Recently the theory of multistate reliability models has been developed to cope with many real-life situations. The present paper introduces multistate coherent systems of order k, where k refers to the number of levels for which the underlying components of the system are relevant. It is shown that many multistate systems introduced earlier by different authors are included in the class of multistate coherent systems of order k. The dual class, k-parallel and k-series systems are introduced and studied. The main structural properties of this class, which are analogous to the well-known results for coherent systems, are established. © 1995.
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