A method is proposed for quantifying the expected number of accidents for a transportation system during some operating period. The operating period is divided into two parts. There is normal operation where everything is working correctly. These intervals can be studied deterministically by arguments-from-design or by tests. There is unsafe operation where equipment has failed, an error has occurred, or traffic perturbations have produced unusual circumstances. Such stochastic phenomena can be studied by experiments or simulation. These two types of operation create a natural partition. This paper proposes a Monte Carlo method based on this partition that appears appropriate for studying scarce events. Estimators for this method are developed. It is shown they are unbiased, and confidence intervals derived. There is also a discussion of integrating random failures with traffic flow in a discrete event simulation.
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