{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T18:27:56Z","timestamp":1777919276873,"version":"3.51.4"},"reference-count":35,"publisher":"SAGE Publications","issue":"8","license":[{"start":{"date-parts":[[2018,6,20]],"date-time":"2018-06-20T00:00:00Z","timestamp":1529452800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The Journal of Strain Analysis for Engineering Design"],"published-print":{"date-parts":[[2018,11]]},"abstract":"<jats:p>Knowledge of the stochastic nature of fatigue life of composite materials can be modeled by the failure time with the Weibull distribution. This task becomes complex when the samples are small and scattered. In this way, it is necessary to know and to improve robust models of estimation of the parameters of the distribution of Weibull. The aim of this work is to compare the performance of least squares, least squares weighted, maximum likelihood estimator and momentum method and to suggest a method that obtains better performance in life behavior to fatigue with small samples. Monte Carlo simulations were performed to estimate the distribution parameters with different sample sizes and an application with real fatigue data that compares performance using goodness-of-fit. The results of the simulations showed that the weighted least squares estimation was able to generate more reliable estimators for fatigue behavior during its useful life. In this way, it is possible to conclude that small samples make the real representation of life difficult to the material fatigue, but using the weighted least squares estimation method, it is possible to obtain more estimates.<\/jats:p>","DOI":"10.1177\/0309324718782245","type":"journal-article","created":{"date-parts":[[2018,6,20]],"date-time":"2018-06-20T06:22:06Z","timestamp":1529475726000},"page":"699-710","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":28,"title":["Analysis of the fatigue life estimators of the materials using small samples"],"prefix":"10.1177","volume":"53","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3447-8240","authenticated-orcid":false,"given":"Joelton Fonseca","family":"Barbosa","sequence":"first","affiliation":[{"name":"Federal University of Rio Grande do Norte, Natal, Brazil"},{"name":"Faculty of Engineering, University of Porto, Porto, Portugal"},{"name":"Federal Rural University of the Semi-Arid Region, Mossor\u00f3, Brazil"}]},{"given":"Raimundo","family":"Carlos Silverio Freire J\u00fanior","sequence":"additional","affiliation":[{"name":"Federal University of Rio Grande do Norte, Natal, Brazil"}]},{"given":"Jose AFO","family":"Correia","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, University of Porto, Porto, Portugal"}]},{"given":"Abilio MP","family":"De Jesus","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, University of Porto, Porto, Portugal"}]},{"given":"RAB","family":"Cal\u00e7ada","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, University of Porto, Porto, Portugal"}]}],"member":"179","published-online":{"date-parts":[[2018,6,20]]},"reference":[{"key":"bibr1-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1177\/1464420712458201"},{"key":"bibr2-0309324718782245","volume-title":"A unified statistical methodology for modeling fatigue damage","author":"Castillo E","year":"2009"},{"key":"bibr3-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijfatigue.2015.03.012"},{"key":"bibr4-0309324718782245","doi-asserted-by":"publisher","DOI":"10.15623\/ijret.2015.0404038"},{"key":"bibr5-0309324718782245","first-page":"1","author":"Zhu SP","year":"2018","journal-title":"Fatigue Fract Eng Mater Struct"},{"key":"bibr6-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijfatigue.2017.06.019"},{"key":"bibr7-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1016\/j.matdes.2007.05.005"},{"key":"bibr8-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1016\/j.compositesb.2013.08.036"},{"key":"bibr9-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84800-113-8_3"},{"key":"bibr10-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1016\/j.compositesb.2015.03.051"},{"key":"bibr11-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1016\/S1359-835X(96)00088-7"},{"key":"bibr12-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijfatigue.2005.11.006"},{"key":"bibr13-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijfatigue.2007.11.007"},{"key":"bibr14-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1016\/j.compscitech.2008.09.016"},{"key":"bibr15-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1016\/j.cageo.2008.04.004"},{"key":"bibr16-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1080\/02331888.2011.559657"},{"key":"bibr17-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijfatigue.2017.03.031"},{"key":"bibr18-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijfatigue.2009.09.004"},{"key":"bibr19-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1016\/j.engfracmech.2017.05.039"},{"key":"bibr20-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2006.04.008"},{"key":"bibr21-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1201\/9781420087444"},{"key":"bibr22-0309324718782245","first-page":"7","volume":"21","author":"Kantar YM.","year":"2016","journal-title":"Math Comput Appl"},{"key":"bibr23-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1002\/qre.778"},{"key":"bibr24-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1016\/j.proeng.2015.08.103"},{"key":"bibr25-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1007\/BF02402669"},{"key":"bibr26-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1002\/qre.423"},{"key":"bibr27-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1002\/qre.570"},{"key":"bibr28-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1002\/qre.1472"},{"key":"bibr29-0309324718782245","first-page":"81","volume":"9","author":"Kantar YM","year":"2016","journal-title":"Int J Informatics Technol"},{"key":"bibr30-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1016\/j.compositesa.2007.07.005"},{"key":"bibr31-0309324718782245","volume-title":"Introdu\u00e7\u00e3o \u00c0 Infer\u00eancia Estat\u00edstica","author":"Bolfarine H","year":"2001"},{"key":"bibr32-0309324718782245","volume-title":"Statistical inference","author":"Casella G","year":"2002"},{"key":"bibr33-0309324718782245","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(66)90115-6"},{"key":"bibr34-0309324718782245","unstructured":"Tomblin J, Seneviratne W. Determining the fatigue life of composite aircraft structures using life and load-enhancement factors. Final report, Air Traffic Organization, Washington, DC, http:\/\/www.tc.faa.gov\/its\/worldpac\/techrpt\/ar10-6.pdf"},{"key":"bibr35-0309324718782245","first-page":"97","volume":"68","author":"D\u2019Agostinho RB","year":"1986","journal-title":"GOF Tech"}],"container-title":["The Journal of Strain Analysis for Engineering Design"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0309324718782245","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/0309324718782245","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0309324718782245","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T18:59:16Z","timestamp":1777661956000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0309324718782245"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,20]]},"references-count":35,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2018,11]]}},"alternative-id":["10.1177\/0309324718782245"],"URL":"https:\/\/doi.org\/10.1177\/0309324718782245","relation":{},"ISSN":["0309-3247","2041-3130"],"issn-type":[{"value":"0309-3247","type":"print"},{"value":"2041-3130","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,20]]}}}