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Multivariate dependent renewal processes

Published online by Cambridge University Press:  01 July 2016

Eric Slud
Eric Slud*
Affiliation:
University of Maryland
*
∗Postal address: Department of Mathematics, University of Maryland, College Park, MD 20742, USA.
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Abstract

A new class of reliability point-process models for dependent components is introduced. The dependence is expressed through a regression, following a form suggested by Cox (1972) for survival data analysis involving the current life-length of the components. After formulating the current-life process as a Markov process with stationary transitions and stating some general results on asymptotic behavior, we describe the stationary distributions in some bivariate examples. Finally, we discuss statistical inference for the new models, exhibiting and justifying full- and partial-likelihood methods for their analysis.

Keywords

DEPENDENT COMPONENTSMARKOV PROCESSRELIABILITY THEORYPARTIAL LIKELIHOODMULTIVARIATE COUNTING PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 2 , June 1984 , pp. 347 - 362
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

Research supported by Air Force Office of Scientific Research under contract AFOSR-82–0187.

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