This paper showed design reliability estimation results of Low Energy Exploding Foil Initiator(LEEFI) with uncertain components. LEEFI is an explosive ignition system that utilizes metallic bridge burst of thin film and flyer formation. This research constructed a meta-model of flyer velocity over time in order to increase computational efficiency in design reliability estimation. Design reliability for different distributions components, in this paper, was estimated using the meta-model of flyer velocity. And computational efficiency and accuracy results of the meta-model based reliability estimation were given.