{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T16:57:35Z","timestamp":1780937855883,"version":"3.54.1"},"reference-count":51,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52572419"],"award-info":[{"award-number":["52572419"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008867","name":"Department of Education of Zhejiang Province","doi-asserted-by":"publisher","award":["Y202454518"],"award-info":[{"award-number":["Y202454518"]}],"id":[{"id":"10.13039\/501100008867","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Reliability Engineering & System Safety"],"published-print":{"date-parts":[[2026,11]]},"DOI":"10.1016\/j.ress.2026.112759","type":"journal-article","created":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T13:17:10Z","timestamp":1776172630000},"page":"112759","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"P1","title":["A novel framework for the reliability modelling and availability assessment of multi-state performance-sharing systems"],"prefix":"10.1016","volume":"275","author":[{"given":"Faqun","family":"Qi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongdan","family":"Ding","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiajia","family":"Ni","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mengmeng","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.ress.2026.112759_bib0001","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2019.106613","article-title":"Optimal configuration of a power grid system with a dynamic performance sharing mechanism","volume":"193","author":"Yan","year":"2020","journal-title":"Reliab Eng Syst Saf"},{"issue":"4","key":"10.1016\/j.ress.2026.112759_bib0002","doi-asserted-by":"crossref","first-page":"1555","DOI":"10.1109\/TR.2021.3111031","article-title":"Reliability of a distributed computing system with performance sharing","volume":"71","author":"Xiao","year":"2021","journal-title":"IEEE Trans Reliab"},{"key":"10.1016\/j.ress.2026.112759_bib0003","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2023.109661","article-title":"Designing preventive maintenance for multi-state systems with performance sharing","volume":"241","author":"Wu","year":"2024","journal-title":"Reliab Eng Syst Saf"},{"issue":"7","key":"10.1016\/j.ress.2026.112759_bib0004","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1080\/0740817X.2010.523770","article-title":"Reliability of multi-state systems with common bus performance sharing","volume":"43","author":"Levitin","year":"2011","journal-title":"Iie Trans"},{"key":"10.1016\/j.ress.2026.112759_bib0005","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.ress.2018.01.012","article-title":"Reliability evaluation of multi-state series systems with performance sharing","volume":"173","author":"Wang","year":"2018","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0006","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.ress.2016.09.008","article-title":"Of multi-state systems with a performance sharing group of limited size","volume":"166","author":"Peng","year":"2017","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0007","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2024.110144","article-title":"Reliability modeling of k-out-of-n: f balanced systems with common bus performance sharing","volume":"248","author":"Zhao","year":"2024","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0008","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/j.cie.2018.07.034","article-title":"Reliability analysis of multi-state k-out-of-n: g system with common bus performance sharing","volume":"124","author":"Zhao","year":"2018","journal-title":"Comput Ind Eng"},{"key":"10.1016\/j.ress.2026.112759_bib0009","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2025.110859","article-title":"Reliability analysis of weighted k-out-of-n: g performance sharing systems with multiple transmission loss levels","volume":"257","author":"Wu","year":"2025","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0010","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2025.116704","article-title":"Reliability evaluation of multi-state (k1, k2,\u2026, km)-out-of-(n1, n2,\u2026, nm) system with common bus performance sharing","volume":"470","author":"Shi","year":"2025","journal-title":"J Comput Appl Math"},{"key":"10.1016\/j.ress.2026.112759_bib0011","doi-asserted-by":"crossref","DOI":"10.1016\/j.cie.2020.107092","article-title":"Reliability evaluation of consecutive-k-out-of-n: f systems with two performance sharing groups","volume":"153","author":"Wu","year":"2021","journal-title":"Comput Ind Eng"},{"key":"10.1016\/j.ress.2026.112759_bib0012","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2025.111024","article-title":"Availability analysis of phase mission weighted components system with common bus performance sharing","volume":"260","author":"Bhatt","year":"2025","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0013","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.ress.2015.12.001","article-title":"Optimal loading and protection of multi-state systems considering performance sharing mechanism","volume":"149","author":"Xiao","year":"2016","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0014","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2020.106900","article-title":"Optimal design of a linear sliding window system with consideration of performance sharing","volume":"198","author":"Xiao","year":"2020","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0015","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2025.130935","article-title":"Availability assessment of demand-driven multi-state phased-mission system with performance sharing under reconfiguration mechanism","volume":"305","author":"Hu","year":"2026","journal-title":"Expert Syst Appl"},{"key":"10.1016\/j.ress.2026.112759_bib0016","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2021.108003","article-title":"Reliability evaluation of a k-out-of-n (G)-subsystem based multi-state phased mission system with common bus performance sharing subjected to common cause failures","volume":"216","author":"Cheng","year":"2021","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0017","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2020.106917","article-title":"Reliability assessment of multi-state phased mission systems with common bus performance sharing considering transmission loss and performance storage","volume":"199","author":"Cheng","year":"2020","journal-title":"Reliab Eng Syst Saf"},{"issue":"6","key":"10.1016\/j.ress.2026.112759_bib0018","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1002\/nav.21922","article-title":"Reliability of a two-dimensional demand-based networked system with multistate components","volume":"67","author":"Xiao","year":"2020","journal-title":"Nav Res Logist"},{"key":"10.1016\/j.ress.2026.112759_bib0019","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1016\/j.ress.2019.04.029","article-title":"Reliability evaluation of multi-state series-parallel systems with common bus performance sharing considering transmission loss","volume":"189","author":"Qiu","year":"2019","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0020","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2025.111093","article-title":"Graph-based reliability evaluation of a reconfigurable multi-stage system using sequential unconnected path sets","volume":"261","author":"Yang","year":"2025","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0021","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.cie.2014.03.014","article-title":"Optimal allocation and maintenance of multi-state elements in series\u2013parallel systems with common bus performance sharing","volume":"72","author":"Xiao","year":"2014","journal-title":"Comput Ind Eng"},{"key":"10.1016\/j.ress.2026.112759_bib0022","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2025.112070","article-title":"Reliability analysis of a complex series-parallel performance sharing system with performance excess failure and storage units","author":"Gu","year":"2026","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0023","doi-asserted-by":"crossref","DOI":"10.1016\/j.cie.2020.106991","article-title":"Reliability analysis for k-out-of-(n+1): g star configuration multi-state systems with performance sharing","volume":"152","author":"Su","year":"2021","journal-title":"Comput Ind Eng"},{"key":"10.1016\/j.ress.2026.112759_bib0024","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2022.108556","article-title":"Reliability optimization of multi-state networks in a star configuration with bi-level performance sharing mechanism and transmission losses","volume":"226","author":"Azhdari","year":"2022","journal-title":"Reliab Eng Syst Saf"},{"issue":"7","key":"10.1016\/j.ress.2026.112759_bib0025","doi-asserted-by":"crossref","first-page":"2623","DOI":"10.1002\/qre.1963","article-title":"A study of reliability of multi-state systems with two performance sharing groups","volume":"32","author":"Peng","year":"2016","journal-title":"Qual Reliab Eng Int"},{"issue":"4","key":"10.1016\/j.ress.2026.112759_bib0026","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1080\/01605682.2018.1448697","article-title":"Optimal component allocation in a multi-state system with hierarchical performance sharing groups","volume":"70","author":"Peng","year":"2019","journal-title":"J Oper Res Soc"},{"key":"10.1016\/j.ress.2026.112759_bib0027","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2023.109580","article-title":"Reliability optimization of multi-state systems with two performance sharing groups","volume":"241","author":"Gu","year":"2024","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0028","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.ress.2014.07.017","article-title":"Reliability analysis of repairable multi-state system with common bus performance sharing","volume":"132","author":"Yu","year":"2014","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0029","doi-asserted-by":"crossref","first-page":"88820","DOI":"10.1109\/ACCESS.2021.3090405","article-title":"Multi-state system reliability evaluation and component allocation optimization under multi-level performance sharing","volume":"9","author":"Huang","year":"2021","journal-title":"IEEE Access"},{"key":"10.1016\/j.ress.2026.112759_bib0030","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/j.ress.2019.05.007","article-title":"Reliability of capacitated systems with performance sharing mechanism","volume":"189","author":"Wu","year":"2019","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0031","article-title":"Optimal mission abort policy for a system subject to dependent deterioration and shock failures","volume":"265","author":"Zhang","year":"2025","journal-title":"Reliab Eng Syst Saf"},{"issue":"11","key":"10.1016\/j.ress.2026.112759_bib0032","doi-asserted-by":"crossref","first-page":"1060","DOI":"10.1080\/24725854.2021.1972184","article-title":"Reliability assessment of multi-state performance sharing systems with transmission loss and random shocks","volume":"54","author":"Wu","year":"2022","journal-title":"IISE Trans"},{"key":"10.1016\/j.ress.2026.112759_bib0033","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.ress.2019.04.010","article-title":"Optimal mission abort policy for systems subject to random shocks based on virtual age process","volume":"189","author":"Qiu","year":"2019","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0034","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2024.110531","article-title":"A multi-valued decision diagrams-based method for reliability analysis of performance-sharing k-out-of-n: g system considering component degradation","volume":"253","author":"Zhang","year":"2025","journal-title":"Reliab Eng Syst Saf"},{"issue":"5","key":"10.1016\/j.ress.2026.112759_bib0035","first-page":"1134","article-title":"MDD-based reliability analysis of multi-state system with common bus performance sharing","volume":"239","author":"Zhang","year":"2025","journal-title":"Proc Inst Mech Eng O: J Risk Reliab"},{"key":"10.1016\/j.ress.2026.112759_bib0036","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.fss.2020.08.013","article-title":"A fuzzy universal generating function-based method for the reliability evaluation of series systems with performance sharing between adjacent units under parametric uncertainty","volume":"424","author":"Qiu","year":"2021","journal-title":"Fuzzy Sets Syst"},{"key":"10.1016\/j.ress.2026.112759_bib0037","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2020.107139","article-title":"Reliability evaluation of power systems with multi-state warm standby and multi-state performance sharing mechanism","volume":"204","author":"Jia","year":"2020","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0038","article-title":"Semi-supervised cross-domain fault diagnosis via contrastive pre-training and annotation-efficient alignment strategy","volume":"50","author":"Yang","year":"2026","journal-title":"J Ind Inf Integr"},{"key":"10.1016\/j.ress.2026.112759_bib0039","doi-asserted-by":"crossref","DOI":"10.1016\/j.cie.2025.110893","article-title":"An evidence-based likelihood approach for the reliability of a complex system with overlapped failure data","volume":"201","author":"Yang","year":"2025","journal-title":"Comput Ind Eng"},{"key":"10.1016\/j.ress.2026.112759_bib0040","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.ress.2019.04.007","article-title":"Dynamic availability and performance deficiency of common bus systems with imperfectly repairable components","volume":"189","author":"Levitin","year":"2019","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0041","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2023.109412","article-title":"Inspection interval optimization of a weighted-K-out-of-N system with identical multi-state load-sharing components","volume":"238","author":"Sharifi","year":"2023","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0042","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/j.cie.2019.07.030","article-title":"Trade-off between maintenance and protection for multi-state performance sharing systems with transmission loss","volume":"136","author":"Yi","year":"2019","journal-title":"Comput Ind Eng"},{"key":"10.1016\/j.ress.2026.112759_bib0043","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2022.108910","article-title":"Performance-based maintenance analysis and resource allocation in irrigation networks","volume":"230","author":"Dui","year":"2023","journal-title":"Reliab Eng Syst Saf"},{"issue":"7","key":"10.1016\/j.ress.2026.112759_bib0044","doi-asserted-by":"crossref","first-page":"3675","DOI":"10.1002\/qre.3610","article-title":"Optimal resource allocation in common bus performance sharing systems with transmission loss","volume":"40","author":"Gu","year":"2024","journal-title":"Qual Reliab Eng Int"},{"key":"10.1016\/j.ress.2026.112759_bib0045","article-title":"Reliability analysis of a capacitated series-parallel multi-state system subject to performance sharing mechanism and transmission loss","author":"Zhang","year":"2025","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0046","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2021.107865","article-title":"Reliability analysis of performance-based balanced systems with common bus performance sharing","volume":"215","author":"Wu","year":"2021","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0047","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2025.111040","article-title":"Resilience modeling and evaluation of multi-state system with common bus performance sharing under dynamic reconfiguration","volume":"260","author":"Hu","year":"2025","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112759_bib0048","doi-asserted-by":"crossref","DOI":"10.1016\/j.cie.2026.111814","article-title":"Importance measured-based maintenance strategy for systems with auxiliary subsystems subject to degradation dependence","volume":"213","author":"Qi","year":"2026","journal-title":"Comput Ind Eng"},{"key":"10.1016\/j.ress.2026.112759_bib0049","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2023.109133","article-title":"Reliability assessment of performance-based balanced systems with rebalancing mechanisms","volume":"233","author":"Tian","year":"2023","journal-title":"Reliab Eng Syst Saf"},{"issue":"3","key":"10.1016\/j.ress.2026.112759_bib0050","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1002\/qre.3465","article-title":"A novel condition-based maintenance policy considering imperfect switching for warm standby systems","volume":"40","author":"Qi","year":"2024","journal-title":"Qual Reliab Eng Int"},{"issue":"5","key":"10.1016\/j.ress.2026.112759_bib0051","doi-asserted-by":"crossref","first-page":"2423","DOI":"10.1002\/qre.3550","article-title":"Optimal maintenance policy considering imperfect switching for a multi-state warm standby system","volume":"40","author":"Qi","year":"2024","journal-title":"Qual Reliab Eng Int"}],"container-title":["Reliability Engineering & System Safety"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0951832026005703?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0951832026005703?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T15:57:50Z","timestamp":1780934270000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0951832026005703"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,11]]},"references-count":51,"alternative-id":["S0951832026005703"],"URL":"https:\/\/doi.org\/10.1016\/j.ress.2026.112759","relation":{},"ISSN":["0951-8320"],"issn-type":[{"value":"0951-8320","type":"print"}],"subject":[],"published":{"date-parts":[[2026,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A novel framework for the reliability modelling and availability assessment of multi-state performance-sharing systems","name":"articletitle","label":"Article Title"},{"value":"Reliability Engineering & System Safety","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.ress.2026.112759","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"112759"}}