###### Abstract  
Residual life estimation is an important problem in reliability engineering. Traditional methods, which are based on time-to-failure distribution, have limitations for components of on-orbit satellites characterized as high reliability with small sample size. Various types of reliability information can be collected during test and operation, including historical lifetime data, degradation data, similar data, expert information, etc. Therefore, making full use of multi-source information  
Then, the point estimation of the residual life can be represented as  
\[\mu_{\tau}=\int\limits_{0}^{\infty}tf_{\tau}(t)dt. \tag{3}\]  
Weibull distributions are widely used [4; 5]. Therefore, in this study, we assume the lifetime of the on-orbit component follows the Weibull distribution, denoted by \(\mathrm{W}(\lambda,\beta)\), with the CDF [6]  
\[F(t;\lambda,\beta)=1-e^{-\lambda t^{\beta}},t\geq 0,\lambda>0,\beta>0. \tag{4}\]  
The residual life PDF can be obtained by substituting Equation (4) into Equation (2), which can be written as [5]  
\[f_{\tau}(t;\lambda,\beta)=\frac{f(t+\tau)}{1-F(\tau)}=\lambda\beta(t+\tau)^{ \beta-1}\exp\Bigl{(}\lambda\tau^{\beta}-\lambda(t+\tau)^{\beta}\Bigr{)}. \tag{5}\]  
With the development of the techniques of science and technology, the components in satellites are highly reliable. Therefore, applications of traditional methods based on failure times are limited [7]. However, multi-source information can be collected for these components [8], including historical lifetime data, degradation data, similar data, and expert information. The Bayesian method could be a useful tool for the information fusion. Because of its strong ability at data fusion [9], it has received considerable attention in various engineering fields [10; 11]. For highly reliable components, it is difficult to estimate the residual life with data containing a small number of failures and even zero failure. However, the available degradation data could reflect the real-time state of components and could be used to enrich the information for residual life estimation [12]. For example, a hierarchical Bayesian model was built and effectively fitted the nonlinear paths of organic light-emitting diodes [13]. Parameters of the Wiener process and the field data were fused to obtain the posterior distributions of degradation parameters [14]. In addition, a systematic method for using a degradation-based model selection to analyze Bayesian reliability was discussed by [PERSON] et al. [15]. Additionally, Bernoulli data, lifetime data, and degradation data were integrated to improve the accuracy of reliability prediction [16]. Parameters of the degradation model were determined by fusing prior degradation information and prior lifetime data, and prior distribution was updated by the field degradation data [17]. By synthesizing multi-source data, including bivariate degradation data and lifetime data, remaining useful life (RUL) was estimated for a satellite rechargeable lithium battery [2]. The inverse Gaussian process was used to analyze the accelerated degradation model and both the Jeffreys prior and reference prior were derived and compared [18]. Based on the functional principal component analysis (PCA) and the Bayesian method, a new prediction method for Li ion battery residual lifetime evaluation was presented [19]. Simultaneously, historical lifetime data and similar data can also obviously provide more reliability information. Historical lifetime data, often obtained before test and use, and the similar data are usually used to determine prior distribution based on empirical Bayes (EB) [20] and linear empirical Bayes (LEB) methods [21]. In practical engineering, conjugate prior is also commonly used [22]. The moment method, as well as the ML-II method, are typically used to determine the parameters of prior distribution [23]. Degradation data and historical lifetime data were fused to estimate the residual life [24].