Properties of System Lifetime in the Classical Model with I.I.D. Exponential Component Lifetimes

Szymkowiak, Magdalena

doi:10.1007/978-3-030-62900-7_3

Cited by 3 publications

(2 citation statements)

References 22 publications

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“…Preservation properties for NBUE/NWUE classes can be seen in [15] and [16]. Recent preservation results for systems under the exponential distribution were obtained in [24].…”

Section: Introductionmentioning

confidence: 95%

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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“…Preservation properties for NBUE/NWUE classes can be seen in [15] and [16]. Recent preservation results for systems under the exponential distribution were obtained in [24].…”

Section: Introductionmentioning

confidence: 95%

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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“…component lifetimes. Recently, Rychlik and Szymkowiak [16] considered coherent systems composed of components with i.i.d. exponential lifetimes and presented conditions on the system signature which determine monotonicity, unimodality, and strong unimodality of density functions of system lifetimes.…”

Section: Introductionmentioning

confidence: 99%

Preservation properties of some reliability classes by lifetimes of coherent and mixed systems and their signatures

Izadkhah

Amini-Seresht²

2022

Prob. Eng. Inf. Sci.

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This paper examines the preservation of several aging classes of lifetime distributions in the formation of coherent and mixed systems with independent and identically distributed (i.i.d.) or identically distributed (i.d.) component lifetimes. The increasing mean inactivity time class and the decreasing mean time to failure class are developed for the lifetime of systems with possibly dependent and i.d. component lifetimes. The increasing likelihood ratio property is also discussed for the lifetime of a coherent system with i.i.d. component lifetimes. We present sufficient conditions satisfied by the signature of a coherent system with i.i.d. components with exponential distribution, under which the decreasing mean remaining lifetime, the increasing mean inactivity time, and the decreasing mean time to failure are all satisfied by the lifetime of the system. Illustrative examples are presented to support the established results.

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Preservation of distributional properties of component lifetimes by system lifetimes

Arnold

Szymkowiak

2022

TEST

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Properties of System Lifetime in the Classical Model with I.I.D. Exponential Component Lifetimes

Cited by 3 publications

References 22 publications

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

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

Preservation properties of some reliability classes by lifetimes of coherent and mixed systems and their signatures

Preservation of distributional properties of component lifetimes by system lifetimes

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