Abstract: Usually, only two states (failuse/success) of the bottom and top event are considered in FTA. But in the real world, the system and its components are capable of being in different failure modes and in a whole range of failure. Therefore, it necessary to develop the multi-state FTA approach. In this article, the multiple-valued logic is discussed, the disjaint Boolean algebraic method to analyze the fault tree with multi-state components is presented, and an example of FTA is introduced, in the later the statistically depedent events is replaced by a multi-state component.