## 6 Illustrative Example  
As a critical component of a satellite platform, it is meaningful to estimate the residual life of the momentum wheel [50]. Characterized as being highly reliable and having a long life, the failure of the momentum wheel is rare and failure data are usually nonexistent [51]. The traditional method for residual life estimation, which is based on failure distribution, is limited. Therefore, prior information is useful and can be fused to estimate the component's residual life. As a typical electromechanical component, the lifetime of the momentum wheel follows the Weibull distribution. Lifetime data and \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Parameters** & **Method** & **Bias** & **MAE** & **MSE** & **AIW** & **CP** \\ \hline \(\lambda=2\times 10^{-8}\) & Bayes & \(-1.1480\) & 23.9 & 868.8 & 361.4 & 0.87 \\ \(\beta=3\) & MLE & \(-0.7568\) & 28.0 & 1242.8 & 350.0 & 0.83 \\ \(\lambda=4\times 10^{-8}\) & Bayes & \(1.4438\) & 18.2 & 527.9 & 272.3 & 0.84 \\ \(\beta=3\) & MLE & \(1.1924\) & 20.4 & 678.5 & 273.6 & 0.84 \\ \(\lambda=2\times 10^{-10}\) & Bayes & \(-0.3157\) & 12.3 & 226.1 & 131.5 & 0.87 \\ \(\beta=4\) & MLE & \(0.1472\) & 16.0 & 379.9 & 185.3 & 0.82 \\ \hline \end{tabular}
\end{table} 
Table 1: The results of the residual life estimation using Bayesian method and MLE with \(n=10\). \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Parameters** & **Method** & **Bias** & **MAE** & **MSE** & **AIW** & **CP** \\ \hline \(\lambda=2\times 10^{-8}\) & Bayes & \(-1.3760\) & 30.0 & 1362.0 & 345.8 & 0.84 \\ \(\beta=3\) & MLE & \(-5.3046\) & 40.6 & 2497.0 & 319.6 & 0.72 \\ \(\lambda=4\times 10^{-8}\) & Bayes & \(-0.8615\) & 20.9 & 687.8 & 265.6 & 0.87 \\ \(\beta=3\) & MLE & \(-1.7226\) & 28.3 & 1276.5 & 247.3 & 0.83 \\ \(\lambda=2\times 10^{-10}\) & Bayes & \(1.5557\) & 16.6 & 418.5 & 195.6 & 0.82 \\ \(\beta=4\) & MLE & \(2.2144\) & 23.4 & 869.0 & 175.2 & 0.72 \\ \hline \end{tabular}
\end{table} 
Table 2: The results of residual life estimation using Bayesian method and MLE with \(n=5\). \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Parameters** & **Method** & **Bias** & **MAE** & **MSE** & **AIW** & **CP** \\ \hline \(\lambda=2\times 10^{-8}\) & Bayes & \(6.0742\) & 29.0 & 1274.0 & 342.8 & 0.82 \\ \(\beta=3\) & MLE & \(12.8385\) & 47.4 & 3884.9 & 272.3 & 0.64 \\ \(\lambda=4\times 10^{-8}\) & Bayes & \(-1.3443\) & 24.6 & 973.10 & 255.8 & 0.81 \\ \(\beta=3\) & MLE & \(-3.3908\) & 35.7 & 1999.2 & 197.6 & 0.59 \\ \(\lambda=2\times 10^{-10}\) & Bayes & \(-4.1098\) & 20.1 & 605.9 & 190.1 & 0.72 \\ \(\beta=4\) & MLE & \(-5.8645\) & 32.5 & 1639.9 & 147.9 & 0.52 \\ \hline \end{tabular}
\end{table} 
Table 3: The results of residual life estimation using Bayesian method and MLE with \(n=3\). degradation data were fused by [PERSON] et al. (2019). To illustrate the method introduced in this paper, we consider the data published in [PERSON] et al. (2019), which include the right censored life data on 15 components. This is shown in Table 4.  
We choose the momentum wheels on S3 as the research objects. The right censored life data on S1 and S2 are the historical life data. Using the Bayesian method, the reliability estimation at current time \(\tau=24\) months is 0.9954 [PERSON] et al. (2019), which is taken as the expert information. Simultaneously, by analyzing the degradation data, the CDF of the lifetime was obtained, and its life was estimated, (i.e., 537 months). The point estimation and 95% CI were calculated: 512.85 months and [47.9, 1288.0] months, respectively [PERSON] et al. (2019). By fusing multi-source information, Bayesian estimation and 95% CI of residual life corresponding to each prior information can be calculated. These results are shown in Table 5.  
To guarantee the safety of the data fusion, a consistency test is necessary. We can obtain the 95% Bayesian CI under each prior distribution determined by the corresponding prior information using Algorithm 1.