An assumption that pervades the current transportation system reliability assessment literature is that probability distributions of the sources of uncertainty (i.e. road capacities and travel demand) are known explicitly. However, this distribution may be unavailable (inaccurate) in reality as we may have no (insufficient) data to calibrate the distribution. We relax this assumption and present a method to assess travel time reliability that is distribution-free, i.e. the methodology only requires that the mean values of capacity and demand are known and that they reside in a bounded and known interval. Moreover, the proposed methodology eliminates the need to specify the dependence structure among the random variables. Instead of deriving exact probabilities on travel times exceeding certain thresholds via computationally intensive methods, we develop analytical probability inequalities to quickly obtain bounds on the desired probability. Numerical experiments demonstrate that the derived bounds are nontrivial for the most interesting cases.