{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T15:59:21Z","timestamp":1784735961299,"version":"3.55.0"},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2018,1,30]],"date-time":"2018-01-30T00:00:00Z","timestamp":1517270400000},"content-version":"unspecified","delay-in-days":1066,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Probability"],"published-print":{"date-parts":[[2015,3]]},"abstract":"<jats:p>Let <jats:italic>X<\/jats:italic><jats:sub>\u03bb<jats:sub>1<\/jats:sub><\/jats:sub>, <jats:italic>X<\/jats:italic><jats:sub>\u03bb<jats:sub>2<\/jats:sub><\/jats:sub>, \u2026, <jats:italic>X<\/jats:italic><jats:sub>\u03bb<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub><\/jats:sub>\nbe independent Weibull random variables with <jats:italic>X<\/jats:italic><jats:sub>\u03bb<jats:sub><jats:italic>i<\/jats:italic><\/jats:sub><\/jats:sub> \u223c W(\u03b1, \u03bb<jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>), where \u03bb<jats:sub><jats:italic>i<\/jats:italic><\/jats:sub> &gt; 0 for <jats:italic>i<\/jats:italic> = 1, \u2026, <jats:italic>n<\/jats:italic>. Let <jats:italic>X<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic>:<jats:italic>n<\/jats:italic><\/jats:sub><jats:sup>\u03bb<\/jats:sup> denote the lifetime of the parallel system formed from <jats:italic>X<\/jats:italic><jats:sub>\u03bb<jats:sub>1<\/jats:sub><\/jats:sub>, <jats:italic>X<\/jats:italic><jats:sub>\u03bb<jats:sub>2<\/jats:sub><\/jats:sub>, \u2026, <jats:italic>X<\/jats:italic><jats:sub>\u03bb<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub><\/jats:sub>. We investigate the effect of the changes in the scale parameters (\u03bb<jats:sub>1<\/jats:sub>, \u2026, \u03bb<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>) on the magnitude of <jats:italic>X<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic>:<jats:italic>n<\/jats:italic><\/jats:sub><jats:sup>\u03bb<\/jats:sup> according to reverse hazard rate and likelihood ratio orderings.<\/jats:p>","DOI":"10.1239\/jap\/1429282609","type":"journal-article","created":{"date-parts":[[2015,4,17]],"date-time":"2015-04-17T11:09:24Z","timestamp":1429268964000},"page":"102-116","source":"Crossref","is-referenced-by-count":48,"title":["Stochastic Order Relations Among Parallel Systems from Weibull Distributions"],"prefix":"10.1017","volume":"52","author":[{"given":"Nuria","family":"Torrado","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Subhash C.","family":"Kochar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2018,1,30]]},"reference":[{"key":"S0021900200120923_ref10","volume-title":"Life Distributions","author":"Marshall","year":"2007"},{"key":"S0021900200120923_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-68276-1"},{"key":"S0021900200120923_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-3758(97)00058-X"},{"key":"S0021900200120923_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2008.09.010"},{"key":"S0021900200120923_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2004.12.013"},{"key":"S0021900200120923_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-34675-5"},{"key":"S0021900200120923_ref1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1009605613222"},{"key":"S0021900200120923_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jkss.2011.05.004"},{"key":"S0021900200120923_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2009.07.023"},{"key":"S0021900200120923_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/S0021900200018301"},{"key":"S0021900200120923_ref7","doi-asserted-by":"publisher","DOI":"10.1080\/03610920601077212"},{"key":"S0021900200120923_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2010.06.006"},{"key":"S0021900200120923_ref9","doi-asserted-by":"publisher","DOI":"10.5402\/2012\/839473"},{"key":"S0021900200120923_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2006.08.011"},{"key":"S0021900200120923_ref15","doi-asserted-by":"publisher","DOI":"10.1017\/S0269964811000064"},{"key":"S0021900200120923_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-6892-9_5"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200120923","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,20]],"date-time":"2019-04-20T22:55:49Z","timestamp":1555800949000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200120923\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3]]},"references-count":16,"aliases":["10.1017\/s0021900200012225"],"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,3]]}},"alternative-id":["S0021900200120923"],"URL":"https:\/\/doi.org\/10.1239\/jap\/1429282609","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3]]}}}