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In this article, we develop a formula for the reliability of the most reliable maximal series\u2010parallel networks. The most reliable maximal series\u2010parallel networks are those maximal series\u2010parallel networks with the minimum number of vertices of degree 2, independent of many of the simpler reliability estimates. A two\u2010dimensional recurrence relating networks of varying sizes and edge deficiencies provides a generating function which in turn is exploited to give a simple closed expression for reliability.<\/jats:p>","DOI":"10.1002\/net.3230150104","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T18:49:26Z","timestamp":1178909366000},"page":"27-32","source":"Crossref","is-referenced-by-count":18,"title":["The most reliable series\u2010parallel networks"],"prefix":"10.1002","volume":"15","author":[{"given":"Eric M.","family":"Neufeld","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Charles J.","family":"Colbourn","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230100206"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230130210"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230110304"},{"key":"e_1_2_1_5_2","first-page":"444","article-title":"Connectivity of probabilistic networks","volume":"28","author":"Kel'mans A. K.","year":"1967","journal-title":"Automation and Remote Control"},{"key":"e_1_2_1_6_2","first-page":"627","article-title":"The analysis of redundancy networks","volume":"39","author":"Moskowitz F.","year":"1958","journal-title":"AIEE Trans. Commun. Electron."},{"key":"e_1_2_1_7_2","volume-title":"Introduction to Combinatorial Mathematics","author":"Liu C. L.","year":"1968"},{"key":"e_1_2_1_8_2","unstructured":"E. M.Neufeld andC. J.Colbourn The construction of reliable series\u2010parallel networks.Congressus Numeratium in press."},{"key":"e_1_2_1_9_2","unstructured":"E. M.Neufeld Construction of reliable series\u2010parallel networks. M. Sc. thesis University of Saskatchewan (1983)."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(74)90042-9"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230110402"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1137\/0132031"},{"key":"e_1_2_1_13_2","doi-asserted-by":"crossref","unstructured":"A.Satyanarayana andR. K.Wood Polygon\u2010to\u2010chain reductions and network reliability. Research Report 82\u20104 Operations Research Center University of California at Berkeley (1982).","DOI":"10.21236\/ADA116276"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1137\/0208032"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230130202"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/0026-2714(83)91008-9"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCOM.1972.1091214"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230150104","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230150104","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T15:44:55Z","timestamp":1697816695000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230150104"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,3]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1985,3]]}},"alternative-id":["10.1002\/net.3230150104"],"URL":"https:\/\/doi.org\/10.1002\/net.3230150104","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1985,3]]}}}