{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T15:29:29Z","timestamp":1783438169236,"version":"3.54.6"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T00:00:00Z","timestamp":1747958400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T00:00:00Z","timestamp":1747958400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2025,7]]},"DOI":"10.1007\/s10479-025-06663-z","type":"journal-article","created":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T16:21:48Z","timestamp":1748017308000},"page":"1169-1206","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On random weighted coherent systems based on a new structure-based performance measure"],"prefix":"10.1007","volume":"350","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-5873-5935","authenticated-orcid":false,"given":"Tanmay","family":"Sahoo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nil Kamal","family":"Hazra","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Narayanaswamy","family":"Balakrishnan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,5,23]]},"reference":[{"key":"6663_CR1","doi-asserted-by":"publisher","first-page":"408","DOI":"10.1109\/24.406574","volume":"44","author":"MJ Armstrong","year":"1995","unstructured":"Armstrong, M. J. (1995). Joint reliability-importance of components. IEEE Transactions on Reliability, 44, 408\u2013412.","journal-title":"IEEE Transactions on Reliability"},{"key":"6663_CR2","doi-asserted-by":"crossref","unstructured":"Arriaza, A., Navarro, J., Sordo, M. \u00c1., & Su\u00e1rez-Llorens, A. (2023). A variance-based importance index for systems with dependent components. Fuzzy Sets and Systems, 467, Article 108482.","DOI":"10.1016\/j.fss.2023.02.003"},{"key":"6663_CR3","volume-title":"Statistical Theory of Reliability and Life Testing: Probability Models","author":"RE Barlow","year":"1975","unstructured":"Barlow, R. E., & Proschan, F. (1975). Statistical Theory of Reliability and Life Testing: Probability Models. Rinehart and Winston, New York: Holt."},{"key":"6663_CR4","doi-asserted-by":"publisher","first-page":"1238","DOI":"10.1109\/59.32623","volume":"4","author":"R Billinton","year":"1989","unstructured":"Billinton, R., Kumar, S., Chowdhury, N., Chu, K., Debnath, K., Goel, L., & Oteng-Adjei, J. (1989). A reliability test system for educational purposes-basic data. IEEE Transactions on Power Systems, 4, 1238\u20131244.","journal-title":"IEEE Transactions on Power Systems"},{"key":"6663_CR5","doi-asserted-by":"crossref","unstructured":"Birnbaum, Z. W. (1968). On the importance of different components in a multicomponent system. In P.R. Krishnaiah (Ed.), Multivariate Analysis-II, pp. 581-592.","DOI":"10.21236\/AD0670563"},{"key":"6663_CR6","doi-asserted-by":"crossref","unstructured":"Boland, P. J., & Proschan, F. (1983). The reliability of $$k$$-out-of-$$n$$ systems. The Annals of Probability, 760-764.","DOI":"10.21236\/ADA145505"},{"key":"6663_CR7","doi-asserted-by":"publisher","first-page":"807","DOI":"10.1002\/1520-6750(198912)36:6<807::AID-NAV3220360606>3.0.CO;2-I","volume":"36","author":"PJ Boland","year":"1989","unstructured":"Boland, P. J., Proschan, F., & Tong, Y. L. (1989). Optimal arrangement of components via pairwise rearrangements. Naval Research Logistics, 36, 807\u2013815.","journal-title":"Naval Research Logistics"},{"key":"6663_CR8","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1109\/TR.2005.853274","volume":"54","author":"Y Chen","year":"2005","unstructured":"Chen, Y., & Yang, Q. (2005). Reliability of two-stage weighted-$$k$$-out-of-$$n$$ systems with components in common. IEEE Transactions on Reliability, 54, 431\u2013440.","journal-title":"IEEE Transactions on Reliability"},{"key":"6663_CR9","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1109\/TR.2010.2048659","volume":"59","author":"Y Ding","year":"2010","unstructured":"Ding, Y., Zuo, M. J., Lisnianski, A., & Li, W. (2010). A framework for reliability approximation of multi-state weighted $$ k $$-out-of-$$ n $$ systems. IEEE Transactions on Reliability, 59, 297\u2013308.","journal-title":"IEEE Transactions on Reliability"},{"key":"6663_CR10","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/j.ress.2012.07.010","volume":"109","author":"S Eryilmaz","year":"2013","unstructured":"Eryilmaz, S. (2013). On reliability analysis of a $$k$$-out-of-$$n$$ system with components having random weights. Reliability Engineering and System Safety, 109, 41\u201344.","journal-title":"Reliability Engineering and System Safety"},{"key":"6663_CR11","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1007\/s10479-012-1138-x","volume":"212","author":"S Eryilmaz","year":"2014","unstructured":"Eryilmaz, S. (2014). A new look at dynamic behavior of binary coherent system from a state-level perspective. Annals of Operations Research, 212, 115\u2013125.","journal-title":"Annals of Operations Research"},{"key":"6663_CR12","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/j.cie.2014.03.025","volume":"72","author":"S Eryilmaz","year":"2014","unstructured":"Eryilmaz, S., & Bozbulut, A. R. (2014). Computing marginal and joint Birnbaum, and Barlow-Proschan importances in weighted-k-out-of-n: G systems. Computers and Industrial Engineering, 72, 255\u2013260.","journal-title":"Computers and Industrial Engineering"},{"key":"6663_CR13","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1016\/j.ress.2014.12.008","volume":"136","author":"S Eryilmaz","year":"2015","unstructured":"Eryilmaz, S. (2015). Capacity loss and residual capacity in weighted k-out-of-n: G systems. Reliability Engineering and System Safety, 136, 140\u2013144.","journal-title":"Reliability Engineering and System Safety"},{"key":"6663_CR14","doi-asserted-by":"crossref","unstructured":"Eryilmaz, S., & Navarro, J. (2022). A decision theoretic framework for reliability-based optimal wind turbine selection. Reliability Engineering and System Safety, 221, Article 108291.","DOI":"10.1016\/j.ress.2021.108291"},{"key":"6663_CR15","doi-asserted-by":"publisher","first-page":"843","DOI":"10.1109\/TR.2015.2499959","volume":"65","author":"C Franko","year":"2015","unstructured":"Franko, C., & T\u00fct\u00fcnc\u00fc, G. Y. (2015). Signature based reliability analysis of repairable weighted $$k$$-out-of-$$n$$: G systems. IEEE Transactions on Reliability, 65, 843\u2013850.","journal-title":"IEEE Transactions on Reliability"},{"key":"6663_CR16","unstructured":"Hagstrom, J. N. (1990). Redundancy, substitutes and complements in system reliability. Technical report, College of Business Administration, University of Illinois, Urbana Champaign, USA."},{"key":"6663_CR17","doi-asserted-by":"publisher","DOI":"10.1002\/9781118314593","volume-title":"Importance Measures in Reliability, Risk, and Optimization: Principles and Applications","author":"W Kuo","year":"2012","unstructured":"Kuo, W., & Zhu, X. (2012). Importance Measures in Reliability, Risk, and Optimization: Principles and Applications. New York: John Wiley and Sons."},{"key":"6663_CR18","volume-title":"The Universal Generating Function in Reliability Analysis and Optimization","author":"G Levitin","year":"2005","unstructured":"Levitin, G. (2005). The Universal Generating Function in Reliability Analysis and Optimization. London: Springer."},{"key":"6663_CR19","doi-asserted-by":"crossref","unstructured":"Li, Y. F., Huang, H. Z., Mi, J., Peng, W., & Han, X. (2022). Reliability analysis of multi-state systems with common cause failures based on Bayesian network and fuzzy probability. Annals of Operations Research, 1-15.","DOI":"10.1007\/s10479-019-03247-6"},{"key":"6663_CR20","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1016\/j.ejor.2017.06.022","volume":"263","author":"JL Marichal","year":"2017","unstructured":"Marichal, J. L., Mathonet, P., Navarro, J., & Paroissin, C. (2017). Joint signature of two or more systems with applications to multistate systems made up of two-state components. European Journal of Operational Research, 263, 559\u2013570.","journal-title":"European Journal of Operational Research"},{"key":"6663_CR21","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1016\/j.cam.2017.05.042","volume":"326","author":"RS Meshkat","year":"2017","unstructured":"Meshkat, R. S., & Mahmoudi, E. (2017). Joint reliability and weighted importance measures of a $$k$$-out-of-$$n$$ system with random weights for components. Journal of Computational and Applied Mathematics, 326, 273\u2013283.","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"6663_CR22","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1109\/TR.2019.2895400","volume":"68","author":"P Miziu\u0142a","year":"2019","unstructured":"Miziu\u0142a, P., & Navarro, J. (2019). Birnbaum importance measure for reliability systems with dependent components. IEEE Transactions on Reliability, 68, 439\u2013450.","journal-title":"IEEE Transactions on Reliability"},{"key":"6663_CR23","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1002\/nav.20285","volume":"55","author":"J Navarro","year":"2008","unstructured":"Navarro, J., Samaniego, F. J., Balakrishnan, N., & Bhattacharya, D. (2008). On the application and extension of system signatures in engineering reliability. Naval Research Logistics, 55, 313\u2013327.","journal-title":"Naval Research Logistics"},{"key":"6663_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cam.2015.09.009","volume":"296","author":"RA Rahmani","year":"2016","unstructured":"Rahmani, R. A., Izadi, M., & Khaledi, B. E. (2016). Importance of components in $$k$$-out-of-$$n$$ system with components having random weights. Journal of Computational and Applied Mathematics, 296, 1\u20139.","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"6663_CR25","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-71797-5","volume-title":"System Signatures and Their Applications in Engineering Reliability","author":"FJ Samaniego","year":"2007","unstructured":"Samaniego, F. J. (2007). System Signatures and Their Applications in Engineering Reliability. New York: Springer."},{"key":"6663_CR26","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1016\/j.spl.2007.09.049","volume":"78","author":"FJ Samaniego","year":"2008","unstructured":"Samaniego, F. J., & Shaked, M. (2008). Systems with weighted components. Statistics and Probability Letters, 78, 815\u2013823.","journal-title":"Statistics and Probability Letters"},{"key":"6663_CR27","first-page":"37","volume":"236","author":"H Sun","year":"2022","unstructured":"Sun, H., Zhang, Y., & Zhao, P. (2022). Allocating hot standbys to randomly weighted k-out-of-n: G systems. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 236, 37\u201354.","journal-title":"Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability"},{"key":"6663_CR28","first-page":"79","volume":"25","author":"I Ushakov","year":"1987","unstructured":"Ushakov, I. (1987). Optimal standby problems and a universal generating function. Soviet Journal of Computer and Systems Sciences, 25, 79\u201382.","journal-title":"Soviet Journal of Computer and Systems Sciences"},{"key":"6663_CR29","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1109\/24.295016","volume":"43","author":"JS Wu","year":"1994","unstructured":"Wu, J. S., & Chen, R. J. (1994). An algorithm for computing the reliability of weighted-$$k$$-out-of-$$n$$ systems. IEEE Transactions on Reliability, 43, 327\u2013328.","journal-title":"IEEE Transactions on Reliability"},{"key":"6663_CR30","doi-asserted-by":"publisher","first-page":"654","DOI":"10.1002\/nav.22036","volume":"69","author":"J Wu","year":"2022","unstructured":"Wu, J., Ding, W., Zhang, Y., & Zhao, P. (2022). On reliability improvement for coherent systems with a relevation. Naval Research Logistics (NRL), 69, 654\u2013666.","journal-title":"Naval Research Logistics (NRL)"},{"key":"6663_CR31","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1016\/j.spl.2017.12.002","volume":"135","author":"Y Zhang","year":"2018","unstructured":"Zhang, Y. (2018). Optimal allocation of active redundancies in weighted $$k$$-out-of-$$n$$ systems. Statistics and Probability Letters, 135, 110\u2013117.","journal-title":"Statistics and Probability Letters"},{"key":"6663_CR32","doi-asserted-by":"crossref","unstructured":"Zhang, Y. (2021). Reliability analysis of randomly weighted k-out-of-n systems with heterogeneous components. Reliability Engineering and System Safety, 205, Article 107184.","DOI":"10.1016\/j.ress.2020.107184"},{"key":"6663_CR33","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1002\/nav.21810","volume":"65","author":"Y Zhang","year":"2018","unstructured":"Zhang, Y., Ding, W., & Zhao, P. (2018). On total capacity of k?out?of?n systems with random weights. Naval Research Logistics, 65, 347\u2013359.","journal-title":"Naval Research Logistics"},{"key":"6663_CR34","doi-asserted-by":"publisher","first-page":"865","DOI":"10.1007\/s11749-023-00855-0","volume":"32","author":"J Zhang","year":"2023","unstructured":"Zhang, J., & Zhang, Y. (2023). Stochastic comparisons of relevation allocation policies in coherent systems. TEST, 32, 865\u2013907.","journal-title":"TEST"},{"key":"6663_CR35","doi-asserted-by":"crossref","unstructured":"Zhang, D., Luo, Y., & Liu, Q. (2024). Reliability evaluation of production systems with finite buffers subject to time-dependent and operation-dependent failures. Annals of Operations Research, 1-21.","DOI":"10.1007\/s10479-024-05891-z"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-025-06663-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-025-06663-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-025-06663-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T15:37:39Z","timestamp":1757173059000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-025-06663-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,23]]},"references-count":35,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,7]]}},"alternative-id":["6663"],"URL":"https:\/\/doi.org\/10.1007\/s10479-025-06663-z","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,23]]},"assertion":[{"value":"13 May 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 May 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 May 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no conflict of interest\/competing interests to declare.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}