Characterizing the Barlow-Wu structure functions

Various mathematical models for multistate systems have been proposed in the literature. Among them the model introduced by Barlow and Wu is the one most intimately related to that of binary systems; hence the Barlow-Wu class possesses many nice properties inherited from the binary system. This article obtains several characterization results for multistate systems, which closely relate the Barlow-Wu class to other classes of multistate systems. The characterizations it obtains originate from the invariance properties of the Barlow-Wu functions, and are easy to apply in verifying whether a particular model is of the Barlow-Wu type.