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Some bivariate notions of IFR and DMRL and related properties

Part of: Stochastic processes Survival analysis and censored data Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Bruno Bassan ,
Subhash Kochar  and
Fabio Spizzichino
Bruno Bassan*
Affiliation:
Università di Roma ‘La Sapienza’
Subhash Kochar*
Affiliation:
Indian Statistical Institute
Fabio Spizzichino*
Affiliation:
Università di Roma ‘La Sapienza’
*
∗ Postal address: Dipartimento di Matematica, Università di Roma ‘La Sapienza’, Piazzale Aldo Moro 5, 00185 Roma, Italy.
∗∗∗ Postal address: Indian Statistical Institute, 7 S. J. S. Sansanwal Marg, New Delhi 110016, India.
∗ Postal address: Dipartimento di Matematica, Università di Roma ‘La Sapienza’, Piazzale Aldo Moro 5, 00185 Roma, Italy.
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Abstract

Recently Bassan and Spizzichino (1999) have given some new concepts of multivariate ageing for exchangeable random variables, such as a special type of bivariate IFR, by comparing distributions of residual lifetimes of dependent components of different ages. In the same vein, we further study some properties of these concepts of IFR in the bivariate case. Then we introduce certain concepts of bivariate DMRL ageing and we develop a treatment that parallels those developed for bivariate IFR. For both the IFR and DMRL concepts, we analyse a weak and a strong version, and discuss some of the differences between them.

Keywords

Residual lifetimemean residual life functionmultivariate extensions of IFR and DMRLlog-concavitySchur-concavityageing properties of mixtures

MSC classification

Primary: 62N05: Reliability and life testing 60G09: Exchangeability 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 3 , September 2002 , pp. 533 - 544
Copyright
Copyright © Applied Probability Trust 2002 

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