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Stochastic comparisons of interfailure times under a relevation replacement policy

Part of: Distribution theory - Probability Sufficiency and information

Published online by Cambridge University Press:  04 April 2017

Miguel A. Sordo  and
Georgios Psarrakos
Miguel A. Sordo*
Affiliation:
University of Cádiz
Georgios Psarrakos*
Affiliation:
University of Piraeus
*
* Postal address: Department of Statistics and Operation Research, University of Cádiz, 11510 Puerto Real, Cádiz, Spain. Email address: mangel.sordo@uca.es
** Postal address: Department of Statistics and Insurance Science, University of Piraeus, 18534 Piraeus, Greece. Email address: gpsarr@unipi.gr
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Abstract

We provide some results for the comparison of the failure times and interfailure times of two systems based on a replacement policy proposed by Kapodistria and Psarrakos (2012). In particular, we show that when the first failure times are ordered in terms of the dispersive order (or, the excess wealth order), then the successive interfailure times are ordered in terms of the usual stochastic order (respectively, the increasing convex order). As a consequence, we provide comparison results for the cumulative residual entropies of the systems and their dynamic versions.

Keywords

Stochastic orderdispersive orderexcess wealth orderincreasing convex ordercumulative residual entropy

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62B10: Information-theoretic topics
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 1 , March 2017 , pp. 134 - 145
Copyright
Copyright © Applied Probability Trust 2017 

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