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Dynamic multivariate mean residual life functions

Published online by Cambridge University Press:  14 July 2016

Moshe Shaked  and
J. George Shanthikumar
Moshe Shaked*
Affiliation:
University of Arizona
J. George Shanthikumar*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Department of Mathematics, Building #89, Universify of Arizona, Tucson, AZ 85721, USA.
∗∗ Postal address: Management Science Group, W. A. Haas School of Business, University of California, Berkeley, CA 94720, USA.
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Abstract

In this paper we introduce and study a dynamic notion of mean residual life (mrl) functions in the context of multivariate reliability theory. Basic properties of these functions are derived and their relationship to the multivariate conditional hazard rate functions is studied.

A partial ordering, called the mrl ordering, of non-negative random vectors is introduced and its basic properties are presented. Its relationship to stochastic ordering and to other related orderings (such as hazard rate ordering) is pointed out. Using this ordering it is possible to introduce a weak notion of positive dependence of random lifetimes. Some properties of this positive dependence notion are given.

Finally, using the mrl ordering, a dynamic notion of multivariate DMRL (decreasing mean residual life) is introduced and studied. The relationship of this multivariate DMRL notion to other notions of dynamic multivariate aging is highlighted in this paper.

Keywords

DECREASING MEAN RESIDUAL LIFEHAZARD RATE ORDERINGNOTIONS OF POSITIVE DEPENDENCESTOCHASTIC ORDERINGMULTIVARIATE AGING NOTIONSRELIABILITY THEORYWEAKENED BY FAILUREASSOCIATION OF RANDOM VARIABLESFREUND DISTRIBUTIONSTOCHASTIC MODELING
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 3 , September 1991 , pp. 613 - 629
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

Supported by the Air Force Office of Scientific Research, U.S.A.F., under Grant ADOSR-84–0205. Reproduction in whole or in part is permitted for any purpose by the United States Government.

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