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

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 k^ 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 fcth values with respect to different system states and we provide there exists an equivalent definition to Huang s definition when the fcvalues 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).