elements. Reliability Engineering and System Safety, 84: 285–292.

Levitin, G. & Lisnianski, A. (1999). Importance and sensitivity analysis of multi-state systems using the universal generating function method. Reliability Engineering and System Safety, 65: 271–282.

Lisnianski, A & Levitin, G. (2003). Multi-state System Reliability:Assessment, Optimization and Applications. Singapore: World Scientific.

Lin, J.S., Jane, C.C. & Yuan, J. (1995). On reliability evaluation of a capacitated-flow network in terms of minimal pathsets. Network, 25: 131–138.

Lin, Y. K. & Chang, P. C. (2011). Estimated and exact system reliabilities of a maintainable computer network. Journal of Systems Science and Systems Engineering, 20: 229–248.

Lin, Y. K. & Huang C. F. (2014). System reliability of assured accuracy rate for multi-state computer networks from service level agreements viewpoint. Journal of Systems Science and Systems Engineering, 23: 196–211.

Lin, Y. K. & Chang, P. C. (2015). Predecessor-set technique for reliability evaluation of a stochastic manufacturing system. Journal of Systems Science and Systems Engineering, 24: 190–210.

Lin, Y. K. (2001). A simple algorithm for reliability evaluation of a stochastic-flow network with node failure. Computers & Operations Research, 28: 1277–1285.

Lin, Y. K. (2002). Using minimal cuts to evaluate the system reliability of a stochastic-flow network with failures at nodes and arcs. Reliability Engineering and System Safety, 75: 41–46.

Mishra, R., Saifi, M.A. & Chaturvedi, S.K. (2015). Enumeration of minimal cutsets for directed networks with comparative reliability study for paths or cuts. Quality and Reliability Engineering International, 32: 555–565.

Mo, Y., Xing, L., Cui, L. & Si, S. (2017). MDD-based performability analysis of multi-state linear consecutive-k-out-of-n: F systems. Reliability Engineering and System Safety. DOI: 10.1016/J.ress.2016.08.027.

Niu, Y. F. & Shao, F. M. (2011). A practical bounding algorithm for computing two-terminal reliability based on decomposition technique. Computers and Mathematics with Application, 61: 2241–2246.

Niu, Y. F. & Xu, X. Z. (2012). Reliability evaluation of multi-state systems under cost consideration. Applied Mathematical Modelling, 36: 4261–4270.

Volkanovski, A., Cepin, M. & Mavko, B. (2009). Application of the fault tree analysis for assessment of power system reliability. Reliability Engineering and System Safety, 94: 1116–1127.

Wu, W. W., Ning, A. & Ning, X. X. (2008). Evaluation of the reliability of transport networks based on the stochastic flow of moving objects. Reliability Engineering and System Safety, 93: 838–844.

Ramirez, J.E. & Coit, D.W. (2005). A Monte-Carlo simulation approach for approximating multi-state two-terminal reliability. Reliability Engineering and System Safety, 87: 253–264.

Ramirez-Marquez, J. E., Coit, D. W. & Tortorella, M. (2006). A generalized multi-state-based path vector approach to multi-state two-terminal reliability. IIE Transaction, 38: 477–488.

Satitsatian, S. & Kapur, K. C. (2006). An algorithm for lower reliability bounds of multi-state two-terminal networks. IEEE Transaction on Reliability, 55: 199–206.

Yeh, W. C. (2002). A simple method to verify all d-minimal path candidates of a limited-flow network and its reliability. International Journal of Advanced Manufacturing Technology, 20: 77–81.

Yeh, W. C. (2005). A novel method for the network reliability in terms of capacitated minimum-paths without knowing minimum-paths in advance. Journal of the Operational Research Society, 56: 1235–1240.

Yeh, W. C., Bae, C. & Huang, C. L. (2015). A new cut-based algorithm for the multi-state flow network reliability problem. Reliability Engineering and System Safety, 136: 1–7.

Yeh, W. C. (2008). A fast algorithm for searching all multi-state minimal cuts. IEEE Transaction on Reliability, 57: 581–588.

Yeh, W. C. (2015). An improved sum-of-disjoint-products technique for symbolic multi-state flow network reliability. IEEE Transaction on Reliability, 64: 1185–1193.

Yeh, W. C. (2009). A simple universal generating function method to search for all minimal paths in networks. IEEE Transaction on System Man Cybernetics -Part A: System Humans, 39: 1247–1254.

Yeh, W. C. (2016). New method in searching for all minimal paths for the directed acyclic network reliability problem. IEEE Transaction on Reliability, 65: 1263–1270.

Yeh, W. C. (2017). Evaluation of the one-to-all-target-subsets reliability of a novel deterioration-effect acyclic multi-state information network. Reliability Engineering and System Safety. DOI: 10.1016/J.ress.2016.11.012.

Zuo, M. J., Tian, Z. G. & Huang, H. Z. (2007). An efficient method for reliability evaluation of multistate networks given all minimal path vectors. IIE Transaction, 39: 811–817.

Zhou, Y. & Meng, Q. (2007). Improving efficiency of solving d-MC problem in stochastic-flow network. Reliability Engineering and System Safety, 92: 30–39.