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Load-Sharing Reliability Models with Different Component Sensitivities to Other Components’ Working States

Part of: Survival analysis and censored data Nonparametric inference

Published online by Cambridge University Press:  17 March 2021

Tomasz Rychlik  and
Fabio Spizzichino
Tomasz Rychlik*
Affiliation:
Polish Academy of Sciences
Fabio Spizzichino*
Affiliation:
Sapienza University of Rome
*
*Postal address: Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00 656 Warsaw, Poland. Email address: [email protected]
**Postal address: Sapienza University of Rome, Rome, Italy. Email address: [email protected]
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Abstract

We study the distributions of component and system lifetimes under the time-homogeneous load-sharing model, where the multivariate conditional hazard rates of working components depend only on the set of failed components, and not on their failure moments or the time elapsed from the start of system operation. Then we analyze its time-heterogeneous extension, in which the distributions of consecutive failure times, single component lifetimes, and system lifetimes coincide with mixtures of distributions of generalized order statistics. Finally we focus on some specific forms of the time-nonhomogeneous load-sharing model.

Keywords

Multivariate conditional hazard ratelinear breakdown modelMarkov property of failure processdecomposition of reliability functiongeneralized order statisticsexchangeabilityuniform supporting abilityuniform frailty

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 62G30: Order statistics; empirical distribution functions
Type
Original Article
Information
Advances in Applied Probability , Volume 53 , Issue 1 , March 2021 , pp. 107 - 132
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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