  The coherent potential approximation (CPA) within full counting statistics
(FCS) formalism is shown to be a suitable method to investigate average
electric conductance, shot noise as well as higher order cumulants in
disordered systems. We develop a similar FCS-CPA formalism for phonon transport
through disordered systems. As a byproduct, we derive relations among
coefficients of different phonon current cumulants. We apply the FCS-CPA method
to investigate phonon transport properties of graphene systems in the presence
of disorders. For binary disorders as well as Anderson disorders, we calculate
up to the $8$-th phonon transmission moments and demonstrate that the numerical
results of the FCS-CPA method agree very well with that of the brute force
method. The benchmark shows that the FCS-CPA method achieves $20$ times more
speedup ratio. Collective features of phonon current cumulants are also
revealed.
