{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T22:55:15Z","timestamp":1768690515204,"version":"3.49.0"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2020,6,13]],"date-time":"2020-06-13T00:00:00Z","timestamp":1592006400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,6,13]],"date-time":"2020-06-13T00:00:00Z","timestamp":1592006400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math Meth Oper Res"],"published-print":{"date-parts":[[2020,10]]},"DOI":"10.1007\/s00186-020-00715-9","type":"journal-article","created":{"date-parts":[[2020,6,13]],"date-time":"2020-06-13T15:02:31Z","timestamp":1592060551000},"page":"311-341","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A long-time asymptotic solution to the g-renewal equation for underlying distributions with nondecreasing hazard functions"],"prefix":"10.1007","volume":"92","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2144-9208","authenticated-orcid":false,"given":"Serguei","family":"Maximov","sequence":"first","affiliation":[]},{"given":"Consuelo\u00a0de J.","family":"Cortes-Penagos","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,6,13]]},"reference":[{"key":"715_CR1","volume-title":"Mathematical theory of reliability","author":"RE Barlow","year":"1965","unstructured":"Barlow RE, Proschan F (1965) Mathematical theory of reliability. Wiley, New York"},{"key":"715_CR2","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.ress.2008.03.002","volume":"94","author":"M Bartholomew-Biggs","year":"2009","unstructured":"Bartholomew-Biggs M, Zuo MJ, Li X (2009) Modelling and optimizing sequential imperfect preventive maintenance. Reliab Eng Syst Saf 94:53\u201362","journal-title":"Reliab Eng Syst Saf"},{"key":"715_CR3","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1109\/TR.2005.857633","volume":"54","author":"CR Cassady","year":"2005","unstructured":"Cassady CR, Iyoob IM, Schneider K, Pohl EA (2005) A generic model of equipment availability under imperfect maintenance. IEEE Trans Reliab 54:564\u2013571","journal-title":"IEEE Trans Reliab"},{"key":"715_CR4","volume-title":"Failure rate modedling for reliability and risk","author":"M Finkelstein","year":"2008","unstructured":"Finkelstein M (2008) Failure rate modedling for reliability and risk. Springer, London"},{"issue":"3","key":"715_CR5","doi-asserted-by":"publisher","first-page":"432","DOI":"10.1080\/10920277.2011.10597629","volume":"15","author":"LA Gavrilov","year":"2011","unstructured":"Gavrilov LA, Gavrilova NS (2011) Mortality measurement at advanced ages: a study of the social security administration death master file. N Am Actuar J 15(3):432\u2013447","journal-title":"N Am Actuar J"},{"key":"715_CR6","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1016\/j.ress.2006.05.004","volume":"92","author":"W Kahle","year":"2007","unstructured":"Kahle W (2007) Optimal maintenance policies in incomplete repair models. Reliab Eng Syst Saf 92:563\u2013565","journal-title":"Reliab Eng Syst Saf"},{"key":"715_CR7","first-page":"29","volume":"1","author":"MP Kaminskiy","year":"2006","unstructured":"Kaminskiy MP, Krivtsov VV (2006) A monte carlo approach to estimation of g-renewal process in warranty data analysis. Reliab Theory Appl 1:29\u201331","journal-title":"Reliab Theory Appl"},{"key":"715_CR8","doi-asserted-by":"publisher","first-page":"71","DOI":"10.2307\/3214117","volume":"23","author":"M Kijima","year":"1986","unstructured":"Kijima M, Sumita M (1986) A useful generalization of renewal theory: counting processes governed by nonnegative Markovian increments. J Appl Prob 23:71\u201388","journal-title":"J Appl Prob"},{"key":"715_CR9","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1016\/0377-2217(88)90329-3","volume":"37","author":"M Kijima","year":"1988","unstructured":"Kijima M, Morimura H, Susuki Y (1988) Periodical replacement problem without assuming minimal repair. Eur J Oper Res 37:194\u2013203","journal-title":"Eur J Oper Res"},{"key":"715_CR10","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1016\/j.ress.2013.02.005","volume":"115","author":"V Krivtsov","year":"2013","unstructured":"Krivtsov V, Yevkin O (2013) Estimation of g-renewal process parameters as an ill-posed inverse problem. Reliab Eng Syst Saf 115:10\u201318","journal-title":"Reliab Eng Syst Saf"},{"key":"715_CR11","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1109\/24.87135","volume":"40","author":"DNP Murthy","year":"1991","unstructured":"Murthy DNP (1991) A note on minimal repair. IEEE Trans Reliab 40:245\u2013246","journal-title":"IEEE Trans Reliab"},{"key":"715_CR12","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1109\/TR.1979.5220624","volume":"R\u201328","author":"T Nakagawa","year":"1979","unstructured":"Nakagawa T (1979) Optimum policies when preventive maintenance is imperfect. IEEE Trans Reliab R\u201328:331\u2013332","journal-title":"IEEE Trans Reliab"},{"key":"715_CR13","doi-asserted-by":"publisher","first-page":"176","DOI":"10.1016\/0377-2217(83)90221-7","volume":"12","author":"T Nakagawa","year":"1983","unstructured":"Nakagawa T, Kowada M (1983) Analysis of a system with minimal repair and its application to replacement policy. Eur J Oper Res 12:176\u2013182","journal-title":"Eur J Oper Res"},{"key":"715_CR14","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1016\/j.ress.2013.10.007","volume":"124","author":"M Tanwar","year":"2014","unstructured":"Tanwar M, Rai RN, Bolia N (2014) Imperfect repair modeling using Kijima type generalized renewal process. Reliab Eng Syst Saf 124:24\u201331","journal-title":"Reliab Eng Syst Saf"},{"key":"715_CR15","volume-title":"Equations of mathematical physics","author":"VS Vladimirov","year":"2004","unstructured":"Vladimirov VS, Zharinov VV (2004) Equations of mathematical physics. Phys. Mat. Lit., Moscow"},{"key":"715_CR16","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/0022-247X(76)90108-6","volume":"53","author":"JSW Wong","year":"1976","unstructured":"Wong JSW, Wong R (1976) On asymptotic solutions of the renewal equation. J Math Anal Appl 53:243\u2013250","journal-title":"J Math Anal Appl"},{"issue":"1","key":"715_CR17","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1109\/TR.2011.2182399","volume":"61","author":"O Yevkin","year":"2012","unstructured":"Yevkin O, Krivtsov V (2012) Approximate solution to g-renewal equation with underlying Weibull distribution. IEEE Trans Reliab 61(1):68\u201373","journal-title":"IEEE Trans Reliab"},{"issue":"1","key":"715_CR18","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1109\/TR.2013.2241196","volume":"62","author":"O Yevkin","year":"2013","unstructured":"Yevkin O, Krivtsov V (2013) Comparative analysis of optimal maintenance policies under general repair with underlying Weibull distributions. IEEE Trans Reliab 62(1):82\u201391","journal-title":"IEEE Trans Reliab"}],"container-title":["Mathematical Methods of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-020-00715-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00186-020-00715-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-020-00715-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,12]],"date-time":"2021-06-12T23:09:45Z","timestamp":1623539385000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00186-020-00715-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,13]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,10]]}},"alternative-id":["715"],"URL":"https:\/\/doi.org\/10.1007\/s00186-020-00715-9","relation":{},"ISSN":["1432-2994","1432-5217"],"issn-type":[{"value":"1432-2994","type":"print"},{"value":"1432-5217","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,13]]},"assertion":[{"value":"13 November 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 April 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 June 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}