Abstract
Few papers study the reliability of consecutive-   1 2 3 r , r , r -out-of-   1 2 3 n ,n ,n : F system, since
the computation of reliability in the 3- dimensional system is more complicated than the other
systems; most of researchers study special cases.
In this paper, we study a special case of 3-dimentional systems, it is 1,1,2 , 1,2,1 or 2,1,1 -
out- of- n,2,2 : F or connected 2-out-of- n,2,2 : F system, we compute reliability of the
system using three methods; the 1st method, is a direct computation of reliability, we
determine the configurations of n parallel 22 of the system. Secondly, we find the transition
probability matrix of Markov chain to compute system reliability, where the 3rd method, we
uses “the recursive algorithm of a connected 1,2or 2,1-out-of-m,n : F system to
compute the reliability of the system" [1] for computing the reliability of the system.