RELIABILITY OF A CIRCULAR CONNECTED-(r,s)-OUT-OF-(m,n) : F LATTICE SYSTEM

Abstract

A circular connected-(r,s)-out-of-(m,n):F lattice system has m・ n components and is consisted of n rays and m circles. The system fails if and only if a connected (r,s)-matrix of components fail. Firstly, this paper proposes a recursive algorithrn for the reliability of the system, which requires O(r^n^2sm) computing time. In the statist,ically independent identically distributed case, the computing time is able to be reduced. Secondly, the upper and lower bounds for the system reliability are obtained for the circular connected-(r,s)-out-of-(m,n):F lattice systern. Finally, it is proved that the reliability of the large system tends to exp[-μλ^<rs>] as n = μn^<n-1>, n → ∞ if every component has failure probability λn^<-η/rs>, where μ, λ and η are constant, μ, λ > 0, η > r.