Modules of Coherent Binary Systems

The concept of a “module”, i.e., a package of components of a system which can be removed and replaced as a whole, has been long in use in systems design and analysis. In this paper a formal definition of this concept is given and its properties are studied. Most of the results are obtained for “coherent” systems, i.e., for systems whose performance improves as the performance of their components improves. For such systems the relationship between modules and minimal paths can be fully clarified, and the results obtained lead to a criterion for deciding whether or not a given set of components constitutes a module of a given system. It is shown that a coherent system always has uniquely determined maximal modules which have the property that either all are disjoint or no two of them are disjoint. These maximal modules determine uniquely a decomposition of the system into disjoint modular factors. Furthermore, a theorem on the union of modules (the “three modules theorem”), which has been previously known for general systems, is obtained by a rather simple argument for coherent systems.