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System Reliability Analysis in the Presence of Dependent Component Failures

Published online by Cambridge University Press:  27 July 2009

Jane N. Hagstrom
Affiliation:
College of Business Administration University of lllinois at Chicago Chicago, lllinois 60680
King-Tim Mak
Affiliation:
College of Business Administration University of lllinois at Chicago Chicago, lllinois 60680

Abstract

We consider the impact that the introduction of dependent component failures has on the computational difficulty of system reliability analysis. We develop general strategies for computing system reliability when components are subject to dependent failures. In the process, we identify a significant number of cases where computing the system reliability in the presence of dependent failures is not significantly harder than writing down the joint probability distribution and computing the system reliability when the components fail independently.

Type
Articles
Copyright
Copyright © Cambridge University Press 1987

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References

Ball, M.O. (1980). Complexity of network reliability computations. Networks 10:153165.CrossRefGoogle Scholar
Ball, M.O. (1979). Computing network reliability. Operations Research 27:823838.CrossRefGoogle Scholar
Ball, M.O. & Van Slyke, R.M. (1977). Backtracking algorithms for network reliability analysis. Ann. of Discrete Math. 1:4964.CrossRefGoogle Scholar
Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing. New York: Holt, Rinehart, and Winston.Google Scholar
Billinton, R., Medicherla, T.K.P., & Sachdev, M.S. (1978). Common-cause outages in multiple circuit transmission lines. IEEE Trans. on Reliability R-27:128131.CrossRefGoogle Scholar
Birnbaum, Z.W., Esary, J., & Saunders, S.C. (1961). Multicomponent systems and structures and their reliability. Technometrics 3:5577.CrossRefGoogle Scholar
Buzacott, J.A. (1987). Node partition formula for directed graph reliability. Networks 17:227240.CrossRefGoogle Scholar
Buzacott, J.A. (1983). A recursive algorithm for directed graph reliability. Networks 13:241246.CrossRefGoogle Scholar
El-Neweihi, E. (1980). A relationship between partial derivatives of the reliability function of a coherent system and its minimal path (cut) sets. Math, of Operations Research 5:553555.Google Scholar
Fleming, K.N., Mosleh, A., & Kelley, Jr, , A.P. (1983). On the analysis of dependent failures in risk assessment and reliability evaluation. Nuclear Safety 24:637657.Google Scholar
Hagstrom, J.N. (1986). Computational complexity issues in determining network reliability in the presence of correlated component failures. Technical report 86−22, College of Business Administration, University of Illinois, Chicago 60680.Google Scholar
Hagstrom, J.N. & Mak, K. (1986). Computing network reliability with dependent failures. In Vogt, W.G. & Mickle, M.H. (eds.), Proceedings of the 17th Annual Modeling and Simulation Conference. Pittsburgh, Pennsylvania, 04: 17931798.Google Scholar
Hammer, P.L. & Rudeanu, S. (1968). Boolean methods in operations research and related areas. New York: Springer-Verlag.CrossRefGoogle Scholar
Knuth, D.E. (1976). Big omicron and big omega and big theta. SIGACT News 0406: 1824.Google Scholar
Mirchandani, P.B. (1976). Shortest distance and reliability of probabilistic networks. Computers and Operations Research 3:347355.CrossRefGoogle Scholar
Satyanarayana, A. (1982). A unified formula for the analysis of some network reliability problems. IEEE Trans. on Reliability R-31:2332.CrossRefGoogle Scholar
Satyanarayana, A. & Prabhakar, A. (1978). New topological formula and rapid algorithm for reliability analysis of complex networks. IEEE Trans. on Reliability R-27:82–100.CrossRefGoogle Scholar
Shier, D.R. & Spragins, J.D. (1985). Exact and approximate dependent failure reliability models for telecommunications networks. IEEE Proceedings INFOCOMWashington, D.C., 03:200204.Google Scholar
Valdes, J., Tarjan, R.E., & Lawler, E.L. (1982). The recognition of series-parallel digraphs. SIAM J. on Computing 11:298313.CrossRefGoogle Scholar
Wood, R.K. (1980). Efficient calculation of the reliability of lifeline networks subject to seismic risk. Technical report ORC8O-13, Operations Research Center, University of California, Berkeley 94720.Google Scholar