An analytic structural reliability analysis is performed for first contact miscible, two-phase flow in a one-dimensional porous medium. The sensitivity of the probability for time-to-breakthrough is examined for two common models of the joint probability distribution between the porosity and the permeability of the medium. First-order analysis is essentially exact for the normal-normal model. The accuracy of first-order analysis for the normal-lognormal model is determined using a specific example of field data. A cyclical dependence on the breakthrough probability to the statistical nature of the porosity and permeability is found in the normal-normal model. In the normal-lognormal model, this cyclical variation is reduced, if not entirely eliminated, in favor of dependence on the statistical nature of the permeability.