We investigate fast simulation techniques for estimating the
unreliability in large Markovian models of highly reliable systems for
which analytical/numerical techniques are difficult to apply. We
first show mathematically that for “small” time horizons,
the relative simulation error, when using the importance sampling
techniques of failure biasing and forcing, remains bounded as component
failure rates tend to zero. This is in contrast to naive simulation
where the relative error tends to infinity. For “large”
time horizons where these techniques are not efficient, we use the
approach of first bounding the unreliability in terms of
regenerative-cycle-based measures and then estimating the
regenerative-cycle-based measures using importance sampling; the latter
can be done very efficiently. We first use bounds developed in the
literature for the asymptotic distribution of the time to hitting a
rare set in regenerative systems. However, these bounds are
“close” to the unreliability only for a certain range of
time horizons. We develop new bounds that make use of the special
structure of the systems that we consider and are “close”
to the unreliability for a much wider range of time horizons. These
techniques extend to non-Markovian, highly reliable systems as long as
the regenerative structure is preserved.