Monte Carlo has for a long time been the high fidelity model of choice in particle transport. The current state of the art in uncertainty propagation in particle transport is the so called Total Monte Carlo (TMC) method, a method which relies on the repeated execution of the same transport simulation. This however is often computationally intractable even with modern high performance computing standards. In this paper we review the TMC method, with a slight modification, and propose an alternative based on interval analysis; which provides a robust bound on the uncertainty in a single model evaluation.