On The Static Reliability Of Binary-State And Multi-State K-Out-Of-N:G Systems

Abstract

The k-out-of-n:G (or k/n:G) system structure is a very popular of redundancy in
fault-tolerant systems, with wide applications in so many fields. This paper presents
two states of multi-state k/n:G systems. The first part, we present the definition that
introduced by Al-Neweihi et al [1], where the values are the same with respect
to all system states and we show that there exists an alternative equivalent definition
to Al-Neweihi's definition. In the second part of this paper we give more general
definition proposed by Huang et al [2], where it allows different values with
respect to different system states and we provide there exists an equivalent definition
to Huang's definition when the values are increasing. We show it is simply to
generalize the mathematical theory of static reliability of binary k/n:G systems to the
multistate k/n:G systems. Several new results are established concerning the
evaluation of the stochastic of the system static performance measures, together with
their computer algorithm (Belfour algorithm).