A polytope approach to the optimal assembly problem

Abstract

The problem of assembling components into series modules to maximize the system reliability has been intensively studied in the literature. Invariably, the methods employed exploit special properties of the reliability function through standard analytical optimization techniques. We propose a geometric approach by exploiting the assembly polytope - a polytope generated by the potential assembly configurations. The new approach yields simpler proofs of known results, as well as new results about systems where the number of components in a module is not fixed, but subject to lower and upper bounds.