The classical three-loop servo system is researched, and the influences of the four kinds of random noises on the tracking precision are discussed particularly, which come from the processes of measuring current, speed, position and torque disturbance. Then the transfer functions are deduced between these random noises and tracking precision. Based on the transmutation of the transfer functions, the relation among system bandwidth, tuning arithmetic and random noises is deduced, which offers reference for choosing the sensor, processing the measured data and ensuring tuning arithmetic parameter. Moreover, an emulation experiment has been done under these random noises which obey the Gauss-distributing. And a segment linearization method is put forward upon the amplitude-frequency curve of the random noises and tracking precision, by which the influences of four kinds of the random noise on tracking precision are quantized. Comparing the quantized results with the emulated results, it has been proved that this method is correct and feasible. At last, comparing the method with the emulation under the four sorts of noise acting on the servo system at the same time, the same conclusion is gained.