Lattice set theoretic treatment of multi-state coherent systems

In this paper we present a definition of multi-state coherent systems, the state spaces of which are lattice and not necessarily totally ordered sets. We focus on an examination of series and parallel systems and give an existence theorem of the systems, which shows us conditions on the state spaces making us possible to consider series and parallel systems. We also present an expression of multi-state systems by series systems which is a generalization of well-known max–min formula for the binary-state case. This formula may be used for evaluation of stochastic performance of the systems.