{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,22]],"date-time":"2025-11-22T11:40:57Z","timestamp":1763811657972,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T00:00:00Z","timestamp":1740355200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Graduate Studies and Scientific Research at Qassim University","award":["QU-APC-2025"],"award-info":[{"award-number":["QU-APC-2025"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper proposes a system made up of four subsystems connected in sequence. The first and third subsystems each have one unit, the second has two, and the fourth has three. Every subsystem operates in parallel and is governed by the K-Out-of-n:G rule. Nonetheless, each subsystem needs at least one operational unit in order for the system to work. While a unit\u2019s failure has an exponential distribution, repair is simulated using a general distribution and a distribution from the Gumbel\u2013Hougaard family of copula. This study\u2019s primary objective is to assess and contrast the system performance while our system is running under these two different repair policies. The problem is solved by combining the supplementary variable technique with Laplace transforms. We use reliability metrics to assess system performance. The second objective of this study is to present a reduction approach plan aimed at improving the overall reliability metrics of our system.<\/jats:p>","DOI":"10.3390\/axioms14030163","type":"journal-article","created":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T05:36:47Z","timestamp":1740375407000},"page":"163","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Reliability and Performance Optimization of Multi-Subsystem Systems Using Copula-Based Repair"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8099-8768","authenticated-orcid":false,"given":"Elsayed E.","family":"Elshoubary","sequence":"first","affiliation":[{"name":"Pyramids Higher Institute Engineering and Technology, Cairo 12573, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1466-8821","authenticated-orcid":false,"given":"Taha","family":"Radwan","sequence":"additional","affiliation":[{"name":"Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3246-1293","authenticated-orcid":false,"given":"Rasha Abd El-Wahab","family":"Attwa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,24]]},"reference":[{"key":"ref_1","first-page":"115","article-title":"Performance Evaluation of a Complex Reverse Osmosis Machine System in Water Purification using Reliability, Availability, Maintainability and Dependability Analysis","volume":"16","author":"Maihulla","year":"2021","journal-title":"Reliab. Theory Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4807","DOI":"10.1007\/s12206-016-0953-4","article-title":"Multi objective optimization of reverse osmosis desalination plant with energy approach","volume":"30","author":"Sadri","year":"2016","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.desal.2008.12.023","article-title":"Artificial neural network model for optimizing operation of a seawater reverse osmosis desalination plant","volume":"247","author":"Lee","year":"2009","journal-title":"Desalination"},{"key":"ref_4","unstructured":"Ezugbe, E.O., and Rathilal, S. (2020). Membrane technologies in wastewater treatment. Membranes, 5."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1080\/01919510701864031","article-title":"Evaluation of Ozone Pretreatment on Flux Parameters of Reverse Osmosis for Surface Water Treatment","volume":"30","author":"Shalana","year":"2008","journal-title":"Ozone Sci. Eng."},{"key":"ref_6","first-page":"812","article-title":"Performance analysis of complex system in series configuration under different failure and repair discipline using copula","volume":"23","author":"Gulati","year":"2016","journal-title":"Int. J. Reliab. Qual. Saf. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3337","DOI":"10.1007\/s13369-013-0908-3","article-title":"A comparative analysis of three redundant unit systems with three types of failures","volume":"39","author":"Yusuf","year":"2014","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_8","first-page":"58","article-title":"Meantime to system failure analysis of a linear consecutive 3-out-of-5 warm standby system in the presence of common cause failure","volume":"4","author":"Yusuf","year":"2014","journal-title":"J. Math. Comput. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1080\/24754269.2021.1971489","article-title":"Time-dependent reliability analysis for repairable consecutive k-out-of-n: F system","volume":"6","author":"Gokdere","year":"2021","journal-title":"Stat. Theory Rel. Fields"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1402","DOI":"10.46481\/jnsps.2023.1402","article-title":"Effect of reduction method on the performance a software defined network system using Gumbel Hougaard family copula distribution","volume":"5","author":"Elshoubary","year":"2023","journal-title":"J. N Soc. Phys. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Elshoubary, E.E., and Radwan, T. (2024). Studying the Efficiency of the Apache Kafka System Using the Reduction Method, and Its Effectiveness in Terms of Reliability Metrics Subject to a Copula Approach. Appl. Sci., 14.","DOI":"10.3390\/app14156758"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1007\/s40430-014-0227-y","article-title":"Performability analysis of a system under 1-out-of-2: G scheme with perfect reworking","volume":"37","author":"Ram","year":"2015","journal-title":"J. Braj. Soc. Mech. Sci. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1002","DOI":"10.1007\/s13198-019-00829-2","article-title":"Availability and reliability of a parallel system under imperfect repair and replacement: Analysis and cost optimization","volume":"10","author":"Temraz","year":"2019","journal-title":"Int. J. Syst. Assur. Eng. Manag."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1504\/IJCSYSE.2021.113261","article-title":"Reliability analysis of (n) clients system under startopology and copula linguistic approach","volume":"6","author":"Singh","year":"2021","journal-title":"Int. J. Comput. Syst. Eng."},{"key":"ref_15","first-page":"11","article-title":"Reliability modeling and performance analysis of reverse osmosis machine in water purification using Gumbel\u2013Hougaard family copula","volume":"12","author":"Anas","year":"2022","journal-title":"Life Cycle Reliab. Saf. Eng."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/3\/163\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:41:07Z","timestamp":1760028067000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/3\/163"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,24]]},"references-count":15,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["axioms14030163"],"URL":"https:\/\/doi.org\/10.3390\/axioms14030163","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,2,24]]}}}