Discrete Order Statistics

Dembińska, Anna

doi:10.1002/0471667196.ess7111

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2023

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“…However, for the discrete case, the preservation of the IFR and DFR properties is not straightforward because of the complexity of the discrete failure rate. Some properties on ageing notions and order statistics in the discrete case can be found in [2], [7], [8], [11] and [14].…”

Section: Introductionmentioning

confidence: 99%

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

Alimohammadi,

Navarro

2023

J. Appl. Probab.

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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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