Commonly used equations have been developed which allow application of failure rate data for safeguards. While these equations often give reasonable results, they can significantly over predict the risk for sonic conditions. This can lead the analyst to believe that a given operation presents an unacceptable risk. requiring additional safety measures when, in fact, the operation may actually meet the risk criteria. This paper shows the limitations of the commonly used equations by comparing those equations with hazard rates generated from Monte Carlo simulations. A little-known equation is then presented, which is shown to precisely match the Monte Carlo simulations. It is suggested that this equation be used when accuracy is required. (c) 2005 Elsevier B.V. All rights reserved.