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Properties of classes of life distribution based on the conditional variance

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

Published online by Cambridge University Press:  14 July 2016

Jordan Stoyanov  and
M. H. M. Al-Sadi
Jordan Stoyanov*
Affiliation:
University of Newcastle upon Tyne
M. H. M. Al-Sadi*
Affiliation:
University of Newcastle upon Tyne
*
∗ Postal address: School of Mathematics and Statistics, University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, UK
∗ Postal address: School of Mathematics and Statistics, University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, UK
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Abstract

We consider two classes of life distribution, V D and V I , the members of which are defined in terms of the conditional variance σ 2(t) of the remaining lifetime of a system: a life distribution F belongs to V D if is a decreasing function and to V I if is increasing. We study closure properties of these classes under relevant reliability operations such as mixing, convolution and formation of coherent systems. We show, for example, that the class V D is not closed under convolution or mixing, and that the class V I is not closed under formation of coherent systems.

Keywords

Conditional variancedecreasing-variance life distributionincreasing-variance life distributionmixingconvolutionformation of coherent system

MSC classification

Primary: 62N05: Reliability and life testing 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 4 , December 2004 , pp. 953 - 960
Copyright
Copyright © Applied Probability Trust 2004 

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