Due to the heterogeneity of natural groundwater systems, any quantitative description of aquifer hydraulic properties is subject to uncertainty. Consequently, prediction of groundwater transport is also subject to uncertainty. Stochastic approaches to transport simulation quantify this uncertainty in terms of random variables and processes. An important practical consideration in the application of such methods is their computational cost. In recent years, the first-order reliability method (FORM) has been introduced as a possible technique for obtaining stochastic results with low computational cost. Specifically, the implementation of FORM known as advanced FORM (AFORM) has been shown to produce reasonably accurate results when applied to simple problems. However, recently published results indicate that the computational burden of AFORM can equal, or even exceed, that of Monte Carlo simulations when applied to groundwater contamination problems with a large number of variables. If FORM is to be a viable alternative, the computational cost of the method must be lowered. In. this work, we propose a more efficient implementation of FORM. The primacy numerical difficulty that arises in AFORM is locating the linearization point, a procedure that requires the solution of a non-linearly constrained optimization problem. We reduce the number of variables in the constraint by zoning the aquifer parameters during this stage of the calculation, resulting in an algorithm with lower computational cost. The new approach is shown to produce results that are nearly identical to those obtained with AFORM when applied to a one-dimensional transport problem. Future work will be aimed at generalising the procedure described herein.