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 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. We 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. © 1994 IEEE
Veeraraghavan, M., and K. S. Trivedi. “A Combinatorial Algorithm for Performance and Reliability Analysis Using Multistate Models.” IEEE Transactions on Computers 43, no. 2 (January 1, 1994): 229–34. https://doi.org/10.1109/12.262129.