Multistate Markov Models and Structural Properties of the Transition-Rate Matrix

This paper explains how to use Markov models for evaluating the availability and reliability of a system when the transition rates of each component depend on the state of the system. To this purpose, the structural properties of the system transition-rate matrix, obtained by the Kronecker sum of transition rate matrices of the components, are analyzed. As a result, an efficient use of the Markov model is possible by mapping the transition rates of the single components into the elements of the system transition-rate matrix. The potential of parallel computers can facilitate this approach, giving renewed interest to the Markov method for complex systems.