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Comparison of replacement policies via point processes

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

Moshe Shaked  and
Ryszard Szekli
Moshe Shaked*
Affiliation:
University of Arizona
Ryszard Szekli*
Affiliation:
Wrocław University
*
* Postal address: Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA. Supported by NSF Grant DMS 9303891.
** Postal address: Mathematical Institute, Wrocław University, 50–384 Wrocław, pl. Grunwaldzki 2/4, Poland.
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Abstract

First, some basic concepts from the theory of point processes are recalled and expanded. Then some notions of stochastic comparisons, which compare whole processes, are introduced. The use of these notions is illustrated by stochastically comparing renewal and related processes. Finally, applications of the different notions of stochastic ordering of point processes to many replacement policies are given.

Keywords

AGE REPLACEMENT POLICIESBLOCK REPLACEMENT POLICIESMINIMAL REPAIRSTOCHASTIC ORDERDISPERSIVE ORDERHAZARD RATE ORDERCOMPENSATORSRENEWAL PROCESSNON-HOMOGENEOUS POISSON PROCESSCOUNTING PROCESSESDFRIFRNBUNWUTHINNING OF POINT PROCESSES

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 4 , December 1995 , pp. 1079 - 1103
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

This work was done while this author was visiting the Department of Industrial Engineering, Texas A&M University, College Station, and in part during his visit to the Department of Mathematics, University of Arizona, Tucson, hospitality of which is gratefully acknowledged.

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