{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T18:07:42Z","timestamp":1778782062244,"version":"3.51.4"},"reference-count":33,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Reliability Engineering & System Safety"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.ress.2026.112369","type":"journal-article","created":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T23:34:15Z","timestamp":1770507255000},"page":"112369","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Resilience analysis of four-state engineering systems under the framework of continuous-time Markov chain model"],"prefix":"10.1016","volume":"274","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8278-3878","authenticated-orcid":false,"given":"Xiaohu","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaonan","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-7297-3289","authenticated-orcid":false,"given":"Jiajie","family":"Lu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.ress.2026.112369_bib0001","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1146\/annurev.es.04.110173.000245","article-title":"Resilience and stability of ecological systems","volume":"4","author":"Holling","year":"1973","journal-title":"Annu Rev Ecol Syst"},{"issue":"4","key":"10.1016\/j.ress.2026.112369_bib0002","doi-asserted-by":"crossref","first-page":"764","DOI":"10.2307\/1936746","article-title":"Energy flow, nutrient cycling, and ecosystem resilience","volume":"61","author":"Deangelis","year":"1980","journal-title":"Ecology"},{"key":"10.1016\/j.ress.2026.112369_bib0003","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.ress.2015.08.006","article-title":"A review of definition and measure of system resilience","volume":"145","author":"Hosseini","year":"2016","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112369_bib0004","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.ress.2015.03.007","article-title":"A systematic literature review of resilience engineering: research areas and a research agenda proposal","volume":"141","author":"Righi","year":"2015","journal-title":"Reliab Eng Syst Saf"},{"issue":"4","key":"10.1016\/j.ress.2026.112369_bib0005","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1193\/1.1623497","article-title":"A framework to quantitatively assess and enhance the seismic resilience of communities","volume":"19","author":"Bruneau","year":"2003","journal-title":"Earthquake Spectra"},{"key":"10.1016\/j.ress.2026.112369_bib0006","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.ress.2013.07.004","article-title":"A metric and frameworks for resilience analysis of engineered and infrastructure systems","volume":"121","author":"Francis","year":"2014","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112369_bib0007","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2024.110720","article-title":"A multi-state resilience analysis framework of critical infrastructure systems based on component importance measures","volume":"256","author":"Wang","year":"2025","journal-title":"Reliab Eng Syst Saf"},{"issue":"2","key":"10.1016\/j.ress.2026.112369_bib0008","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1080\/23789689.2017.1345257","article-title":"Resilience analysis: a mathematical formulation to model resilience of engineering systems","volume":"3","author":"Sharma","year":"2018","journal-title":"Sustain Resilient Infrastruct"},{"issue":"11","key":"10.1016\/j.ress.2026.112369_bib0009","doi-asserted-by":"crossref","first-page":"3748","DOI":"10.1080\/00207543.2019.1566656","article-title":"Social and environmental risk management in resilient supply chains: a periodical study by the grey-verhulst model","volume":"57","author":"Rajesh","year":"2010","journal-title":"Int J Prod Res"},{"issue":"11","key":"10.1016\/j.ress.2026.112369_bib0010","doi-asserted-by":"crossref","DOI":"10.1115\/1.4034223","article-title":"Engineering resilience quantification and system design implications: a literature survey","volume":"138","author":"Yodo","year":"2016","journal-title":"J Mech Des"},{"key":"10.1016\/j.ress.2026.112369_bib0011","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.ssci.2010.09.003","article-title":"A risk perspective suitable for resilience engineering","volume":"49","author":"Steen","year":"2011","journal-title":"Saf Sci"},{"issue":"2","key":"10.1016\/j.ress.2026.112369_bib0012","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1080\/00207543.2021.1971789","article-title":"System resilience assessments: a review, framework and metric","volume":"60","author":"Cheng","year":"2022","journal-title":"Int J Prod"},{"key":"10.1016\/j.ress.2026.112369_bib0013","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2023.109207","article-title":"Resilience modeling for multi-state systems based on Markov processes","volume":"235","author":"Tan","year":"2023","journal-title":"Reliab Eng Syst Saf"},{"issue":"1","key":"10.1016\/j.ress.2026.112369_bib0014","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1029\/WR018i001p00014","article-title":"Reliability, resiliency, and vulnerability criteria for water resource system performance evaluation","volume":"18","author":"Hashimoto","year":"1982","journal-title":"Water Resour Res"},{"key":"10.1016\/j.ress.2026.112369_bib0015","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.strusafe.2017.05.002","article-title":"Stochastic post-disaster functionality recovery of community building portfolios I: modeling","volume":"69","author":"Lin","year":"2017","journal-title":"Struct Saf"},{"key":"10.1016\/j.ress.2026.112369_bib0016","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.ress.2017.02.009","article-title":"Hybrid hidden Markov models for resilience metrics in a dynamic infrastructure system","volume":"164","author":"Zhao","year":"2017","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112369_bib0017","doi-asserted-by":"crossref","DOI":"10.1016\/j.strusafe.2021.102091","article-title":"A Markov framework for generalized post-event systems recovery modeling: from single to multihazards","volume":"91","author":"Dhulipala","year":"2021","journal-title":"Struct Saf"},{"key":"10.1016\/j.ress.2026.112369_bib0018","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2021.107443","article-title":"A Markov reward process-based framework for resilience analysis of multistate energy systems under the threat of extreme events","volume":"209","author":"Zeng","year":"2021","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112369_bib0019","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2022.108423","article-title":"A demand-based framework for resilience assessment of multistate networks under disruptions","volume":"222","author":"Geng","year":"2022","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112369_bib0020","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2022.108663","article-title":"Modeling and evaluation method for resilience analysis of multi-state networks","volume":"226","author":"Liu","year":"2022","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112369_bib0021","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2023.109606","article-title":"A multistate network approach for resilience analysis of UAV swarm considering information exchange capacity","volume":"241","author":"Liu","year":"2024","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112369_bib0022","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2022.108939","article-title":"A Markov resilience assessment framework for tension leg platform under mooring failure","volume":"231","author":"Wu","year":"2023","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112369_bib0023","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2023.109773","article-title":"Competing risks-based resilience approach for multi-state systems under multiple shocks","volume":"242","author":"Dui","year":"2024","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112369_bib0024","article-title":"Resilience evaluation of multi-feature system based on hidden Markov model","volume":"235","author":"Liu","year":"2025","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112369_bib0025","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2025.111426","article-title":"Resilience modeling for discrete-time multi-state systems based on aggregated Markov chains","volume":"264","author":"Wu","year":"2025","journal-title":"Reliab Eng Syst Saf"},{"issue":"3","key":"10.1016\/j.ress.2026.112369_bib0026","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/j.ress.2005.01.010","article-title":"Reliability analysis of a repairable k-out-of-n system with some components being suspended when the system is down","volume":"91","author":"Li","year":"2006","journal-title":"Reliab Eng Syst Saf"},{"issue":"7","key":"10.1016\/j.ress.2026.112369_bib0027","doi-asserted-by":"crossref","first-page":"2331","DOI":"10.1080\/00207543.2021.1887532","article-title":"On reliability analysis of a load-sharing k-out-of-n: G system with interacting Markov subsystems","volume":"60","author":"Wu","year":"2022","journal-title":"Int J Prod Res"},{"issue":"2","key":"10.1016\/j.ress.2026.112369_bib0028","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1109\/TPWRS.2003.821613","article-title":"A comparison of four-state generating unit reliability models for peaking units","volume":"19","author":"Billinton","year":"2004","journal-title":"IEEE Trans Power Syst"},{"issue":"2","key":"10.1016\/j.ress.2026.112369_bib0029","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1109\/TR.2015.2506610","article-title":"Semi-Markov model for the oxidation degradation mechanism in gas turbine nozzles","volume":"65","author":"Compare","year":"2016","journal-title":"IEEE Trans Reliab"},{"key":"10.1016\/j.ress.2026.112369_bib0030","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.ress.2009.08.004","article-title":"Performance evaluation of multi-state degraded systems with minimal repairs and imperfect preventive maintenance","volume":"95","author":"Soro","year":"2010","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112369_bib0031","article-title":"Stochastic processes with applications, 2nd edition","author":"Bhattacharya","year":"2009","journal-title":"Soc Ind Appl Math"},{"key":"10.1016\/j.ress.2026.112369_bib0032","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1038\/s41597-024-03095-5","article-title":"A data set of recorded electricity outages by united states county 2014\u20132022","volume":"11","author":"Brelsford","year":"2024","journal-title":"Sci Data"},{"issue":"3","key":"10.1016\/j.ress.2026.112369_bib0033","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1111\/j.1467-9868.2005.00508.x","article-title":"Statistical inference for discretely observed Markov jump processes","volume":"67","author":"Bladt","year":"2005","journal-title":"J R Stat Soc - Ser B"}],"container-title":["Reliability Engineering & System Safety"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0951832026001857?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0951832026001857?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T17:10:54Z","timestamp":1778778654000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0951832026001857"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":33,"alternative-id":["S0951832026001857"],"URL":"https:\/\/doi.org\/10.1016\/j.ress.2026.112369","relation":{},"ISSN":["0951-8320"],"issn-type":[{"value":"0951-8320","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Resilience analysis of four-state engineering systems under the framework of continuous-time Markov chain model","name":"articletitle","label":"Article Title"},{"value":"Reliability Engineering & System Safety","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.ress.2026.112369","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":"112369"}}