The method of moments and probabilistic methods such as simulation are usually employed for uncertainty propagation. In particular, the method of moments has been widely used in reliability engineering to calculate the expected value and variance of a reliability estimate given uncertain parameter estimates. However, applying this method in an attempt to obtain the reliability estimate and its variance sometimes can present significant error. Hence, it is important to understand the applicable conditions that the source of uncertainty must uphold to control estimation error. In this paper, two cases are analyzed. The first case involves the Exponential distribution with the failure rate defined according to the Normal distribution. The second case deals with the Weibull distribution with the parameter estimates following the Uniform distribution. Derivations are provided to quantify the error in approximation.