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Univariate and multivariate stochastic orderings of residual lifetimes of live components in sequential (𝑛-π‘Ÿ+ 1)-out-of-𝑛 systems

Published online by Cambridge University Press:Β  16 November 2018

Ghobad Barmalzan*
University of Zabol
Abedin Haidari*
Shahid Beheshti University
Narayanaswamy Balakrishnan*
McMaster University
* Postal address: Department of Statistics, University of Zabol, Sistan and Baluchestan, Iran. Email address:
** Postal address: Department of Mathematical Sciences, Shahid Beheshti University, G.C. Evin, Tehran, Iran.
*** Postal address: Department of Mathematics and Statistics, McMaster University, Hamilton, Canada.


Sequential order statistics can be used to describe the ordered lifetimes of components of a system when the failure of a component may affect the reliability of the remaining components. After a reliability system consisting of n components fails, some of its components may still be alive. In this paper we first establish some univariate stochastic orderings and ageing properties of the residual lifetimes of the live components in a sequential (n-r+1)-out-of-n system. We also obtain a characterizing result for the exponential distribution based on uncorrelated residual lifetimes of live components. Finally, we provide some sufficient conditions for comparing vectors of residual lifetimes of the live components from two sequential (n-r+1)-out-of-n systems. The results established here extend some well-known results in the literature.

Research Papers
Copyright Β© Applied Probability Trust 2018Β 

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