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Multivariate conditional hazard rates and the MIFRA and MIFR properties

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, The University of Arizona, Tucson, AZ 85721, USA.
∗∗ Postal address: School of Business Administration, University of California, Berkeley, CA 94720, USA.
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Abstract

If T = (T1, · ··, Tn) is a vector of random lifetimes then its distribution can be determined by a set λof multivariate conditional hazard rates. In this paper, sufficient conditions on λare found which imply that T is Block–Savits MIFRA (multivariate increasing failure rate average) or Savits MIFR (multivariate increasing failure rate). Applications for a multivariate reliability model of Ross and for load-sharing models are given. The relationship between Shaked and Shanthikumar model of multivariate imperfect repair and the MIFRA property is also discussed.

Keywords

MULTIVARIATE IFR AND IFRALOGCONCAVITYSUBHOMOGENEOUS AND SUPERHOMO-GENEOUS FUNCTIONSRELIABILITY MODELINGLOAD-SHARING MODELINGMULTIVARIATE IMPERFECT REPAIR
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 1 , March 1988 , pp. 150 - 168
Copyright
Copyright © Applied Probability Trust 1988 

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Footnotes

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

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