Based on the theoretical precision of gear movement and the near-point technology of non-standard sprocket wheels, a new involute cylindrical gear system motion is proposed, which is based on the theory of gear motion and the accuracy of gear motion. In order to determine the stochastic factors of gear system probability, Precision non-standard sprocket reliability analysis method to determine the gear system under the influence of random factors to meet the accuracy requirements of the probability. Gear processing often encountered non-standard chain gears to the non-standard modulus gear processing, gears in the processing of this mark and not much difficulty non-standard sprocket, according to the requirements of non-standard gear manufacturing non-standard tool can be non-standard sprocket Processing, when you encounter trouble, but found that the production workshop after the hobbing of the need to double-gear part of the detection, that is, integrated radial gear non-standard sprocket error tolerance non-standard sprocket gear radial integrated error detection . Non-standard sprocket radial synthetic error mainly reflects the eccentric gear ring ring in the non-standard reference wheel axis around the entire history of the ring gear tooth profile caused by the radial position of the maximum error, it is a major error affecting the accuracy of the gear movement Non-standard sprocket wheel, the radial integrated error "Fi" mainly depends on the radial position of adjacent non-standard sprocket two tooth profile error and tooth profile error analysis gear machining error of non-standard gear grinding, shaft And the eccentricity error movement of the gear system is deduced. The influence of the gear system on the motion error of the mean non - standard sprocket, variance and third - order and fourth - order functions of the moment expression is derived. Probability Density Function and Probability Distribution Function of System Error. Combined with national standard gear system motion accuracy reliability analysis model. Numerical examples show that the method has high accuracy and efficiency