Fault tree analysis is one of the most useful techniques in reliability analysis of multistate systems that analyze and handle complex systems via Monte Carlo simulations or mathematical approaches. Traditional fault tree cannot depict the exact evaluation of components and systems failures with respect to simplex analysis. On the other hand, the exact evaluation of system reliability with unknown data owning to components and elements is still difficult. Therefore, in this paper, in order to overcome this problem as for the quantitative analysis of fault trees, the reliability analysis of a multistate system (i.e. Launch Emergency Detection System) based on fault tree analysis and fuzzy failure rates is studied. Accordingly, using fuzzy arithmetic, events time-to-failure are generated and then the Top Event time to failure is calculated. Finally, the results of the analytical solution are compared with the results attained by presented approach and shows that, in spite of less effort and time consuming, this method has more accuracy and suitable for all real industrial and complex systems. This paper has further developed the method of FTA for the most generic case where both the system and the components have multiple failure states.