Abstract: In order to study the reliability of a linear consecutive-(1,2)or(2,1)-out-of-(m,n):F system that can be applied to many engineering fields, such as video monitoring systems, phased-array radar systems and so on, a finite Markov chain imbedding approach is used to obtain its reliability analytic formula. Numerical examples show that the method can be used not only for the system with independent identical distribution components, but also with independent non-identical distribution components. From the numerical examples and time-complexity analysis, it can be seen that the proposed algorithm is very efficient for evaluating the system reliability when n is large and that the computing time of the proposed algorithm becomes shorter than that of the previous algorithms.