(Master’s Program in Social Systems Engineering) Adviser

The class of counting processes constitutes a significant part of applied probability. The classic counting processes of importance include a Poisson process, a non-homogeneous Poisson process (NHPP) and a renewal process. More sophisticated counting processes have been developed in order to accommodate a wider range of applications. All of these counting processes seem to be quite different on surface, forcing one to understand each of them separately. The purpose of this thesis is to develop a unified multivariate counting process which would contain all of the above examples as special cases. The dynamic behavior of the unified multivariate counting process is captured through analysis of the underlying Laplace transform generating functions, yielding asymptotic results. As an application, a manufacturing system with certain maintenance policies is considered, where the unified multivariate counting process enables one to determine numerically the optimal maintenanc