In order to study the influence of component failure rates on failure probability in dynamic systems, a new importance measure technique for component failure rates is presented in this paper. Characteristics of systematic dynamic failure probability in the presence of uncertainty are analyzed. Based on the Borgonovo moment-independent importance measure analysis method and Monte Carlo simulation, two new moment-independent uncertainty importance measures are proposed to estimate the contribution of component failure rates to system failure probabilities in two situations:A fixed and an interval variant working time. Moreover, an efficient algorithm of importance measure is developed to decrease the runs of performance function by combining the sparse grid integration (SGI) with the Edgeworth series. The SGI technique successfully transfers the multivariate functional integral to the tensor product of one-variable integrals, and the ES method transfers the cumulative distribution function of system response to a failure probability estimation of the response first four moments. Rationality and efficiency of the proposed method are finally illustrated by two examples.