In this paper, we first investigate the solution of the
two correlated units redundant system with two types of failure.
By using the method of functional analysis, especially, the $c_0$
semigroup theory of bounded linear operators on Banach space, we
prove the well-posedness and the existence of positive solution of
the system. By analyzing the spectra distribution of the system
operator, we prove that the dynamic solution of the system
asymptotically converges to the nonnegative steady-state solution
which is the eigenfunction corresponding to eigenvalue 0 of the
system operator. Furthermore, we discuss the exponential stability
of the system. Finally, we analyze the reliability the system with
the help of our main results and present some reliability indices
of the system at the end of the
paper.