## 5 Conclusions  
In this paper, time-varying reliability models of the mechanism systems under fatigue failure mode are developed by considering the combined effects of clearance, local structural stiffness, random load and random strength degradation. The traditional mechanism reliability models pay more attention to the reliability change of the mechanism accuracy under the influences of failure factors. However, in practical engineering, the fatigue damage, time-varying reliability and remaining life of the mechanisms are also important factors affecting the safe operation and durability of the systems. By establishing a time-varying reliability model under the combined influences of multiple failure and degradation factors, a quantitative analysis method that can take into account the influence of nonlinear factors and strength degradation factors on the time-varying reliability of the mechanism systems is proposed, which is validated by the Monte Carlo simulation method. The results show that the mechanism clearance, local stiffness, and initial strength dispersion have a significant effect on the time-varying reliability of the mechanisms. The increase in clearance causes an increase in the maximum stress matrix and cumulative damage matrix, which reduces the time-varying reliability of the mechanism. The increase in local stiffness attenuated the effect of clearance on the reliability of the mechanisms. In addition, the initial strength dispersion has different effects on mechanism reliability at different stages. Larger initial strength dispersion decreases early mechanism reliability and increases later mechanism reliability. Meanwhile, the effect of clearance on the time-varying reliability of the mechanisms will be weakened with the increase in initial strength dispersion. The effect of initial strength dispersion on the time-varying reliability of the mechanisms will be weakened with the decrease in clearance. The proposed models can quantitatively analyze the time-varying effects of failure factors on the reliability of the mechanisms and can also be used for the stochastic remaining life evaluation and fault diagnosis of the mechanism systems. The proposed method provides a basis for time-varying reliability analysis of mechanisms in fatigue failure mode. In future work, more in-depth research will be carried out for the analysis of mechanism dynamics and reliability evaluation of complex mechanisms with multiple failure modes.  
Figure 11: Reliability with a journal diameter of 0.018 m.  
**Funding:** This work was supported by Fushun Revitalization Talents Program (FSYC202107014), Scientific Research Funds Project of Liaoning Education Department of China (L2019019), Program for Liaoning Innovative Talents in University (LR2017070) and National Natural Science Foundation of China (51505207).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the author. The data are not publicly available due to privacy issues.  
**Conflicts of Interest:** The author declares no conflicts of interest.