{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T10:25:17Z","timestamp":1758709517845},"reference-count":33,"publisher":"Cambridge University Press (CUP)","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2014,3]]},"abstract":"<jats:p>Suppose that a system consists of<jats:italic>n<\/jats:italic>independent and identically distributed components and that the life lengths of the<jats:italic>n<\/jats:italic>components are<jats:italic>X<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>,<jats:italic>i<\/jats:italic>= 1, \u2026,<jats:italic>n<\/jats:italic>. For<jats:italic>k<\/jats:italic>\u2208 {1, \u2026,<jats:italic>n<\/jats:italic>- 1}, let<jats:italic>X<\/jats:italic><jats:sup>(<jats:italic>k<\/jats:italic>)<\/jats:sup><jats:sub>1<\/jats:sub>, \u2026,<jats:italic>X<\/jats:italic><jats:sup>(<jats:italic>k<\/jats:italic>)<\/jats:sup><jats:sub><jats:italic>n<\/jats:italic>-<jats:italic>k<\/jats:italic><\/jats:sub>be the residual life lengths of the live components following the<jats:italic>k<\/jats:italic>th failure in the system. In this paper we extend various stochastic ordering results presented in Bairamov and Arnold (2008) on the residual life lengths of the live components in an (<jats:italic>n<\/jats:italic>-<jats:italic>k<\/jats:italic>+ 1)-out-of-<jats:italic>n<\/jats:italic>system, and also present a new result concerning the multivariate stochastic ordering of live components in the two-sample situation. Finally, we also characterize exponential distributions under a weaker condition than those introduced in Bairamov and Arnold (2008) and show that some special ageing properties of the original residual life lengths get preserved by residual life lengths.<\/jats:p>","DOI":"10.1017\/s002190020001007x","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:49:37Z","timestamp":1459262977000},"page":"58-68","source":"Crossref","is-referenced-by-count":1,"title":["Stochastic Orderings and Ageing Properties of Residual Life Lengths of Live Components in (n-k+1)-Out-Of-n 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