Approach for combinatorial performance and availability analysis

The common approach to formulating and solving combined reliability/availability and performance problems is to use Markov reward models. However, the large size of state spaces is a problem that plagues Markovian models. Combinatorial models have been used for modeling reliability and availability of complex systems without paying the price of large Markov models. But, assumptions of two-state behavior of components (and that of the system), independence assumptions of component failure behavior and restrictive repair assumptions decrease the potential of combinatorial models for realistic systems. We propose a combinatorial approach for the combined performance and availability analysis of coherent repairable systems with multi-stat components, allowing interdependent component state transitions. Examples showing the usefulness of the approach are presented.