In a fault tree analysis, an uncertainty importance measure is often used to assess how much uncertainty of the top event probability (Q) is attributable to the uncertainty of a basic event probability ($q_i$), and thus, to identify those basic events whose uncertainties need to be reduced to effectively reduce the uncertainty of Q. For evaluating the measures suggested by many authors which assess a percentage change in the variance V of Q with respect to unit percentage change in the variance $v_i$ of $q_i$, V and ${partial}V/{partial}v_i$ need to be estimated analytically or by Monte Carlo simulation. However, it is very complicated to analytically compute V and ${partial}V/{partial}v_i$ for large-sized fault trees, and difficult to estimate them in a robust manner by Monte Carlo simulation. In this paper, we propose a method for evaluating the measure using discretization technique and Monte Carlo simulation. The proposed method provides a stable uncertainty importance of each basic event.