Approximation of First Passage Time Distributions of Compositions of Independent Markov Chains

To improve performance or reliability, systems frequently include multiple components that operate in parallel or with limited interaction, e.g., replicated components for triple modular redundancy. We consider components modeled by independent and possibly different continuous-time Markov chains and propose an approach to estimate the distribution of first passage times for a combination of component states (e.g., a system state where all components have failed) without generating the joint state space of the underlying Markov chain nor evaluating probabilities for each of its states. Our results highlight that the approach leads to accurate approximations with significant reductions of computational complexity.