# Systemic Evaluation of PSS in the Early Concept Phase Using Graph-Based Reasoning
## 3 State of the Art
### Graph-Based Reasoning in the PSS Concept Phase  
Bayesian Networks (BNs) represent an approach that allows for the modeling of complex cause-effect relationships. BNs have been used for many applications, including system evaluation, in order to infer uncertain effects, primarily in areas outside the PSS domain, like technical systems and environmental assessment [46; 47]. Bayesian networks (BNs) are powerful tools for this, representing uncertainty in complex systems based on a priori knowledge [47]. They require that the understanding of the semantic domain is made explicit in a graph-based form in order to conduct reasoning operations [48]. Syntactically, BNs represents dependencies between a set of random variables represented as nodes of a directed acyclic graph (DAG), where the edges symbolize the direct probabilistic dependencies between these variables [24]. The variables in the graph are characterized by conditional probabilities, the sum of which represents a joint probability distribution of the system. With the help of the graph model, probabilistic \"if-then\" questions can be answered by \"thinking backwards\" [24; 49; 50]. This means that they provide information about the most likely manifestations of the variables if the manifestations of other variables are fixed (no longer uncertain), for example, because they have been observed or a scenario-based analysis is carried out. This enables them to conduct different analytic operations based on reasoning like diagnostic tasks, explaining the contributions of different factors and thereby optimizing the configuration of the graph for a given target variable [51]. In addition, they allow for determination of the overall effect of changes in uncertainties of individual parts of the cause-effect network through the concept of Value of Information (VOI), which has been discussed for structural health assessments, e.g., of bridges [52; 53]. These approaches inherently do not focus on the evaluation of the PSS concept and its variations. However drawing on the concept of VOI is useful in the PSS context, as decision makers can quantify the potential benefits of obtaining additional information, thereby determining whether corresponding information-gathering efforts, such as the building of prototypes, are justified [54]. VOI is based on the idea of minimizing critical epistemic uncertainty so that the overall value metric of a decision is optimizing improved [52]. In the context of PSS concept detailing, reducing epistemic uncertainty can mean both acquiring new information through studies or exploring design concepts in more detail by synthesizing new concept alternatives [55]. BNs have also been used in the context of PSSs, e.g., by [PERSON] et al. [56], who discussed the development of a PSS with a focus on life-cycle cost estimation, emphasizing the elicitation of uncertain knowledge for PSS assessment. In their approach, they used a BN to probabilistically combine key metrics for cost estimation in a hierarchical way but lacking a causal perspective on how the underlying behavior of the PSS is anticipated and which associated knowledge gaps influence the assessment. [PERSON] et al. [57] used rule mining to learn the causal conditions for the occurrence of errors in a PSS on the basis of operational data using a BN. They aimed to provide heuristic knowledge for PSS designers evaluating different design options but did not aim to identify the impact of uncertainty on overall PSS concept evaluation. [PERSON] et al. [58] investigated how risk factors from operations can have negative consequences for existing PSSs and represented these relationships as a BN in order to enable effective risk management in operations. However, they did not consider how risk is driven by knowledge gaps. [PERSON] [59] investigated the risks that arise for PSSs with availability-based contracts that require the rapid provision of spare parts.