## 4 Numerical Examples
When the stiffness of the mechanism is high, the collision forces and stresses on the members of the mechanism are greater. The increase in member flexibility slows down the rate of damage accumulation and strength decline. The ability of the system to resist the effects of external forces increases. This slows down the rate of decrease in the time-varying reliability of the system. Overall, when the local stiffness is the same, the trend of the effect of clearance on the time-varying reliability of the mechanism is the same. However, the effect of clearance on the reliability of the mechanism is greater when the local stiffness is higher because the increase in the flexibility of the components can slow down the rate of decrease in the reliability of the mechanism. The difference in the time-varying reliability of \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Modulus of Elasticity \(E\) in Flexible Element (Pa)**} & **Diameter of Journal (m)** \\ \hline \multirow{2}{*}{Case 1} & \multirow{2}{*}{\(1\times 10^{10}\)} & 0.0176 \\ \cline{3-3}  & & 0.0178 \\ \cline{3-3}  & & 0.018 \\ \hline \multirow{2}{*}{Case 2} & \multirow{2}{*}{\(5\times 10^{9}\)} & 0.0176 \\ \cline{3-3}  & & 0.0178 \\ \cline{3-3}  & & 0.018 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Structural parameters. Figure 7: Reliability with different values of clearances in Case 1.  
the mechanism under the two different clearance conditions is more pronounced at higher stiffness and smaller at greater flexibility. (3) In order to consider the effects of different initial strength dispersion and different clearance on the time-varying reliability of the mechanism, the time-varying reliability of the mechanism with different values of standard deviation of initial strength and clearances are shown in Figures 9-11 when the diameter of the journal is 0.0176 m, 0.0178 m, and 0.018 m, respectively. The combined effect of initial strength dispersion and clearance on the time-varying reliability of the mechanism is demonstrated in Figures 9-11. It can be seen that the initial strength dispersion has different effects on the time-varying reliability of the mechanism at different TP when the clearances are the same. When the initial strength dispersion increases, the mechanism reliability decreases in the earlier operating phase and increases in the later part of the operating time. This is due to the fact that an increase in the initial strength increases the likelihood that the system will have a smaller value of initial strength in the early work phase, while increasing the likelihood of a larger residual strength in the latter half of the work period. In addition, for the same initial strength dispersion condition, the reliability of the system is lower when the clearance is larger, which is due to the fact that the increase in clearance causes an increase in the stresses and cumulative damage in the system. Furthermore, the increase in initial strength dispersion will weaken the effect of clearance on the time-varying reliability of the mechanism. Decreasing the value of clearance can also weaken the effect of initial strength dispersion on the time-varying reliability of the mechanism. Figure 8: Reliability with different values of clearances in Case 2. Figure 10: Reliability with a journal diameter of 0.0178 m.  
Figure 9: Reliability with a journal diameter of 0.0176 m.