## 3 Design Assessment Methods
### Complexity Analysis  
To evaluate design complexity, complexity metrics developed for the industrial assembly were used based on a modified version of [PERSON]'s Molecular Orbital Theory. This metric is used to calculate the complexity of systems from different perspectives [21]. In this complexity measurement, total system complexity has three variables: The first variable, \(C_{1}^{\mathrm{s}}\), measures the complexities of each component on the individual level. The second complexity variable, \(C_{2}^{\mathrm{s}}\), measures the complexity during a pairwise interaction (liaison relationship) of two or more components. The last variable, \(C_{3}^{\mathrm{s}}\), is a topology complexity that measures the effect of system architecture or the arrangement of the different interfaces. Thus, the total complexity of the satellite can be calculated with a combination of these three variables using Equation (1). The detailed derivation and explanation of the metrics and each variable can be referred to in [22] (p. 48). The total complexity of the structural assembly of the satellite provides a very good piece of information about the complexity/difficulty level of the two design concepts, especially during integration. System complexity can also easily be visualized using a liaison diagram, as shown in Figure 11.  
Figure 10: Slot-based 3U model. The first complexity variable of the satellite is the summation of the complexity value \(\alpha_{i}^{s}\) for all satellite components, and can be calculated using Equation (2), where \(\alpha_{i}^{s}\) represents the complexity of the satellite components, and \(i\) and \(N_{s}\) denote the total number of parts forming the satellite. This indicates the technical/agronomical difficulty/efforts associated with the development and management of each of the assembly components in isolated conditions. \[C^{s}=C_{1}^{s}+C_{2}^{s}C_{3}^{s} \tag{1}\]  
\[C_{1}^{s}=\sum_{i=1}^{N_{s}}\alpha_{i}^{s} \tag{2}\]  
Similarly, the liaison's complexity of assembly, \(C_{2}^{s}\), is the sum of all the complexities in the pairwise interaction between two linked structural components and is calculated using Equation (3) below. The variables \(\beta_{ij}\) and \(ASM_{ij}\) denote a binary adjacency matrix derived from the components that have physical interaction in the assembled state. \[C_{2}^{s}=\sum_{i=1}^{N_{s}^{s}}\sum_{j=1}^{N_{s}^{s}}\beta_{ij}^{s}ASM_{ij}^{ minimal} \tag{3}\]  
\[\left[ASM\right]_{ij}=\left\{ \begin{array}{ll}1,&if\ i\ and\ j\ are\ connected\\ 0,&otherwise\end{array} \right. \tag{4}\]  
\[\beta_{ij}^{p}=\frac{f_{f}^{E}+f_{f}^{F}+f_{f}^{G}+f_{f}^{H}+f_{f}^{I}+f_{f}^ {I}+f_{f}^{k}}{\beta_{max}^{p}} \tag{5}\]  
On the other hand, in the last term, \(C_{3}^{s}\) is a global measure that encapsulates the inherent arrangement of connections and is calculated by the graph energy [23]. Note that the term \(C_{3}^{s}\) requires knowledge of the complete system architecture and signifies a global effect, the influence of which could be perceived during the system integration phase [22]. The complexity of the product's topology, \(C_{3}^{s}\), is computed by  
\[C_{3}^{s}=\frac{E_{ASM^{minimal}}}{N_{s}^{s}} \tag{6}\]  
\[E_{ASM^{minimal}}=\sum_{i=1}^{N_{s}^{s}}\sigma_{i} \tag{7}\]  
Figure 11: Elements of the overall complexity metrics shown with a liaison diagram. The assembled system can be expressed graphically using a combination of components and liaisons. The components can be essential components that behave as a single unit, quasi-components that are used to connect the essential components, and virtual components, which are non-mechanical components such as solders or glues. However, for simplicity, the graphical expression of the satellite only shows the essential components in compact form. In the diagram, the components are denoted by circular nodes, whereas the liaisons are denoted by edges, as shown in Figures 12 and 13. The spacers and screws are considered quasi-essential components and therefore are not taken into consideration in this liaison diagram.