## 5 Conclusions  
The guidance for choosing the most appropriate approach can be directly extracted from the classification tree, and, therefore, the findings in this work can be extremely helpful for the analysts in the reliability field. In addition, interactions among the input factors might also be revealed from the tree model so that the ranges of values of critical factors that affect the estimated error in reliability can be identified and located. Moreover, other than providing the guidelines for choosing the most appropriate approach under certain conditions, reliability analysts can follow the steps of this work to build their own classification trees by using different threshold values, copula functions, modified parameter settings, and minimum number of terminal nodes based on their professional knowledge and various requirements in different problems in hand. The results of previous research on a parallel beta-binomial system [23] were compared to the Poisson-Bernoulli system analyzed in this study, and it was found that, in both cases, the Absolute Kendall's value and the number of failures were key factors that influence the magnitude of error. However, difference of components' and systems consistency (D-Com-Con and D-Sys-Con), the ratio of consistency, and coefficient of variation for both components (R-C1-Con, R-C2-Con, \(CV_{1}\), and \(CV_{2}\)) were key only in the beta-binomial system. In the Poisson-Bernoulli system, the key influencing factors were the number of failures of Component 2 (\(k_{2}\)) and the difference in components' consistency (D-Com-Con). This information can be useful in deducing which type of data (aggregate or disaggregate) has more impact on either of the systems when evaluating their reliability. It should be noted that this study focused more on the simulated cases in which realizations were obtained by drawing from all the possible situations. Therefore, the numerical value of Kendall's tau was obtained arbitrarily from results of the simulation. While this study focused primarily on simulated cases, if one wants to apply the model to a real world problem, further investigation would need to be conducted in order to establish the connection between the copula-based joint prior and the empirical data or evidence available. Since the reliability engineering expert's opinion would be sought on two or more variables which are dependent, there will also be a need for eliciting association between variables, a task that is much more complex than eliciting subjective distribution for a single variable of interest. Therefore, better performing elicitation methods (see, e.g., [33]) would need to be considered in order to obtain valid results. It is worth noting that it is also theoretically possible to use certain parameters to explicitly formulate or describe the dependence between \(\Lambda_{1}\) and \(P_{2}\) (where they are both random variables with specific distributions) and then use Bayesian update to derive the posterior distributions of these parameters. Bayesian updates of the parameters (that used to formulate dependence structure) might not be analytically tractable but should be able to be dealt with using numerical methods. Additional research focusing on these aspects would be of great interest and value in further understanding the role of dependence and its influence on evaluating the reliability of a system. Furthermore, although the results from this work are confined to the simple parallel system (and especially for the model of products of a probability and a frequency), the theoretical and practical scheme given in this work would still be very useful to be applied on more complex systems. The same process and method used in this work can also be applied to more complex systems such as systems with more than two components or systems combining both series and parallel sub-systems. Poisson-distributed failures are popular in modern science and engineering.