Mathematics of Systems' Reliability: Systems' Structure and Stochastic Performance

Abstract

In this manuscript, by reviewing the mathematical theory of binary state systems, some crucial concepts in the theory, like minimal cut and minimal path vectors, a modular decomposition and stochastic wear processes, are generalized to the case of a multi-state system with totally ordered state spaces. Furthermore, we show the applicability of a model of a multistate system to the reliability analysis of a network.