One of the most difficult problems we face in assessing volcanic hazards is that of evaluating the potential activity of volcanoes with little or no record of Holocene eruptions. Is there some minimum period of inactivity after which we can safely rule out a future eruption of large magnitude? Or, failing that, can we say how likely it is that such a volcano will return to activity within a particular span of time? Violent explosive eruptions are uncommon during the youthful stage of active growth. They are confined almost entirely to large mature volcanoes. Here, we use the global record of volcanic activity (Simkin & Siebert 1994) to evaluate the duration of repose intervals preceding such explosive volcanic eruptions. This analysis indicates that the hazard rate for explosive eruptions is not constant with time, but depends on the time since last eruption and that explosive eruptions may occur at volcanoes that have been quiescent for 10 ka or more. The techniques we employ are common to a class of problems in survival analysis (Cox & Oakes 1984; Woo 1999), and can be applied to a variety of hazard problems on volcanoes (e.g. Hill et al. 1998; Connor et al. 2003; Calder et al. 2005). One of the major lessons of this type of analysis is that applied statistical methods can teach us much about the time scales of volcanic activity, and about the underlying physical mechanisms governing these.