Discrete Time Minimal Repair Process and Its Reliability Applications under Random Environments

In this paper, we define a discrete time version of the nonhomogeneous Poisson process and study its properties. For the definition and analysis, we suggest new general concepts for discrete time point processes. The proposed process possesses several stochastic properties which are analogous to those of continuous time nonhomogeneous Poisson process. It will also be shown that, under certain conditions, the proposed discrete time version of nonhomogeneous Poisson process converges to the continuous time version. Based on the proposed process, useful reliability applications are discussed.