Stochastic comparisons of series, parallel and k-out-of-n systems with heterogeneous bathtub failure rate type components

In this paper, we explore stochastic comparisons of order statistics arising from a two parameter distribution with bathtub shaped failure rate. We obtain detailed results in the contexts of the usual stochastic order, the hazard rate order, the reversed hazard rate order and the likelihood ratio or...

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Bibliographic Details
Published in:Physica A 2020-02, Vol.540, p.123124, Article 123124
Main Authors: Bhattacharyya, Dhrubasish, Khan, Ruhul Ali, Mitra, Murari
Format: Article
Language:English
Subjects:
[formula omitted]-out-of-[formula omitted] system
Chain majorization
Convex transform order
Schur-convexity
Stochastic order
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Summary:In this paper, we explore stochastic comparisons of order statistics arising from a two parameter distribution with bathtub shaped failure rate. We obtain detailed results in the contexts of the usual stochastic order, the hazard rate order, the reversed hazard rate order and the likelihood ratio order for series, parallel and k-out-of-n systems. Results involving multivariate chain majorization are also established. •Lifetimes of systems with heterogeneous Chen distributed components are discussed.•Stochastic comparison results based on vector majorization are established.•Analogous results are also proved under multivariate majorization setup.•Ageing comparisons between systems with Chen and exponentially distributed components.•A smorgasbord of results for k-out-of-n systems with Chen distributed components.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2019.123124