A combinatorial algorithm for performance and reliability analysis using multistate models

The need for the combined performance and reliability analysis of fault tolerant systems is increasing. The common approach to formulating and solving such problems is to use (semi-)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. However, assumptions of two-state behavior of components (and that of the system), independence assumptions of component state transitions, and restrictive repair assumptions decrease the potential of combinatorial models for realistic systems. The authors propose a combinatorial algorithm for the combined performance and reliability analysis of coherent repairable systems with multistate components, allowing interdependent component state transitions. An example illustrating the algorithm is also presented