Multivariate counting processes with application to repairable systems

Bell, S 2012, Multivariate counting processes with application to repairable systems , PhD thesis, University of Salford.

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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.

Item Type:	Thesis (PhD)
Contributors:	Percy, DF (Supervisor)
Schools:	Schools > Salford Business School
Depositing User:	Institutional Repository
Date Deposited:	12 Aug 2021 14:27
Last Modified:	04 Aug 2022 11:22
URI:	https://usir.salford.ac.uk/id/eprint/61503

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