A comparison between aggregation before and after propagation based on a reliability model

Experts are often solicited to provide their opinions on systems unavailable inputs. In certain cases, we can have several opinions for each system input. In such situation, we ask ourselves what is the best way to combine these opinions? For each input, we can either combine them, before their propagation into the system model, or combine them after the propagation of each opinions combination separately. The purpose of this paper is to explore the differences between these two aggregation modes. For our reliability model, outcomes show that the location of the operating point in the probabilistic space and the divergence (gap) between expert opinions are the main factors explaining the difference between both aggregation modes. In this paper, we propose the Divergence Metric δ to measure the divergence between experts' opinions and we suggest the use of the 'Cumulative Distribution Averaging' as an aggregation rule. This rule seems suitable for probabilistic and non-probabilistic opinions and it avoids limitations encountered with expert opinions expressed according to bounded distributions.