The reliability of the electric power transmission system depends on the reliability of its components. As components age, the technical condition degrades, and the probability of failure will increase. Consequently, to estimate the reliability of a transmission system it is valuable to include the effect of deteriorating components. Recent work has demonstrated how this can be done. However, condition dependent reliability models introduce new sources of uncertainty that needs to be accounted for and that may be especially important in a long time horizon. This work presents a novel approach to propagate the uncertainty in input parameters through the system reliability analysis. Monte Carlo simulation is used to create an ensemble to span the sample space of reliability of supply indices. The effect of each source of uncertainty may be seen separately, or the effect of several sources is seen jointly. The methodology is demonstrated using a failure model for high voltage power transformers in the transmission system. The example illustrates that the methodology can identify which sources of uncertainty have significant impact on the uncertainty of system reliability indices and to what degree system uncertainty is amplified or moderated by interactions between the sources of uncertainty. Moreover, it is shown that the uncertainty will not necessarily increase uniformly over time.