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Median Inactivity Time Function and its Reliability Properties

Median Inactivity Time Function and its Reliability Properties Abstract Let the non-negative random variable X denote the life time of a unit, then the random variable X ( t ) = t – X for X ≤ t for a fixed t ∈ { x : F X ( x ) > 0}, is known as inactivity time or reversed residual life time. In this paper, we define a new non-parametric class of life distributions based on the median of the random variable X ( t ) and study its reliability properties. Some new results concerning the proposed class are given including some closure properties and characterizations. We also introduce and study a new stochastic ordering based on the median of X ( t ) and find its relationship with other well-known order relations. Finally, we provide the median inactivity time function of some well-known life time distributions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Economic Quality Control de Gruyter

Median Inactivity Time Function and its Reliability Properties

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Publisher
de Gruyter
Copyright
Copyright © 2010 by the
ISSN
1869-6147
eISSN
1869-6147
DOI
10.1515/eqc.2010.018
Publisher site
See Article on Publisher Site

Abstract

Abstract Let the non-negative random variable X denote the life time of a unit, then the random variable X ( t ) = t – X for X ≤ t for a fixed t ∈ { x : F X ( x ) > 0}, is known as inactivity time or reversed residual life time. In this paper, we define a new non-parametric class of life distributions based on the median of the random variable X ( t ) and study its reliability properties. Some new results concerning the proposed class are given including some closure properties and characterizations. We also introduce and study a new stochastic ordering based on the median of X ( t ) and find its relationship with other well-known order relations. Finally, we provide the median inactivity time function of some well-known life time distributions.

Journal

Economic Quality Controlde Gruyter

Published: Dec 1, 2010

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