As a fundamental component of mechanical machines, gears are widely used in motion and power transmission in wind turbines, aviation, automobiles, ships, machine tools, mining, and other fields. With the growing demand for good performance under heavy-loading and high-speed-loading conditions, the fatigue reliability of gear transmission has become a crucial factor in determining the performance and service life of machines [
1–
5]. As an essential element of wind turbines, gear transmission is subjected to random loading conditions and numerous fatigue cycles [
6,
7]. The fatigue resistance of gears, including contact and bending fatigue strength, could decrease gradually due to repeated loading cycles [
8]. Dynamic fatigue reliability can be explained as the capability or probability that the fatigue resistance of the gear is larger than the fatigue damage during operation. However, the common design methodology for wind turbine gear transmission usually provides the structural parameters once the basic requirements on transmission ratio, mechanical power, input speed, safety factor, and initial reliability are given [
7]. From an engineering point of view, several uncertain factors, such as material properties, geometry size, and load variations, influence fatigue reliability considerably [
9]. Many recent investigations have focused on the effect of uncertainties on reliability. Zhu et al. [
10] quantified the effects of uncertainties, such as experiment data, material properties, and loading conditions, on the reliability of turbine bladed disks fatigue by using an experimental–numerical combined approach. Lu et al. [
11] proposed the weighted regression-based extremum response surface method by considering the randomness of design parameters and the fuzziness of the safety criterion to improve structural dynamic fuzzy reliability analysis. The dynamic fatigue reliabilities of gear transmission reliability are sensitive to changes in loading conditions, material properties, design parameters, and other factors during service. Sensitivity analysis is one of effective approaches to quantify the influence of design variables on fatigue reliability and provide rational means of fatigue design [
12]. Many conditions, including complex loading conditions, dynamic fatigue reliability, and reliability sensitivity, are considered in reliability-based design optimization (RBDO) studies on gear transmissions [
6,
13].