# Systemic Evaluation of PSS in the Early Concept Phase Using Graph-Based Reasoning
## 5 Validation
### GEAR Method--Step 3: Reasoning Analysis  
The individual steps of the reasoning analysis, as described for step 3 of the GEAR method, were applied next. In doing so, all PSS concept variations were systematically activated on the CVL, and their achievement levels for the EVCs were determined. Figure 18 provides an overview of how the individual PSS concept variations fulfill the three EVCs in terms of expected values. The values were exported from the GenNie tool after the concept variants were selected and the a posteriori probabilities were inferred. They indicate the expected amount of powder being recycled internally and externally and disposed of as scrap based on a normalized batch of 100 kg. The results represent the different causal flows within the EVL and illustrate how the amounts of powder propagate causally through the graph, depending on the activated PSS concept variation. This provides an indication of the recyclable quantities of powder that can be expected according to the respective PSS concept variation. The comparative weighting of the EVCs is determined based on their achievement levels (Figure 18), where they are weighted according to the evaluation function from step 1 of the GEAR method (Evaluation \(=20\cdot EVC_{\text{internal}}+10\cdot EVC_{\text{external}}+1\cdot EVC_{\text{ scrap}}\)). The expected utility of the respective PSS concept variation is, thus, determined using utility theory by averaging the probabilistically expected EVC manifestations and weighting them according to the evaluation function. The expected utility (\(E\)U) is formally calculated as follows:  
\[E\textsl{U}=\sum_{i=1}^{3}W_{i}\cdot\left(\sum_{j}kg_{i,j}\cdot P_{i,j}\right)\]  
where \(i\in\{1,2,3\}\) represents the EVCs (internal recycling, external recycling, and scrap disposal), \(W_{i}\) is the weight of the \(i\)-th criterion according to the evaluation function, \(kg_{i,j}\) is the average of the kg interval for the \(i\)-th criterion in the \(j\)-th range, and \(P_{i,j}\) is the probability for the PSS concept variation for the \(j\)-th interval of criterion \(i\). Figure 18: Overview of probabilistic achievement levels for EVCs of PSS concept variations. In the second step of the reasoning analysis, the influence of understanding gaps on the evaluation of the PSS concept variations is systematically determined, following step 3 of the GEAR method. The specific impacts of individual knowledge gaps on the achievement of EVCs for each PSS concept variation are shown in Figure 19. The figures represent the maximum changes in the expected value of the EVCs that an information gap can have based on its extreme scenarios. The strength of the impact is derived from changes in the EVL, reflecting the current understanding of domain experts. Thus, it should be interpreted as an indicator of the significance of the knowledge gap in the reasoning process within the PSS engineers' mental model. However, this means that it could turn out that the actual influence of a knowledge gaps is smaller in reality if revealed by findings from subsequent studies regarding a particular knowledge gap. The importance of these knowledge gaps varies across the different PSS concept variations due to differences in evaluation logic. For example, the knowledge gap related to \"willingness to pay\" is particularly significant in the PSS concept variation where only external recycling is used because the entire material flow is recycled through an external service provider. The worst-case scenario for this knowledge gap would mean that due to a low willingness to pay, no external service provider can be found, resulting in all recyclable powder being disposed of as scrap. The consequence of this extreme scenario is much more severe than that of the PSS concept variation that also includes internal recycling, where a certain portion of powder can still be recycled internally, mitigating the effect of not finding a provider for external recycling.