Multivariate counting processes with application to repairable systems

Bell, S

Abstract

Survival processes and recurrent event processes are the subject of many texts. The works
of Kalbfleisch and Prentice (2002), Cook and Lawless (2008) and Aalen et al. (2008) all
provide detailed discussion of univariate event processes on which we base much of our
presentational style. Andersen et al. (1993) and Daley and Vere-Jones (2002) provide
rigourous discussion of how recurrent event processes can be framed in the context of
counting processes. Our particular interest lies in the multivariate extensions of counting
processes. Briefly the extensions we consider are
Marked counting processes where each event is recorded with supplemental data in
the form of random variables.
Multitype counting processes which considers the evolution of multiple dependent
counting processes.
Two-dimensional counting processes where each event is recorded in two scales such
as age and usage.
Within the above mentioned texts and scientific journals the literature on such multivariate
counting processes is vast. Thus far this literature does not seem to have been
collated into any one resource where all such processes are considered in conjunction.
The intended purpose of this thesis is to provide such a resource, especially for persons
interested in the modelling and analysis of such multivariate processes. Particular focus
is given to the development of parametric models with inference being provided by likelihood
methods. We primarily deal with repairable systems, where many of the processes discussed find a natural home. We attempt to present the material in an assessable manner.
Application is emphasised and we provide numerous examples at the end of each
chapter with all R code being made available via a companion website.

Citation

Bell, S. Multivariate counting processes with application to repairable systems. (Thesis). University of Salford

• Thesis Type: Thesis
• Deposit Date: Aug 12, 2021
• Award Date: May 1, 2012