{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:21:50Z","timestamp":1753888910457,"version":"3.41.2"},"reference-count":24,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T00:00:00Z","timestamp":1722988800000},"content-version":"vor","delay-in-days":219,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007414","name":"Qassim University","doi-asserted-by":"publisher","award":["QU-APC-2024-9\/1"],"award-info":[{"award-number":["QU-APC-2024-9\/1"]}],"id":[{"id":"10.13039\/501100007414","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:p>This paper derives and evaluates the reliability measures for a model pumping system composed of six subsystems linked in series: subsystems 1, 2, and 6, each comprising one unit, while subsystems 3 and 5 each contain three units operating in parallel. Subsystem 4 contains three units effectively operating in series. Unit failure rates are assumed to be constant, while repair rates are modeled by either a general distribution or, in the event of system failure, a Gumbel\u2013Hougaard copula. The Laplace transform and additional supplementary variable approaches are employed to solve the system. The conventional measures of reliability are computed for a range of parameter values and as functions of time. In addition, tables are presented containing parameters for different cases, accompanied by a discussion of how they were chosen and their impact on the results.<\/jats:p>","DOI":"10.1155\/2024\/9559221","type":"journal-article","created":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T10:51:59Z","timestamp":1723027919000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analyzing the Reliability of a Pumping System through the Application of Copula Analysis"],"prefix":"10.1155","volume":"2024","author":[{"given":"Elsayed","family":"Elshoubary","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1466-8821","authenticated-orcid":false,"given":"Taha","family":"Radwan","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2024,8,7]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1108\/IJQRM-12-2018-0322"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0026-2714(93)90014-p"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1142\/s021853930800309x"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1108\/ijqrm-06-2016-0085"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1108\/IJQRM-03-2021-0071"},{"key":"e_1_2_9_6_2","first-page":"28","article-title":"Reliability and cost-benefit analysis of the 2-out-of-3 redundant system with the general distribution of repair and waiting time","volume":"4","author":"Malik S. 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