Characterization of system signatures

TL;DR

This paper introduces a combinatorial method using simplicial sets to characterize and construct system signatures in reliability theory, providing a complete classification of possible signature vectors.

Contribution

It offers a novel combinatorial approach to determine and realize system signatures, expanding the theoretical tools available in system reliability analysis.

Findings

Provides a full characterization of signature vectors.

Develops a method to determine if a vector can be a system signature.

Shows how to construct systems with a given signature.

Abstract

We suggest a purely combinatorial approach to a general problem in system reliability. We show how to determine if a given vector can be the signature of a system, and in the affirmative case exhibit such a system in terms on its structure function. The method employs results from the theory of simplicial sets, and provides a full characterization of signature vectors.