The phenomenon when the results of aggregate and disaggregate analyses do not agree is known as the aggregation error and the absence of the aggregation error is known as perfect aggregation [8]. Aggregation error is not a phenomenon that is limited in the field of reliability analysis. Studies about the aggregation error are largely known in various fields including economics, social sciences, and geo-statistics [9; 10; 11]. Numerous studies about aggregation error in Bayesian reliability analysis have been conducted since it was first introduced in the 1990s. While most of the early research focused on finding the conditions under which perfect aggregation can be obtained, especially in cases where failures of components are independent to each other [8; 12], recent studies tried to identify the sources of the aggregation error [13; 14; 15] (in similar independent cases). [PERSON] [16; 17] used a different term \"Bayesian anomaly\" for the similar phenomenon (i.e., aggregation error) discussed in other papers, but took a more extreme view to argue that the aggregation error is a fundamental problem in a Bayesian reliability analysis and even suggested a basic restructuring of the Bayes procedure [18]. However, other researchers [13; 14; 15] disagreed with such argument and suggested that the aggregation error should not be construed as the evidence of inadequacy of Bayesian methods. When the failures of the components of a system are dependent, implementing disaggregate Bayesian analysis can be even more difficult because a joint prior distribution must be specified and then updated with component-level data. In the real-world situation, a simplified disaggregate analysis (hereafter, DAI) without considering the dependence structure of the components might be used instead of the true disaggregate analysis. Although the computation for this simplified analysis becomes more straightforward and simpler (because only marginal distribution for each component needs to be specified and updated), the accuracy of the analysis might be seriously affected due to the ignorance of the critical information of dependence between components. While the studies conducted before have compared different analysis approaches and investigated the aggregation errors for cases where data are available at both the component and system levels, there is not yet a generalized study on the situation where the components are correlated (even though the dependence assumption among the components is naturally important in evaluating the reliability of a system). Furthermore, while some studies in reliability analysis have used copula theory to handle joint failure or inter-correlation of multiple components [19; 20], few studies (see, e.g., [21; 22]) have reported on the effects of component dependence on the accuracy of Bayesian reliability analyses. Thus, little guidance is available on how to proceed, and how to choose appropriate analysis approach under the practical situations. This study aimed to compare three Bayesian analysis approaches that can be used for evaluating system reliability in parallel systems where failures of components are dependent: disaggregate analysis (DA), aggregate analysis (AA), and simplified disaggregate analysis (DAI). Specifically, a parallel two-component system where Component 1 fails according to a Poisson process and Component 2 fails according to a Bernoulli process was analyzed, compared to the parallel beta-binomial system investigated in [23]. It is expected that the outcome of this study will be practically useful to reliability engineering practitioners who encounter Poisson-distributed failures (which are popular in modern science and engineering). Furthermore, since the component failure of the reliability system in this study are correlated, copulas were thus used to construct bivariate distribution functions with correlated marginal random variables.