Abstract
Probabilistic reliability measures for the performance of water distribution networks are developed and analytical methods for their computation explained. The paper begins with a review of reliability considerations and measures for water supply systems, making use of similar notions in other fields. It classifies reliability analyses according to the level of detail with which the water system is modeled, and then concentrates on methods relevant to networks. Two probabilistic measures, reachability (connection of a specific demand node to at least one source) and connectivity, are explored for use in water distribution systems. Two algorithms for their computation are presented, one for series‐parallel networks and one for general networks. These measures are computed for two systems, each with ten nodes. Additionally, the probability that a given point receives sufficient supply is proposed for use as a reliability measure. For the calculation of this measure, an algorithm is provided that combines a capacitated network algorithm with a method to efficiently search through network configurations involving multiple link failures. This measure is calculated for the two sample systems.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Agrawal, A., and Barlow, R. E. (1984). “A survey of network reliability and domination theory.” Oper. Res., 32(3), 478–492.
2.
Agrawal, A., and Satyanarayana, A. (1984). “An O(IEI) time algorithm for computing the reliability of a class of directed networks.” Oper. Res., 32(3), 493–515.
3.
Aneja, Y. P., and Nair, K. P. K. (1980). “Maximal expected flow in a network subject to arc failures.” Networks, 10(1), 45–57.
4.
Ang, A. H.‐S., and Tang, W. H. (1984). Probability concepts in engineering planning and design. Volume II: decision, risk, and reliability. John Wiley and Sons, New York, N.Y.
5.
Ball, M. O. (1980). “Complexity of network reliability calculations.” Networks, 10(2), 153–165.
6.
Ball, M. O., and Provan, J. S. (1983). “Calculating bounds on reachability and connectedness in stochastic networks.” Networks, 13(2), 253–278.
7.
Barlow, R. E., and Proschan, F. (1975). Statistical theory of reliability and life testing: probability models. Holt, Rinehart, and Winston, New York, N.Y.
8.
Billinton, R. (1972). “Bibliography on the application of probability methods in power system reliability evaluation.” IEEE Trans. Power Appar. Syst., PAS‐91(2), 649–660.
9.
Billinton, R., and Allan, R. N. (1983). Reliability evaluation of engineering systems: concepts and techniques. Plenum Press, New York, N.Y.
10.
Billinton, R., and Allan, R. N. (1984). Reliability evaluation of power systems. Plenum Press, New York, N.Y.
11.
Bradley, S. P., Hax, A. C., and Magnanti, T. L. (1977). Applied mathematical programming. Addison‐Wesley, Reading, Mass.
12.
Buzacott, J. A. (1980). “A recursive algorithm for finding reliability measures related to the connection of nodes in a graph.” Networks, 10(4), 311–327.
13.
Carey, M., and Hendrickson, C. (1984). “Bounds on expected performance of networks with links subject to failure.” Networks, 14(3), 439–456.
14.
Charles Howard and Associates, Ltd. (1984). Water distribution network analysis: SDP8 user's manual. Charles Howard and Associates, Ltd., Victoria, B.C., Canada.
15.
Damelin, E., Shamir, U., and Arad, N. (1972). “Engineering and economic evaluation of the reliability of water supply.” Water Resour. Res., 8(4), 861–877.
16.
De Jong, J. J., Snijders, J. A. C., and Wedmijer, A. (1983). “Reliability of the Rotterdam drinking water system.” 16(1), 10–16 (in Dutch).
17.
Endrenyi, J. (1978). Reliability modeling in electric power systems. Wiley Interscience Publications, New York, N.Y.
18.
Henley, E. J., and Kumamoto, H. (1981). Reliability engineering and risk assessment. Prentice Hall, Inc., Englewood Cliffs, N.J.
19.
Hobbs, B. F. (1985a). “Reliability analysis of urban water supply.” Computer applications in water resources, H. Tourno, ed., ASCE, New York, N.Y.
20.
Hobbs, B. F. (1985b). “Reliability analysis of water system capacity.” Hydrology and hydraulics in the small computer age, W. Waldrop, ed., ASCE, New York, N.Y.
21.
IEEE Subcommittee on the Application of Probability Methods. (1978). “Bibliography on the application of probability methods in power system reliability evaluation.” IEEE Trans. Power Appar. Syst., PAS‐97(6), 2235–2242.
22.
Johnson, R. (1984). “Network reliability and acyclic orientation.” Networks, 14(4), 489–505.
23.
Lee, S. H. (1980). “.Reliability evaluation of a flow network.” IEEE Trans. Reliab., R‐29(1), 24–26.
24.
Lie, C. H., Hwang, C. L., and Tillman, F. A. (1977). “Availability of maintained systems: a state‐of‐the‐art survey.” AIEE Trans., 9(3), 247–259.
25.
Mays, L. W., and Cullinane, M. J. (1986). A review and evaluation of reliability concepts for design of water distributions systems. Miscellaneous Paper EL‐86‐1, U.S. Engineer Waterways Experiment Station, Vicksburg, Miss.
26.
O'Day, K. (1982). “Organizing and analyzing leak and break data for making main replacement decisions.” J. Am. Water Works Assoc., 74(11). 588–594.
27.
Provan, J. S., and Ball, M. O. (1983). “The complexity of counting cuts and of computing the probability that a graph is connected.” SIAM J. Comput., 12(4), 777–788.
28.
Provan, J. S., and Ball, M. O. (1984). “Computing network reliability in time polynomial in the number of cuts.” Oper. Res., 32(3), 516–526.
29.
Rosenthal, A. (1977). “Computing the reliability of complex networks.” SIAM J. Appl. Math., 32(2), 384–393.
30.
Rosenthal, A. (1981). “Series‐parallel reduction for difficult measures of network reliability.” Networks, 11(4), 323–334.
31.
Satyanarayana, A., and Wood, R. K. (1982). “Polygon‐to‐chain reductions and network reliability.” ORC 82‐4, Operations Research Center, University of California, Berkeley, Calif.
32.
Shamir, U., and Howard, C. D. D. (1968). “Water distribution systems analysis.” J. Hydr. Div., ASCE, 94(HY1), 219–234.
33.
Shamir, U., and Howard, C. D. D. (1981). “Water supply reliability theory.” J. Am. Water Works Assoc., 73(7), 379–384.
34.
Shamir, U., and Howard, C. D. D. (1985). “Reliability and risk assessment for water supply systems.” Computer applications in water resources, H. Tourno, ed., ASCE, New York, N.Y.
35.
Shogan, A. W. (1982). “Modular decomposition and reliability computation in stochastic transportation networks having cutnodes.” Networks, 12(3), 255–275.
36.
Tangena, B. H., and Koster, P. K. (1983). “Reliability of drinking water supply systems.” Proc. Int. Water Supply Assoc. Specialized Conference on Security in Water Supply, Int. Water Supply Assoc., Brussels, Belgium.
37.
Valiant, L. G. (1979). “The complexity of enumeration and reliability problems.” SIAM J. Comput., 8(3), 410–421.
38.
Wagner, J. M., Shamir, U., and Marks, D. H. (1986). “Reliability of water distribution systems.” R86‐18, Ralph M. Parsons Laboratory, Massachusetts Institute of Technology, Cambridge, Mass.
39.
Wagner, J. M., Shamir, U., and Marks, D. H. (1988). “Water distribution reliability: simulation methods.” J. Water Resour. Plng. and Mgmt., ASCE, 114(3), 276–294.
40.
Walski, T. M. (1984). Analysis of water distribution systems. Van Nostrand Reinhold Co., New York, N.Y.
41.
Walski, T. M. (1985). “State‐of‐the‐art pipe network optimization,” Computer applications in water resources, H. Tourno, ed., ASCE, New York, N.Y.
42.
Walski, T. M., et al. (1987). “Battle of the network models: epilogue.” J. Water Resour. Plng. and Mgmt., ASCE, 113(2), 191–203.
43.
Willie, R. R. (1978). “Computer‐aided fault tree analysis,” ORC 78‐14, Operations Research Center, University of California, Berkeley, Calif.
44.
Willie, R. R. (1979). Combinatorial methods for reliability analysis of flow networks.” Mathematical theory of power system reliability evaluation, Memorandum No. UCBIERL M79I67, Electronics Research Laboratory, Univ. of Calif., Berkeley, Calif.
Information & Authors
Information
Published In
Copyright
Copyright © 1988 ASCE.
History
Published online: May 1, 1988
Published in print: May 1988
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.