Abstract
The study or analysis of a system of components can be immensely simplified if subsets of components can be viewed as single elements. The concept of replacing a subset of components of a system by a “module” has been used in systems analysis and design for a long period of time. A result that aids in system reduction or decomposition is the “three modules theorem,” proved by Birnbaum and Esary (1965) for binary coherent systems. The three modules theorem is extended to a special class of discrete multi-state coherent systems.
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