The analysis of discrete accident data and aggregate exposure data frequently necessitates compromises that can obscure the relationship between accident occurrence and potential causal risk components. One way to overcome these difficulties is to develop a model of accident occurrence that includes accident and exposure data at a mathematically consistent disaggregate level. This paper describes the conceptual and mathematical development of such a model using principals of survival theory. The model predicts the probability of being involved in an accident at time t given that a vehicle has survived until that time. Several alternative functional forms are discussed including additive, proportional hazards and accelerated failure time models. Model estimation is discussed for the case in which both accident and nonaccident trips are included and for the case with only accident data. As formulated, the model has the distinct advantage of being able to consider accident and exposure data at a disaggregate level in an entirely consistent analytic framework. A conditional accident analysis is undertaken using truck accident data obtained from a major national carrier in the United States. Model results are interpretable and generally reasonable. Of particular interest is that segmenting accidents in several categories yields very different sets of significant parameters. Driver service hours seemed to most strongly effect accident risk: regularly scheduled drivers who take frequent trips are likely to have a reduced risk of an accident, particularly if they have a longer (greater than eight) number of hours off-duty just prior to a trip.