## 6 Discussion  
In this paper, a reliability assessment framework with Bayesian inference was established for a high-reliability product for which limited failure data could be obtained over a period of time. In order to verify the validity and scientifically of the proposed framework, the proposed expert system and different priors for ABM are discussed in this section.  
Different experts make different judgments about the criteria by which a products' reliability are affected, as shown in Table 4; e.g., expert 1 felt that the most important factor was T, while expert 2 stated that the most important factor was S. The results of the Bayesian BWM largely revolved around the mean value for each individual, which also suggested that the Bayesian BWM was valid and reasonable. However, there was a fundamental difference between the two approaches. The arithmetic mean method needs to first calculate the weights of each expert using the BWM method and then average them. whereas the Bayesian BWM calculates the final weights at once by a probability model. Moreover, more information could be obtained by Bayesian BWM, as shown in the figure: it could obtain the extent to which one criterion was superior to the other.  
The ABM method introduced the beta distribution as the prior of weights; in this work, we compared the results obtained by the uniform distribution and beta distribution, as shown in Table 5. Overall, the means obtained by the two methods were essentially the same, but the widths of 95% credible intervals were 258.13 h and 244.80 h, respectively. This shows that the prior by beta distribution was superior both in terms of accuracy and uncertainty reduction.  
Based on the above analysis, it is clear that the framework proposed in this paper is effective and reliable. The method has the following advantages: (1) the proposed framework not only considers limited failure data, but also introduces an expert system for more information; (2) the established expert system does not need to consider the weight of each opinion, meaning that the result will not be dominated by one expert; (3) the ABM introduces the beta distribution as the prior of aggregation, and the confidence interval indicates that the results obtained are more reliable.  
In this paper, we applied this framework to the reliability assessment of a servo turret, and this framework can be extrapolated to the reliability assessment of complex systems such as spacecraft, aircraft, reactors, etc., to verify the feasibility of this approach. Moreover, only binary data are used for reliability evaluation. In order to describe the product more accurately, future research could describe a product using a multi-state system.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **S** & **T** & **M** & **A** & **E** \\ \hline Expert 1 & 0.187 & 0.46 & 0.14 & 0.14 & 0.072 \\ Expert 2 & 0.393 & 0.246 & 0.164 & 0.123 & 0.074 \\ Expert 3 & 0.243 & 0.408 & 0.121 & 0.162 & 0.066 \\ Expert 4 & 0.200 & 0.200 & 0.320 & 0.200 & 0.080 \\ Expert 5 & 0.436 & 0.182 & 0.136 & 0.109 & 0.136 \\ Arithmetic mean & 0.292 & 0.299 & 0.176 & 0.147 & 0.086 \\ Bayesian BWM & 0.263 & 0.290 & 0.184 & 0.159 & 0.105 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The comparison of the weights obtained by each expert, the arithmetic mean method and the Bayesian best-worst method (BWM).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Prior of Weight** & **Uniform Distribution** & **Beta Distribution** \\ \hline Mean value (h) & 5774.53 h & 5878.311 h \\
95\% credible interval width & [5870.13 h, 6128.26 h] & [5755.91 h, 6000.71 h] \\
95\% credible interval width & 258.13 h & 244.80 h \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparisons for different priors.