The gear transmission system is a typical time-domain series system, and its fatigue reliability evaluation under variable amplitude loading has long attracted the interests from scholars. The widely used Monte Carlo (MC) method to evaluate the reliability of a system with material and load uncertainties is time consuming, especially when used in combination with a fatigue analysis software. Concerning this problem, this paper proposes a “deterministic damage-random threshold (DDRT)” reliability model. The model converts the randomness from damage to the threshold, thus saving time because only the median damage and the damage for key reliability of each fatigue part are required in reliability evaluation. Based on this model, a reliability calculation flow of a gear transmission system is proposed considering the time-domain characteristic of gears. Finally, the model is verified by numerical examples and the fatigue test data of gears.

The P-S-N curve is a vital tool for dealing with fatigue life analysis, and its fitting under the condition of small samples is always concerned. In the view that the three parameters of the P-S-N curve equation can better describe the relationship between stress and fatigue life in the middle- and long-life range, this paper proposes an improved maximum likelihood method (IMLM). The backward statistical inference method (BSIM) recently proposed has been proven to be a good solution to the two-parameter P-S-N curve fitting problem under the condition of small samples. Because of the addition of an unknown parameter, the problem exists in the search for the optimal solution to the three-parameter P-S-N curve fitting. Considering that the maximum likelihood estimation is a commonly used P-S-N curve fitting method, and the rationality of its search for the optimal solution is better than that of BSIM, a new method combining BSIM and the maximum likelihood estimation is proposed. In addition to the BSIM advantage of expanding the sample information, the IMLM also has the advantage of more reasonable optimal solution search criteria, which improves the disadvantage of BSIM in parameter search. Finally, through the simulation tests and the fatigue test, the P-S-N curve fitting was carried out by using the traditional group method (GM), BSIM, and IMLM, respectively. The results show that the IMLM has the highest fitting accuracy. A test arrangement method is proposed accordingly.