Componentwise decomposition for an efficient reliability computation of systems with repairable components

Fault trees and Markov chains are commonly used for dependability modeling. Markov chains are powerful in that various kinds of dependencies can be easily modeled that fault tree models have difficulty capturing, but the state space grows exponentially in the number of components. Fault tree models are adequate for computing the reliability of nonrepairable systems, but a state space description becomes necessary for repairable systems due to induced dependencies (even when all failure and repair processes are otherwise independent). We demonstrate that a decomposition approach can be used to avoid a full-system Markov reliability model for repairable systems with independent failure and repair processes. For an n-component system, n 3-state sub-models can replace a full-system monolithic model. This is an approximation because the parameters used in the sub-model are approximately derived from the monolithic model.<>