Resolving an old problem on the preservation of the IFR property under the formation of -out-of- systems with discrete distributions

More than half a century ago, it was proved that the increasing failure rate (IFR) property is preserved under the formation of k -out-of- n systems (order statistics) when the lifetimes of the components are independent and have a common absolutely continuous distribution function. However, this pr...

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Bibliographic Details
Published inJournal of applied probability Vol. 61; no. 2; pp. 644 - 653
Main Authors Alimohammadi, Mahdi, Navarro, Jorge
Format Journal Article
LanguageEnglish
Published Sheffield Cambridge University Press 01.06.2024
Subjects
Aging
Concavity
Continuity (mathematics)
Distribution functions
Failure rates
Lifetime
Random variables
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Summary:More than half a century ago, it was proved that the increasing failure rate (IFR) property is preserved under the formation of k -out-of- n systems (order statistics) when the lifetimes of the components are independent and have a common absolutely continuous distribution function. However, this property has not yet been proved in the discrete case. Here we give a proof based on the log-concavity property of the function $f({{\mathrm{e}}}^x)$ . Furthermore, we extend this property to general distribution functions and general coherent systems under some conditions.
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content type line 14
ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2023.63