Bounded normal approximation in simulations of highly reliable Markovian systems

In this paper, we give necessary and sufficient conditions to ensure the va lidity of confidence intervals, based on the central limit theorem, in simu lations of highly reliable Markovian systems. We resort to simulations beca use of the frequently huge state space in practical systems. So far the lit erature has focused on the property of bounded relative error. In this pape r we focus on 'bounded normal approximation' which asserts that the approxi mation of the normal law, suggested by the central limit theorem, does not deteriorate as the reliability of the system increases. Here we see that th e set of systems with bounded normal approximation is (strictly) included i n the set of systems with bounded relative error.