The first section covers structure functions for determining the reliability of a system in terms of the reliability of components. This model assumes that failed components are not repaired or replaced. The next section introduces Markov chains which offer a versatile modelling system. Markov chains with discrete time steps are covered first and classifies as regular, irreducible, and absorbing. Applications include internet routers and Moran’s dam model. Markov chains in continuous time, also known as Markov processes, are then introduce with applications to machine repair and Erlang’s telegraph formulae. The third section covers simulation of systems using MATLAB or R software, The chapter ends with: a summary of :the main results and exercises.