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The limiting failure rate for a convolution of life distributions

Part of: Special processes Survival analysis and censored data

Published online by Cambridge University Press:  30 March 2016

Henry W. Block ,
Naftali A. Langberg  and
Thomas H. Savits
Henry W. Block*
Affiliation:
University of Pittsburgh
Naftali A. Langberg*
Affiliation:
Haifa University
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

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In this paper we investigate the limiting behavior of the failure rate for the convolution of two or more life distributions. In a previous paper on mixtures, Block, Mi and Savits (1993) showed that the failure rate behaves like the limiting behavior of the strongest component. We show a similar result here for convolutions. We also show by example that unlike a mixture population, the ultimate direction of monotonicity does not necessarily follow that of the strongest component.

Keywords

Reliabilityfailure rate functionincreasing failure ratedecreasing failure rateconvolution

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Short Communications
Information
Journal of Applied Probability , Volume 52 , Issue 3 , September 2015 , pp. 894 - 898
Copyright
Copyright © 2015 by the Applied Probability Trust 

References

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