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A new algorithm based on binary decision diagram (BDD) for the analysis of a system with multistate components is proposed. Each state of a multistate component is represented by a boolean variable, and a multistate system is represented by a series of multistate fault trees. A Boolean algebra with restrictions on variables is used to address the dependence among these boolean variables that collectively represent the same component and a new BDD operation is proposed to realize this Boolean algebra. Due to the nature of the BDD, the sum of disjoint products (SDP) can be implicitly represented, which avoids huge storage and high computational complexity for large multistate systems. Some applications are given to illustrate the use of our new algorithm.