In this paper, the reliability assessment based-on fault tree analysis in coherent multi-state emergency detection system in a sounding rocket is explained. A system with more complexity and contains much intersection terms was built, that, the analysis of such system whether by means of minimal cut-set nor Binary Decision Diagram (BDD) approaches need complex analysis and will be time consuming owing to intersection terms. Also, the determined results have less accuracy and contain uncertainty. To overcoming this problems, a combinatorial method for solving static fault tree are used. This method combines minimal cut-set with BDD methods, then, it computes the occurrence probability of top-event in fault tree. To describe and show capability of this method, Emergency Detection system (EDS) of a space craft is studied as a case-study. We assume that, overall system consists of two sub-systems: sending signal sub-system and cabin indicator instrumental sub-system. Two different fault trees are constructed; ones for each are constructed and explained. At the end, the results of the multi-state systems consist of multi-state elements are presented. Also, the reliability value of this system is determined.