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New partial ordering of survival functions based on the notion of uncertainty

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

Published online by Cambridge University Press:  14 July 2016

Nader Ebrahimi  and
Franco Pellerey
Nader Ebrahimi*
Affiliation:
Northern Illinois University
Franco Pellerey*
Affiliation:
Politecnico di Milano
*
∗Postal address: Division of Statistics, Northern Illinois University, Dekalb, IL 60115, USA.
∗∗Postal address: Dipartimento di Matematica, Politecnico di Milano, Piazza L. da Vinci 32, 20139 Milano, Italy.
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Abstract

A new partial ordering among life distributions in terms of their uncertainties is introduced. Our measure of uncertainty is Shannon information applied to the residual lifetime. The relationship between this ordering and various existing orderings of life distributions are discussed. Various properties of our proposed concept are examined. Based on our proposed ordering and various existing orderings, the notion of a ‘better system' is introduced.

Keywords

LIFE DISTRIBUTIONSSHANNON'S MEASURE OF INFORMATIONENTROPYSTOCHASTIC ORDERINGSMONOTONE FAILURE RATE

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 1 , March 1995 , pp. 202 - 211
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Supported by Istituto Nazionale di Alta Matematica ‘F. Severi'.

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