Multivariate counting processes with application to repairable systems

Survival processes and recurrent event processes are the subject of many texts. The worksof Kalbfleisch and Prentice (2002), Cook and Lawless (2008) and Aalen et al. (2008) allprovide detailed discussion of univariate event processes on which we base much of ourpresentational style. Andersen et al. (1993) and Daley and Vere-Jones (2002) providerigourous discussion of how recurrent event processes can be framed in the context ofcounting processes. Our particular interest lies in the multivariate extensions of countingprocesses. Briefly the extensions we consider areMarked counting processes where each event is recorded with supplemental data inthe form of random variables.Multitype counting processes which considers the evolution of multiple dependentcounting processes.Two-dimensional counting processes where each event is recorded in two scales suchas age and usage.Within the above mentioned texts and scientific journals the literature on such multivariatecounting processes is vast. Thus far this literature does not seem to have beencollated 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 personsinterested in the modelling and analysis of such multivariate processes. Particular focusis given to the development of parametric models with inference being provided by likelihoodmethods. 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 eachchapter with all R code being made available via a companion website