In two subsequent parts, Part I and II, monotonicity and comparison results will be studied, as generalization of the pure stochastic case, for arbitrary dynamic systems governed by nonnegative matrices. Part I covers the discrete-time and Part II the continuous-time case. The research has initially been motivated by a reliability application contained in Part II. In the present Part I it is shown that monotonicity and comparison results, as known for Markov chains, do carry over rather smoothly to the general nonnegative case for marginal, total and average reward structures. These results, though straightforward, are not only of theoretical interest by themselves, but also essential for the more practical continuous-time case in Part II (see \cite{DijkSl2}). An instructive discrete-time random walk example is included.
This second Part II, which follows a first Part I for the discrete-time case (see \cite{DijkSl1}), deals with monotonicity and comparison results, as generalization of the pure stochastic case, for stochastic dynamic systems with arbitrary nonnegative generators in the continuous-time case. In contrast with the discrete-time case the generalization is no longer straightforward. A discrete-time transformation will therefore be developed first. Next, results from Part I can be adopted. The conditions, the technicalities and the results will be studied in detail for a reliability application that initiated the research. This concerns a reliability network with dependent components that can breakdown. A secure analytic performance bound is obtained.