## 4 Reliability Analysis of Compressor Disks
### Life Reliability Assessment  
The compressor disk had zero-failure before the designed life of 36,265 cycles. Assuming that the life follows a normal distribution, according to the prediction of the simulation analysis method, the probability of failure for a cycle life of \(<\)36,265 is \(\leq\)0.05, that is, \(q\)\(\leq\) 0.078. The cycles were equally divided into four classes according to the batch, and taking \(q\) = 0.078, the probability of failure was estimated using the Bayes method, as shown in Table 5.  
Similarly, the point \(\hat{\sigma}\) was estimated as 8255.3; then, according to Equation (12), the one-sided lower confidence limit \(x_{N,RL}\) of the life with confidence level \(\gamma\) = 0.95 and reliability \(R\) = 0.9987 was obtained as 16,340. According to the obtained life distribution results, the lower confidence limit \(x_{S,RL}\). of the life with reliability \(R\) = 0.9987 was predicted as 16,251.  
According to the reliability simulation test method proposed in Section 4.2, because \(x_{S,R}<x_{N,RL}\), it could be concluded that the reliability life obtained from the simulation was shorter than the actual reliability life of the disk at the confidence level \(\gamma\) = 0.95; i.e., the simulation results were conservative. Since the compressor disk is the off-weight part of the aero-engine, conservative results are beneficial for ensuring safety, and the disk can be used in engineering. Following Equation (18), \(x_{N,RL}\) and \(x_{S,RL}\) were fused, and the life one-sided lower confidence limit \(x_{T,RL}\) with confidence level \(\gamma\) = 0.95 and reliability \(R\) = 0.9987 was obtained as 17,324 after the fusion.  
The analysis results are presented in Table 6. Although the simulation prediction results were small compared with the test prediction results, they can be used as a valid source of reliability information.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Unit**} & \multirow{2}{*}{**Distribution Type**} & \multirow{2}{*}{**Mean Value**} & **Lower** & **Upper** & \multirow{2}{*}{**Coefficient of**} \\  & & & & **Bound of** & **Bound of** & **the Mean** & **Variation** \\  & & & & **Value** & **Value** & \\ \hline r\({}_{1}\) & mm & normal distribution & 67.15 & 67.13 & 67.18 & 4.77 \(\times\) 10\({}^{-4}\) \\ r\({}_{2}\) & mm & normal distribution & 209.32 & 209.25 & 209.39 & 4.26 \(\times\) 10\(  
The simulation data and test data were fused through the proposed data fusion method. The fusion of test data and simulation data increased the amount of information and improved the accuracy of life prediction. The lower confidence limit of the reliable life of the compressor disk was increased by 6.02% compared with the original prediction using only test data.  
Compressor disk is the important part of aero engine, once failure will cause serious consequences. Thus, the life confidence lower limit is usually used as the safety life of the disks in engineering. By combining simulation data with test data, the life of compressor disk is evaluated more accurately, and the design life of compressor disks is improved. On the other hand, extended maintenance cycle can reduce the waste of life due to conservative estimation.