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Nested renewal processes

Published online by Cambridge University Press:  01 July 2016

J. Ansell ,
A. Bendell  and
S. Humble
J. Ansell*
Affiliation:
University of Keele
A. Bendell*
Affiliation:
Dundee College of Technology
S. Humble*
Affiliation:
Sheffield City Polytechnic
*
∗Postal address: Department of Mathematics, University of Keele, Keele, Staffordshire ST5 5BG, U.K.
∗∗Postal address: Department of Mathematics and Computer Studies, Dundee College of Technology, Bell St, Dundee DD1 1HG, U.K.
∗∗∗Present address: Mathematics and Ballistics Branch, Royal Military College of Science, Shrivenham, Swindon, Wilts SN6 8LA, U.K.
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Abstract

A class of stochastic processes useful in the investigation of the deterioration and replacement of equipment, as well as in the study of group arrival/batch service queues, storage systems, epidemics and computer software, is introduced. These so-called nested renewal processes consist of ordinary and cumulative renewal processes sequentially nested within a hierarchy. The main properties of these processes are discussed with emphasis on the asymptotic results. An example of their application to tyre wear is considered.

Keywords

COMPETING RISKS: DAMAGE MODELS: LAPLACE TRANSFORM TECHNIQUES: RENEWAL PROCESSES: SHOCK MODELS: TYRE WEAR

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 4 , December 1980 , pp. 880 - 892
Copyright
Copyright © Applied Probability Trust 1980 

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References

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