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Some results on the relative ageing of two life distributions

Part of: Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Debasis Sengupta  and
Jayant V. Deshpande
Debasis Sengupta*
Affiliation:
Indian Statistical Institute
Jayant V. Deshpande*
Affiliation:
University of Poona
*
∗Postal address: Computer Science Unit, 203 Barrackpore Trunk Road, Calcutta 700 035, India.
∗∗Postal address: Department of Statistics, University of Poona, Pune 411 007, India.
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Abstract

Kalashnikov and Rachev (1986) have proposed a partial ordering of life distributions which is equivalent to an increasing hazard ratio, when the ratio exists. This model can represent the phenomenon of crossing hazards, which has received considerable attention in recent years. In this paper we study this and two other models of relative ageing. Their connections with common partial orderings in the reliability literature are discussed. We examine the closure properties of the three orderings under several operations. Finally, we give reliability and moment bounds for a distribution when it is ordered with respect to a known distribution.

Keywords

CROSSING HAZARD RATESINCREASING HAZARDS RATIOIFRIFRANBURELIABILITY OF BOUNDSSTABILITY OF DISTRIBUTIONS

MSC classification

Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Research Article
Information
Journal of Applied Probability , Volume 31 , Issue 4 , December 1994 , pp. 991 - 1003
Copyright
Copyright © Applied Probability Trust 1994 

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