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.

全计数统计（FCS）形式内的相干势近似（CPA）被证明是研究无序系统中平均电导率，散粒噪声以及高阶累积量的合适方法。我们为声子通过无序系统的运输开发了类似的FCS-CPA形式主义。作为副产品，我们得出不同声子电流累积量的系数之间的关系。我们应用FCS-CPA方法来研究存在障碍时石墨烯系统的声子传输特性。对于二元障碍和安德森障碍，我们最多计算出第8个声子传递矩，并证明FCS-CPA方法的数值结果与蛮力方法非常吻合。基准测试表明，FCS-CPA方法的加速比提高了20倍。