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Initial and final behaviour of failure rate functions for mixtures and systems

Part of: Survival analysis and censored data Distribution theory

Published online by Cambridge University Press:  14 July 2016

Henry W. Block ,
Yulin Li  and
Thomas H. Savits
Henry W. Block*
Affiliation:
University of Pittsburgh
Yulin Li*
Affiliation:
University of Pittsburgh
Thomas H. Savits*
Affiliation:
University of Pittsburgh
*
∗Postal address: Department of Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA
∗Postal address: Department of Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA
∗Postal address: Department of Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA
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Abstract

In this paper we consider the initial and asymptotic behaviour of the failure rate function resulting from mixtures of subpopulations and formation of coherent systems. In particular, it is shown that the failure rate of a mixture has the same limiting behaviour as the failure rate of the strongest subpopulation. A similar result holds for systems except the role of strongest subpopulation is replaced by strongest min path set.

Keywords

MixtureIFRDFRbathtub shapefailure rateasymptotic behaviourinitial behaviourcoherent system

MSC classification

Primary: 62E10: Characterization and structure theory
Secondary: 62N05: Reliability and life testing
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003 , pp. 721 - 740
Copyright
Copyright © Applied Probability Trust 2003 

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Footnotes

The first and third authors were supported by NSF grant DMS-0072207.

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